%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV419-1.020 : TPTP v9.0.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:32:26 AM UTC 2025
% Result : Unsatisfiable 86.18s 86.38s
% Output : Proof 88.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV419-1.020 : TPTP v9.0.0. Released v3.5.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:48:05 EDT 2025
% 0.13/0.35 % CPUTime :
% 86.18/86.38 % SZS status Unsatisfiable
% 86.18/86.38 % SZS output start Proof
% 86.18/86.38 tff(node26_type, type, (
% 86.18/86.38 node26: $i > $o)).
% 86.18/86.38 tff(s12_type, type, (
% 86.18/86.38 s12: $i)).
% 86.18/86.38 tff(node25_type, type, (
% 86.18/86.38 node25: $i > $o)).
% 86.18/86.38 tff(m_user_v_ack_type, type, (
% 86.18/86.38 m_user_v_ack: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_u_type, type, (
% 86.18/86.38 c_u: $i)).
% 86.18/86.38 tff(c_e_h_2_type, type, (
% 86.18/86.38 c_e_h_2: $i)).
% 86.18/86.38 tff(m_and_h_gate_v_out_type, type, (
% 86.18/86.38 m_and_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_r_type, type, (
% 86.18/86.38 c_r: $i)).
% 86.18/86.38 tff(s11_type, type, (
% 86.18/86.38 s11: $i)).
% 86.18/86.38 tff(s10_type, type, (
% 86.18/86.38 s10: $i)).
% 86.18/86.38 tff(s9_type, type, (
% 86.18/86.38 s9: $i)).
% 86.18/86.38 tff(s8_type, type, (
% 86.18/86.38 s8: $i)).
% 86.18/86.38 tff(s7_type, type, (
% 86.18/86.38 s7: $i)).
% 86.18/86.38 tff(node22_type, type, (
% 86.18/86.38 node22: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(s6_type, type, (
% 86.18/86.38 s6: $i)).
% 86.18/86.38 tff(node21_type, type, (
% 86.18/86.38 node21: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node20_type, type, (
% 86.18/86.38 node20: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_and_h_gate_v_in2_type, type, (
% 86.18/86.38 m_and_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_and_h_gate_h_init_v_out_type, type, (
% 86.18/86.38 m_and_h_gate_h_init_v_out: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_m_type, type, (
% 86.18/86.38 c_m: $i)).
% 86.18/86.38 tff(node9_type, type, (
% 86.18/86.38 node9: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(s5_type, type, (
% 86.18/86.38 s5: $i)).
% 86.18/86.38 tff(m_and_h_gate_h_init_v_in2_type, type, (
% 86.18/86.38 m_and_h_gate_h_init_v_in2: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_n_type, type, (
% 86.18/86.38 c_n: $i)).
% 86.18/86.38 tff(m_and_h_gate_h_init_v_in1_type, type, (
% 86.18/86.38 m_and_h_gate_h_init_v_in1: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(s4_type, type, (
% 86.18/86.38 s4: $i)).
% 86.18/86.38 tff(m_c_h_element_v_out_type, type, (
% 86.18/86.38 m_c_h_element_v_out: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_e_type, type, (
% 86.18/86.38 c_e: $i)).
% 86.18/86.38 tff(m_c_h_element_v_in1_type, type, (
% 86.18/86.38 m_c_h_element_v_in1: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(s3_type, type, (
% 86.18/86.38 s3: $i)).
% 86.18/86.38 tff(node17_type, type, (
% 86.18/86.38 node17: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node18_type, type, (
% 86.18/86.38 node18: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_c_h_element_v_in2_type, type, (
% 86.18/86.38 m_c_h_element_v_in2: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(s2_type, type, (
% 86.18/86.38 s2: $i)).
% 86.18/86.38 tff(c_i_type, type, (
% 86.18/86.38 c_i: $i)).
% 86.18/86.38 tff(s1_type, type, (
% 86.18/86.38 s1: $i)).
% 86.18/86.38 tff(s0_type, type, (
% 86.18/86.38 s0: $i)).
% 86.18/86.38 tff(m_and_h_gate_v_in1_type, type, (
% 86.18/86.38 m_and_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_h_type, type, (
% 86.18/86.38 c_h: $i)).
% 86.18/86.38 tff(trans_type, type, (
% 86.18/86.38 trans: ( $i * $i ) > $o)).
% 86.18/86.38 tff(succ_type, type, (
% 86.18/86.38 succ: ( $i * $i ) > $o)).
% 86.18/86.38 tff(node19_type, type, (
% 86.18/86.38 node19: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node14_type, type, (
% 86.18/86.38 node14: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node16_type, type, (
% 86.18/86.38 node16: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node15_type, type, (
% 86.18/86.38 node15: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_or_h_gate_v_out_type, type, (
% 86.18/86.38 m_or_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_j_type, type, (
% 86.18/86.38 c_j: $i)).
% 86.18/86.38 tff(c_c_type, type, (
% 86.18/86.38 c_c: $i)).
% 86.18/86.38 tff(m_mutex_h_half_v_out_type, type, (
% 86.18/86.38 m_mutex_h_half_v_out: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_a_type, type, (
% 86.18/86.38 c_a: $i)).
% 86.18/86.38 tff(node6_type, type, (
% 86.18/86.38 node6: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node5_type, type, (
% 86.18/86.38 node5: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_or_h_gate_v_in1_type, type, (
% 86.18/86.38 m_or_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_l_type, type, (
% 86.18/86.38 c_l: $i)).
% 86.18/86.38 tff(m_or_h_gate_v_in2_type, type, (
% 86.18/86.38 m_or_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_cell_v_ack_type, type, (
% 86.18/86.38 m_cell_v_ack: ( $i * $i ) > $o)).
% 86.18/86.38 tff(node3_type, type, (
% 86.18/86.38 node3: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(c_e_h_1_type, type, (
% 86.18/86.38 c_e_h_1: $i)).
% 86.18/86.38 tff(m_cell_v_left_type, type, (
% 86.18/86.38 m_cell_v_left: ( $i * $i ) > $o)).
% 86.18/86.38 tff(c_q_type, type, (
% 86.18/86.38 c_q: $i)).
% 86.18/86.38 tff(node11_type, type, (
% 86.18/86.38 node11: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node10_type, type, (
% 86.18/86.38 node10: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_and_h_gate_h_init_v_init_h_out_type, type, (
% 86.18/86.38 m_and_h_gate_h_init_v_init_h_out: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_cell_v_token_type, type, (
% 86.18/86.38 m_cell_v_token: ( $i * $i ) > $o)).
% 86.18/86.38 tff(c_f_type, type, (
% 86.18/86.38 c_f: $i)).
% 86.18/86.38 tff(c_e_h_3_type, type, (
% 86.18/86.38 c_e_h_3: $i)).
% 86.18/86.38 tff(node24_type, type, (
% 86.18/86.38 node24: $i > $o)).
% 86.18/86.38 tff(c_d_type, type, (
% 86.18/86.38 c_d: $i)).
% 86.18/86.38 tff(c_b_type, type, (
% 86.18/86.38 c_b: $i)).
% 86.18/86.38 tff(node23_type, type, (
% 86.18/86.38 node23: $i > $o)).
% 86.18/86.38 tff(s15_type, type, (
% 86.18/86.38 s15: $i)).
% 86.18/86.38 tff(s14_type, type, (
% 86.18/86.38 s14: $i)).
% 86.18/86.38 tff(s13_type, type, (
% 86.18/86.38 s13: $i)).
% 86.18/86.38 tff(c_k_type, type, (
% 86.18/86.38 c_k: $i)).
% 86.18/86.38 tff(s16_type, type, (
% 86.18/86.38 s16: $i)).
% 86.18/86.38 tff(c_g_type, type, (
% 86.18/86.38 c_g: $i)).
% 86.18/86.38 tff(s17_type, type, (
% 86.18/86.38 s17: $i)).
% 86.18/86.38 tff(s19_type, type, (
% 86.18/86.38 s19: $i)).
% 86.18/86.38 tff(s18_type, type, (
% 86.18/86.38 s18: $i)).
% 86.18/86.38 tff(node12_type, type, (
% 86.18/86.38 node12: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node13_type, type, (
% 86.18/86.38 node13: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_mutex_h_half_v_inp_type, type, (
% 86.18/86.38 m_mutex_h_half_v_inp: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_user_v_req_type, type, (
% 86.18/86.38 m_user_v_req: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(m_cell_v_req_type, type, (
% 86.18/86.38 m_cell_v_req: ( $i * $i ) > $o)).
% 86.18/86.38 tff(c_p_type, type, (
% 86.18/86.38 c_p: $i)).
% 86.18/86.38 tff(node1_type, type, (
% 86.18/86.38 node1: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node4_type, type, (
% 86.18/86.38 node4: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node8_type, type, (
% 86.18/86.38 node8: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node7_type, type, (
% 86.18/86.38 node7: ( $i * $i * $i * $i ) > $o)).
% 86.18/86.38 tff(node2_type, type, (
% 86.18/86.38 node2: ( $i * $i * $i ) > $o)).
% 86.18/86.38 tff(until2p29_type, type, (
% 86.18/86.38 until2p29: $i > $o)).
% 86.18/86.38 tff(xuntil2p30_type, type, (
% 86.18/86.38 xuntil2p30: $i > $o)).
% 86.18/86.38 tff(last_type, type, (
% 86.18/86.38 last: $i > $o)).
% 86.18/86.38 tff(xuntil28_type, type, (
% 86.18/86.38 xuntil28: $i > $o)).
% 86.18/86.38 tff(until27_type, type, (
% 86.18/86.38 until27: $i > $o)).
% 86.18/86.38 tff(loop_type, type, (
% 86.18/86.38 loop: $o)).
% 86.18/86.38 tff(1,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s7)), introduced(assumption)).
% 86.18/86.38 tff(2,assumption,(node21(c_e_h_2, c_r, s6, s7)), introduced(assumption)).
% 86.18/86.38 tff(3,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s4)), introduced(assumption)).
% 86.18/86.38 tff(4,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s1)), introduced(assumption)).
% 86.18/86.38 tff(5,assumption,(node21(c_e_h_2, c_i, s0, s1)), introduced(assumption)).
% 86.18/86.38 tff(6,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s0)), introduced(assumption)).
% 86.18/86.38 tff(7,plain,
% 86.18/86.38 (^[I0: $i, I1: $i] : refl((~m_c_h_element_v_out(I0, I1, s0)) <=> (~m_c_h_element_v_out(I0, I1, s0)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(8,plain,
% 86.18/86.38 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[7])).
% 86.18/86.38 tff(9,plain,
% 86.18/86.38 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(10,axiom,(![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_1')).
% 86.18/86.38 tff(11,plain,
% 86.18/86.38 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 86.18/86.38 tff(12,plain,(
% 86.18/86.38 ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 86.18/86.38 inference(skolemize,[status(sab)],[11])).
% 86.18/86.38 tff(13,plain,
% 86.18/86.38 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 86.18/86.38 tff(14,plain,
% 86.18/86.38 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 86.18/86.38 inference(quant_inst,[status(thm)],[])).
% 86.18/86.38 tff(15,plain,
% 86.18/86.38 ($false),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[14, 13, 6])).
% 86.18/86.38 tff(16,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.38 tff(17,plain,
% 86.18/86.38 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(18,plain,
% 86.18/86.38 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[17])).
% 86.18/86.38 tff(19,plain,
% 86.18/86.38 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(20,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_36')).
% 86.18/86.38 tff(21,plain,
% 86.18/86.38 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 86.18/86.38 tff(22,plain,(
% 86.18/86.38 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 86.18/86.38 inference(skolemize,[status(sab)],[21])).
% 86.18/86.38 tff(23,plain,
% 86.18/86.38 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 86.18/86.38 tff(24,plain,
% 86.18/86.38 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(25,plain,
% 86.18/86.38 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 86.18/86.38 inference(quant_inst,[status(thm)],[])).
% 86.18/86.38 tff(26,plain,
% 86.18/86.38 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 86.18/86.38 tff(27,plain,
% 86.18/86.38 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[26, 23, 16])).
% 86.18/86.38 tff(28,plain,
% 86.18/86.38 (^[I0: $i, X: $i, I1: $i] : refl(((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)) <=> ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(29,plain,
% 86.18/86.38 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[28])).
% 86.18/86.38 tff(30,plain,
% 86.18/86.38 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(31,plain,
% 86.18/86.38 (^[I0: $i, X: $i, I1: $i] : rewrite((m_and_h_gate_v_in1(I0, I1, X) | (~node20(I0, I1, X))) <=> ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(32,plain,
% 86.18/86.38 (![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in1(I0, I1, X) | (~node20(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[31])).
% 86.18/86.38 tff(33,axiom,(![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in1(I0, I1, X) | (~node20(I0, I1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_2')).
% 86.18/86.38 tff(34,plain,
% 86.18/86.38 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 86.18/86.38 tff(35,plain,
% 86.18/86.38 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 86.18/86.38 tff(36,plain,(
% 86.18/86.38 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 86.18/86.38 inference(skolemize,[status(sab)],[35])).
% 86.18/86.38 tff(37,plain,
% 86.18/86.38 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[36, 29])).
% 86.18/86.38 tff(38,plain,
% 86.18/86.38 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s0))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(39,plain,
% 86.18/86.38 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s0))),
% 86.18/86.38 inference(quant_inst,[status(thm)],[])).
% 86.18/86.38 tff(40,plain,
% 86.18/86.38 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s0)),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 86.18/86.38 tff(41,plain,
% 86.18/86.38 (~node20(c_e_h_2, c_i, s0)),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 86.18/86.38 tff(42,plain,
% 86.18/86.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(43,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[42])).
% 86.18/86.38 tff(44,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(45,plain,
% 86.18/86.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_and_h_gate_v_out(I0, I1, Y)) | node20(I0, I1, X)) | (~node21(I0, I1, X, Y))) <=> (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(46,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_v_out(I0, I1, Y)) | node20(I0, I1, X)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[45])).
% 86.18/86.38 tff(47,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_v_out(I0, I1, Y)) | node20(I0, I1, X)) | (~node21(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_5')).
% 86.18/86.38 tff(48,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 86.18/86.38 tff(49,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[48, 44])).
% 86.18/86.38 tff(50,plain,(
% 86.18/86.38 ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 86.18/86.38 inference(skolemize,[status(sab)],[49])).
% 86.18/86.38 tff(51,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[50, 43])).
% 86.18/86.38 tff(52,plain,
% 86.18/86.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1)))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(53,plain,
% 86.18/86.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1)))),
% 86.18/86.38 inference(quant_inst,[status(thm)],[])).
% 86.18/86.38 tff(54,plain,
% 86.18/86.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 86.18/86.38 tff(55,plain,
% 86.18/86.38 ($false),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[54, 51, 41, 5, 4])).
% 86.18/86.38 tff(56,plain,((~node21(c_e_h_2, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1))), inference(lemma,lemma(discharge,[]))).
% 86.18/86.38 tff(57,plain,
% 86.18/86.38 (~node21(c_e_h_2, c_i, s0, s1)),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[56, 4])).
% 86.18/86.38 tff(58,plain,
% 86.18/86.38 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(59,plain,
% 86.18/86.38 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[58])).
% 86.18/86.38 tff(60,plain,
% 86.18/86.38 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(61,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound21')).
% 86.18/86.38 tff(62,plain,
% 86.18/86.38 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 86.18/86.38 tff(63,plain,(
% 86.18/86.38 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 86.18/86.38 inference(skolemize,[status(sab)],[62])).
% 86.18/86.38 tff(64,plain,
% 86.18/86.38 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[63, 59])).
% 86.18/86.38 tff(65,plain,
% 86.18/86.38 (succ(s0, s1) <=> succ(s0, s1)),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(66,axiom,(succ(s0, s1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound1')).
% 86.18/86.38 tff(67,plain,
% 86.18/86.38 (succ(s0, s1)),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[66, 65])).
% 86.18/86.38 tff(68,plain,
% 86.18/86.38 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(69,plain,
% 86.18/86.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 86.18/86.38 inference(quant_inst,[status(thm)],[])).
% 86.18/86.38 tff(70,plain,
% 86.18/86.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 86.18/86.38 tff(71,plain,
% 86.18/86.38 (trans(s0, s1)),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[70, 67, 64])).
% 86.18/86.38 tff(72,plain,
% 86.18/86.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(73,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[72])).
% 86.18/86.38 tff(74,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(75,plain,
% 86.18/86.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) | (~trans(X, Y))) <=> ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(76,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[75])).
% 86.18/86.38 tff(77,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_8')).
% 86.18/86.38 tff(78,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[77, 76])).
% 86.18/86.38 tff(79,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[78, 74])).
% 86.18/86.38 tff(80,plain,(
% 86.18/86.38 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 86.18/86.38 inference(skolemize,[status(sab)],[79])).
% 86.18/86.38 tff(81,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[80, 73])).
% 86.18/86.38 tff(82,plain,
% 86.18/86.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(83,plain,
% 86.18/86.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1))),
% 86.18/86.38 inference(quant_inst,[status(thm)],[])).
% 86.18/86.38 tff(84,plain,
% 86.18/86.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1)),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[83, 82])).
% 86.18/86.38 tff(85,plain,
% 86.18/86.38 (node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1)),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[84, 81, 71])).
% 86.18/86.38 tff(86,plain,
% 86.18/86.38 (node22(c_e_h_2, c_i, s0, s1)),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[85, 57])).
% 86.18/86.38 tff(87,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s0)), introduced(assumption)).
% 86.18/86.38 tff(88,plain,
% 86.18/86.38 (^[I0: $i, I1: $i] : refl((~m_and_h_gate_v_out(I0, I1, s0)) <=> (~m_and_h_gate_v_out(I0, I1, s0)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(89,plain,
% 86.18/86.38 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[88])).
% 86.18/86.38 tff(90,plain,
% 86.18/86.38 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(91,axiom,(![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_1')).
% 86.18/86.38 tff(92,plain,
% 86.18/86.38 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[91, 90])).
% 86.18/86.38 tff(93,plain,(
% 86.18/86.38 ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 86.18/86.38 inference(skolemize,[status(sab)],[92])).
% 86.18/86.38 tff(94,plain,
% 86.18/86.38 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 86.18/86.38 inference(modus_ponens,[status(thm)],[93, 89])).
% 86.18/86.38 tff(95,plain,
% 86.18/86.38 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 86.18/86.38 inference(quant_inst,[status(thm)],[])).
% 86.18/86.38 tff(96,plain,
% 86.18/86.38 ($false),
% 86.18/86.38 inference(unit_resolution,[status(thm)],[95, 94, 87])).
% 86.18/86.38 tff(97,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.38 tff(98,plain,
% 86.18/86.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(99,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[98])).
% 86.18/86.38 tff(100,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 86.18/86.38 inference(rewrite,[status(thm)],[])).
% 86.18/86.38 tff(101,plain,
% 86.18/86.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_and_h_gate_v_out(I0, I1, Y)) | m_and_h_gate_v_out(I0, I1, X)) | (~node22(I0, I1, X, Y))) <=> ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)))),
% 86.18/86.38 inference(bind,[status(th)],[])).
% 86.18/86.38 tff(102,plain,
% 86.18/86.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_v_out(I0, I1, Y)) | m_and_h_gate_v_out(I0, I1, X)) | (~node22(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 86.18/86.38 inference(quant_intro,[status(thm)],[101])).
% 86.18/86.38 tff(103,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_v_out(I0, I1, Y)) | m_and_h_gate_v_out(I0, I1, X)) | (~node22(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_7')).
% 86.18/86.39 tff(104,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 86.18/86.39 tff(105,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[104, 100])).
% 86.18/86.39 tff(106,plain,(
% 86.18/86.39 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 86.18/86.39 inference(skolemize,[status(sab)],[105])).
% 86.18/86.39 tff(107,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[106, 99])).
% 86.18/86.39 tff(108,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(109,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 86.18/86.39 inference(quant_inst,[status(thm)],[])).
% 86.18/86.39 tff(110,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0)),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[109, 108])).
% 86.18/86.39 tff(111,plain,
% 86.18/86.39 ($false),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[110, 107, 97, 86, 4])).
% 86.18/86.39 tff(112,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.39 tff(113,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s1)), introduced(assumption)).
% 86.18/86.39 tff(114,assumption,(node18(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 86.18/86.39 tff(115,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(116,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[115])).
% 86.18/86.39 tff(117,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(118,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(119,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[118])).
% 86.18/86.39 tff(120,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_11')).
% 86.18/86.39 tff(121,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[120, 119])).
% 86.18/86.39 tff(122,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[121, 117])).
% 86.18/86.39 tff(123,plain,(
% 86.18/86.39 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 86.18/86.39 inference(skolemize,[status(sab)],[122])).
% 86.18/86.39 tff(124,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[123, 116])).
% 86.18/86.39 tff(125,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(126,plain,
% 86.18/86.39 (((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~node18(c_e_h_2, c_h, s0, s1))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(127,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~node18(c_e_h_2, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)))),
% 86.18/86.39 inference(monotonicity,[status(thm)],[126])).
% 86.18/86.39 tff(128,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~node18(c_e_h_2, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(transitivity,[status(thm)],[127, 125])).
% 86.18/86.39 tff(129,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0) | (~node18(c_e_h_2, c_h, s0, s1)))),
% 86.18/86.39 inference(quant_inst,[status(thm)],[])).
% 86.18/86.39 tff(130,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node18(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[129, 128])).
% 86.18/86.39 tff(131,plain,
% 86.18/86.39 ($false),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[130, 124, 113, 114, 16])).
% 86.18/86.39 tff(132,plain,((~node18(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 86.18/86.39 tff(133,plain,
% 86.18/86.39 (~node18(c_e_h_2, c_h, s0, s1)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[132, 113])).
% 86.18/86.39 tff(134,assumption,(~node19(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 86.18/86.39 tff(135,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node19(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(136,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[135])).
% 86.18/86.39 tff(137,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(138,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_14')).
% 86.18/86.39 tff(139,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[138, 137])).
% 86.18/86.39 tff(140,plain,(
% 86.18/86.39 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 86.18/86.39 inference(skolemize,[status(sab)],[139])).
% 86.18/86.39 tff(141,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[140, 136])).
% 86.18/86.39 tff(142,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(143,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1))),
% 86.18/86.39 inference(quant_inst,[status(thm)],[])).
% 86.18/86.39 tff(144,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1)),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[143, 142])).
% 86.18/86.39 tff(145,plain,
% 86.18/86.39 ($false),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[144, 141, 71, 134])).
% 86.18/86.39 tff(146,plain,(node19(c_e_h_2, c_h, s0, s1)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.39 tff(147,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(148,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[147])).
% 86.18/86.39 tff(149,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(150,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node17(I0, I1, X) | node18(I0, I1, X, Y)) | (~node19(I0, I1, X, Y))) <=> (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(151,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node17(I0, I1, X) | node18(I0, I1, X, Y)) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[150])).
% 86.18/86.39 tff(152,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node17(I0, I1, X) | node18(I0, I1, X, Y)) | (~node19(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_13')).
% 86.18/86.39 tff(153,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[152, 151])).
% 86.18/86.39 tff(154,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[153, 149])).
% 86.18/86.39 tff(155,plain,(
% 86.18/86.39 ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(skolemize,[status(sab)],[154])).
% 86.18/86.39 tff(156,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[155, 148])).
% 86.18/86.39 tff(157,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s0) | node18(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s0) | node18(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(158,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s0) | node18(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))),
% 86.18/86.39 inference(quant_inst,[status(thm)],[])).
% 86.18/86.39 tff(159,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s0) | node18(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[158, 157])).
% 86.18/86.39 tff(160,plain,
% 86.18/86.39 (node17(c_e_h_2, c_h, s0) | node18(c_e_h_2, c_h, s0, s1)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[159, 156, 146])).
% 86.18/86.39 tff(161,plain,
% 86.18/86.39 (node17(c_e_h_2, c_h, s0)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[160, 133])).
% 86.18/86.39 tff(162,assumption,(~node14(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 86.18/86.39 tff(163,assumption,(node15(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 86.18/86.39 tff(164,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(165,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[164])).
% 86.18/86.39 tff(166,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(167,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node15(I0, I1, X, Y))) <=> ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(168,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node15(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[167])).
% 86.18/86.39 tff(169,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node15(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_5')).
% 86.18/86.39 tff(170,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[169, 168])).
% 86.18/86.39 tff(171,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[170, 166])).
% 86.18/86.39 tff(172,plain,(
% 86.18/86.39 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 86.18/86.39 inference(skolemize,[status(sab)],[171])).
% 86.18/86.39 tff(173,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[172, 165])).
% 86.18/86.39 tff(174,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(175,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(quant_inst,[status(thm)],[])).
% 86.18/86.39 tff(176,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[175, 174])).
% 86.18/86.39 tff(177,plain,
% 86.18/86.39 ($false),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[176, 173, 113, 163, 16])).
% 86.18/86.39 tff(178,plain,((~node15(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 86.18/86.39 tff(179,plain,
% 86.18/86.39 (~node15(c_e_h_2, c_h, s0, s1)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[178, 113])).
% 86.18/86.39 tff(180,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(181,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[180])).
% 86.18/86.39 tff(182,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(183,plain,
% 86.18/86.39 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite(((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) <=> (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y))), ((((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) | (~node19(I0, I1, X, Y))) <=> ((node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | (~node19(I0, I1, X, Y))))), rewrite(((node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | (~node19(I0, I1, X, Y))) <=> (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))), ((((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) | (~node19(I0, I1, X, Y))) <=> (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(184,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[183])).
% 86.18/86.39 tff(185,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) | (~node19(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_12')).
% 86.18/86.39 tff(186,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[185, 184])).
% 86.18/86.39 tff(187,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[186, 182])).
% 86.18/86.39 tff(188,plain,(
% 86.18/86.39 ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(skolemize,[status(sab)],[187])).
% 86.18/86.39 tff(189,plain,
% 86.18/86.39 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[188, 181])).
% 86.18/86.39 tff(190,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_h, s0, s1) | node16(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s0, s1) | node16(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(191,plain,
% 86.18/86.39 ((node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1))) <=> (node14(c_e_h_2, c_h, s0, s1) | node16(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(192,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_h, s0, s1) | node16(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1)))),
% 86.18/86.39 inference(monotonicity,[status(thm)],[191])).
% 86.18/86.39 tff(193,plain,
% 86.18/86.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s0, s1) | node16(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1))),
% 86.18/86.39 inference(transitivity,[status(thm)],[192, 190])).
% 86.18/86.39 tff(194,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))),
% 86.18/86.39 inference(quant_inst,[status(thm)],[])).
% 86.18/86.39 tff(195,plain,
% 86.18/86.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s0, s1) | node16(c_e_h_2, c_h, s0) | (~node19(c_e_h_2, c_h, s0, s1)) | node15(c_e_h_2, c_h, s0, s1)),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[194, 193])).
% 86.18/86.39 tff(196,plain,
% 86.18/86.39 (node14(c_e_h_2, c_h, s0, s1) | node16(c_e_h_2, c_h, s0) | node15(c_e_h_2, c_h, s0, s1)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[195, 189, 146])).
% 86.18/86.39 tff(197,plain,
% 86.18/86.39 (node16(c_e_h_2, c_h, s0)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[196, 179, 162])).
% 86.18/86.39 tff(198,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s0)), introduced(assumption)).
% 86.18/86.39 tff(199,assumption,(node17(c_e_h_2, c_h, s0)), introduced(assumption)).
% 86.18/86.39 tff(200,plain,
% 86.18/86.39 (^[I0: $i, X: $i, I1: $i] : refl(((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))) <=> ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(201,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[200])).
% 86.18/86.39 tff(202,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(203,plain,
% 86.18/86.39 (^[I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(204,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[203])).
% 86.18/86.39 tff(205,axiom,(![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_9')).
% 86.18/86.39 tff(206,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[205, 204])).
% 86.18/86.39 tff(207,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[206, 202])).
% 86.18/86.39 tff(208,plain,(
% 86.18/86.39 ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(skolemize,[status(sab)],[207])).
% 86.18/86.39 tff(209,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[208, 201])).
% 86.18/86.39 tff(210,plain,
% 86.18/86.39 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(211,plain,
% 86.18/86.39 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0))) <=> (m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(212,plain,
% 86.18/86.39 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0))))),
% 86.18/86.39 inference(monotonicity,[status(thm)],[211])).
% 86.18/86.39 tff(213,plain,
% 86.18/86.39 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)))),
% 86.18/86.39 inference(transitivity,[status(thm)],[212, 210])).
% 86.18/86.39 tff(214,plain,
% 86.18/86.39 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)))),
% 86.18/86.39 inference(quant_inst,[status(thm)],[])).
% 86.18/86.39 tff(215,plain,
% 86.18/86.39 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[214, 213])).
% 86.18/86.39 tff(216,plain,
% 86.18/86.39 (m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[215, 209, 199])).
% 86.18/86.39 tff(217,plain,
% 86.18/86.39 (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[216, 198])).
% 86.18/86.39 tff(218,assumption,(node16(c_e_h_2, c_h, s0)), introduced(assumption)).
% 86.18/86.39 tff(219,plain,
% 86.18/86.39 (^[I0: $i, X: $i, I1: $i] : refl(((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) <=> ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(220,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[219])).
% 86.18/86.39 tff(221,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(222,plain,
% 86.18/86.39 (^[I0: $i, X: $i, I1: $i] : rewrite(((m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) | (~node16(I0, I1, X))) <=> ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(223,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) | (~node16(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[222])).
% 86.18/86.39 tff(224,axiom,(![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) | (~node16(I0, I1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_6')).
% 86.18/86.39 tff(225,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[224, 223])).
% 86.18/86.39 tff(226,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[225, 221])).
% 86.18/86.39 tff(227,plain,(
% 86.18/86.39 ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 86.18/86.39 inference(skolemize,[status(sab)],[226])).
% 86.18/86.39 tff(228,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[227, 220])).
% 86.18/86.39 tff(229,plain,
% 86.18/86.39 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(230,plain,
% 86.18/86.39 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 86.18/86.39 inference(quant_inst,[status(thm)],[])).
% 86.18/86.39 tff(231,plain,
% 86.18/86.39 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[230, 229])).
% 86.18/86.39 tff(232,plain,
% 86.18/86.39 (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[231, 228, 218])).
% 86.18/86.39 tff(233,plain,
% 86.18/86.39 ($false),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[232, 217, 198])).
% 86.18/86.39 tff(234,plain,(m_c_h_element_v_in2(c_e_h_2, c_h, s0) | (~node16(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0))), inference(lemma,lemma(discharge,[]))).
% 86.18/86.39 tff(235,plain,
% 86.18/86.39 (m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 86.18/86.39 inference(unit_resolution,[status(thm)],[234, 197, 161])).
% 86.18/86.39 tff(236,plain,
% 86.18/86.39 (^[I0: $i, X: $i, I1: $i] : refl((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(237,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[236])).
% 86.18/86.39 tff(238,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(239,plain,
% 86.18/86.39 (^[I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) <=> (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)))), (((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> ((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))))), rewrite(((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))), (((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))))),
% 86.18/86.39 inference(bind,[status(th)],[])).
% 86.18/86.39 tff(240,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(quant_intro,[status(thm)],[239])).
% 86.18/86.39 tff(241,axiom,(![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_8')).
% 86.18/86.39 tff(242,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[241, 240])).
% 86.18/86.39 tff(243,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[242, 238])).
% 86.18/86.39 tff(244,plain,(
% 86.18/86.39 ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(skolemize,[status(sab)],[243])).
% 86.18/86.39 tff(245,plain,
% 86.18/86.39 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 86.18/86.39 inference(modus_ponens,[status(thm)],[244, 237])).
% 86.18/86.39 tff(246,plain,
% 86.18/86.39 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)))),
% 86.18/86.39 inference(rewrite,[status(thm)],[])).
% 86.18/86.39 tff(247,plain,
% 86.18/86.39 ((m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(248,plain,
% 86.18/86.40 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0))))),
% 86.18/86.40 inference(monotonicity,[status(thm)],[247])).
% 86.18/86.40 tff(249,plain,
% 86.18/86.40 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)))),
% 86.18/86.40 inference(transitivity,[status(thm)],[248, 246])).
% 86.18/86.40 tff(250,plain,
% 86.18/86.40 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node17(c_e_h_2, c_h, s0)))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(251,plain,
% 86.18/86.40 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[250, 249])).
% 86.18/86.40 tff(252,plain,
% 86.18/86.40 (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[251, 245, 161])).
% 86.18/86.40 tff(253,plain,
% 86.18/86.40 (m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[252, 235])).
% 86.18/86.40 tff(254,plain,
% 86.18/86.40 (^[I0: $i, X: $i, I1: $i] : refl(((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) <=> ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))))),
% 86.18/86.40 inference(bind,[status(th)],[])).
% 86.18/86.40 tff(255,plain,
% 86.18/86.40 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.40 inference(quant_intro,[status(thm)],[254])).
% 86.18/86.40 tff(256,plain,
% 86.18/86.40 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(257,plain,
% 86.18/86.40 (^[I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node16(I0, I1, X))) <=> ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))))),
% 86.18/86.40 inference(bind,[status(th)],[])).
% 86.18/86.40 tff(258,plain,
% 86.18/86.40 (![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node16(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.40 inference(quant_intro,[status(thm)],[257])).
% 86.18/86.40 tff(259,axiom,(![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node16(I0, I1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_7')).
% 86.18/86.40 tff(260,plain,
% 86.18/86.40 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[259, 258])).
% 86.18/86.40 tff(261,plain,
% 86.18/86.40 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[260, 256])).
% 86.18/86.40 tff(262,plain,(
% 86.18/86.40 ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.40 inference(skolemize,[status(sab)],[261])).
% 86.18/86.40 tff(263,plain,
% 86.18/86.40 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[262, 255])).
% 86.18/86.40 tff(264,plain,
% 86.18/86.40 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(265,plain,
% 86.18/86.40 (((~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(266,plain,
% 86.18/86.40 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0))))),
% 86.18/86.40 inference(monotonicity,[status(thm)],[265])).
% 86.18/86.40 tff(267,plain,
% 86.18/86.40 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)))),
% 86.18/86.40 inference(transitivity,[status(thm)],[266, 264])).
% 86.18/86.40 tff(268,plain,
% 86.18/86.40 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(269,plain,
% 86.18/86.40 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~node16(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[268, 267])).
% 86.18/86.40 tff(270,plain,
% 86.18/86.40 ((~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0))),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[269, 263, 197])).
% 86.18/86.40 tff(271,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[270, 253, 235])).
% 86.18/86.40 tff(272,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | node14(c_e_h_2, c_h, s0, s1)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(273,plain,
% 86.18/86.40 (node14(c_e_h_2, c_h, s0, s1)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[272, 113])).
% 86.18/86.40 tff(274,plain,
% 86.18/86.40 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))))),
% 86.18/86.40 inference(bind,[status(th)],[])).
% 86.18/86.40 tff(275,plain,
% 86.18/86.40 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 86.18/86.40 inference(quant_intro,[status(thm)],[274])).
% 86.18/86.40 tff(276,plain,
% 86.18/86.40 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(277,plain,
% 86.18/86.40 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_in1(I0, I1, X)) | (~node14(I0, I1, X, Y))) <=> ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))))),
% 86.18/86.40 inference(bind,[status(th)],[])).
% 86.18/86.40 tff(278,plain,
% 86.18/86.40 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_in1(I0, I1, X)) | (~node14(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 86.18/86.40 inference(quant_intro,[status(thm)],[277])).
% 86.18/86.40 tff(279,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_in1(I0, I1, X)) | (~node14(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_c_h_element_3')).
% 86.18/86.40 tff(280,plain,
% 86.18/86.40 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[279, 278])).
% 86.18/86.40 tff(281,plain,
% 86.18/86.40 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[280, 276])).
% 86.18/86.40 tff(282,plain,(
% 86.18/86.40 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 86.18/86.40 inference(skolemize,[status(sab)],[281])).
% 86.18/86.40 tff(283,plain,
% 86.18/86.40 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[282, 275])).
% 86.18/86.40 tff(284,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(285,plain,
% 86.18/86.40 (((~node14(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1))) <=> ((~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(286,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0)))),
% 86.18/86.40 inference(monotonicity,[status(thm)],[285])).
% 86.18/86.40 tff(287,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0))),
% 86.18/86.40 inference(transitivity,[status(thm)],[286, 284])).
% 86.18/86.40 tff(288,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(289,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[288, 287])).
% 86.18/86.40 tff(290,plain,
% 86.18/86.40 ((~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[289, 283])).
% 86.18/86.40 tff(291,plain,
% 86.18/86.40 (m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[290, 273, 113])).
% 86.18/86.40 tff(292,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s0)), introduced(assumption)).
% 86.18/86.40 tff(293,plain,
% 86.18/86.40 (^[I0: $i, I1: $i] : refl((~m_or_h_gate_v_out(I0, I1, s0)) <=> (~m_or_h_gate_v_out(I0, I1, s0)))),
% 86.18/86.40 inference(bind,[status(th)],[])).
% 86.18/86.40 tff(294,plain,
% 86.18/86.40 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 86.18/86.40 inference(quant_intro,[status(thm)],[293])).
% 86.18/86.40 tff(295,plain,
% 86.18/86.40 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(296,axiom,(![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_or_h_gate_1')).
% 86.18/86.40 tff(297,plain,
% 86.18/86.40 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[296, 295])).
% 86.18/86.40 tff(298,plain,(
% 86.18/86.40 ![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 86.18/86.40 inference(skolemize,[status(sab)],[297])).
% 86.18/86.40 tff(299,plain,
% 86.18/86.40 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[298, 294])).
% 86.18/86.40 tff(300,plain,
% 86.18/86.40 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(301,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[300, 299, 292])).
% 86.18/86.40 tff(302,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(303,plain,
% 86.18/86.40 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X)) <=> ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X)))),
% 86.18/86.40 inference(bind,[status(th)],[])).
% 86.18/86.40 tff(304,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 86.18/86.40 inference(quant_intro,[status(thm)],[303])).
% 86.18/86.40 tff(305,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(306,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_34')).
% 86.18/86.40 tff(307,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[306, 305])).
% 86.18/86.40 tff(308,plain,(
% 86.18/86.40 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 86.18/86.40 inference(skolemize,[status(sab)],[307])).
% 86.18/86.40 tff(309,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[308, 304])).
% 86.18/86.40 tff(310,plain,
% 86.18/86.40 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(311,plain,
% 86.18/86.40 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(312,plain,
% 86.18/86.40 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[311, 310])).
% 86.18/86.40 tff(313,plain,
% 86.18/86.40 (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[312, 309, 302])).
% 86.18/86.40 tff(314,plain,
% 86.18/86.40 ((~node17(c_e_h_2, c_h, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0))),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[215, 209, 313])).
% 86.18/86.40 tff(315,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[314, 291, 161])).
% 86.18/86.40 tff(316,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(317,plain,
% 86.18/86.40 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(318,plain,
% 86.18/86.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(319,plain,
% 86.18/86.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[318, 317])).
% 86.18/86.40 tff(320,plain,
% 86.18/86.40 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[319, 23, 316])).
% 86.18/86.40 tff(321,plain,
% 86.18/86.40 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s1))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(322,plain,
% 86.18/86.40 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s1))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(323,plain,
% 86.18/86.40 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s1)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[322, 321])).
% 86.18/86.40 tff(324,plain,
% 86.18/86.40 (~node20(c_e_h_2, c_i, s1)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[323, 37, 320])).
% 86.18/86.40 tff(325,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s2)), introduced(assumption)).
% 86.18/86.40 tff(326,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s1)), introduced(assumption)).
% 86.18/86.40 tff(327,assumption,(~node20(c_e_h_2, c_i, s1)), introduced(assumption)).
% 86.18/86.40 tff(328,assumption,(node21(c_e_h_2, c_i, s1, s2)), introduced(assumption)).
% 86.18/86.40 tff(329,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s1) | (~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s1) | (~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(330,plain,
% 86.18/86.40 ((node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2))) <=> (node20(c_e_h_2, c_i, s1) | (~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(331,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s1) | (~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2))))),
% 86.18/86.40 inference(monotonicity,[status(thm)],[330])).
% 86.18/86.40 tff(332,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s1) | (~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)))),
% 86.18/86.40 inference(transitivity,[status(thm)],[331, 329])).
% 86.18/86.40 tff(333,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2)))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(334,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s1) | (~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[333, 332])).
% 86.18/86.40 tff(335,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[334, 51, 328, 325, 327])).
% 86.18/86.40 tff(336,plain,((~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | node20(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(337,plain,
% 86.18/86.40 (~node21(c_e_h_2, c_i, s1, s2)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[336, 325, 327])).
% 86.18/86.40 tff(338,plain,
% 86.18/86.40 (succ(s1, s2) <=> succ(s1, s2)),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(339,axiom,(succ(s1, s2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound2')).
% 86.18/86.40 tff(340,plain,
% 86.18/86.40 (succ(s1, s2)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[339, 338])).
% 86.18/86.40 tff(341,plain,
% 86.18/86.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(342,plain,
% 86.18/86.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(343,plain,
% 86.18/86.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[342, 341])).
% 86.18/86.40 tff(344,plain,
% 86.18/86.40 (trans(s1, s2)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[343, 340, 64])).
% 86.18/86.40 tff(345,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(346,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(347,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[346, 345])).
% 86.18/86.40 tff(348,plain,
% 86.18/86.40 (node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[347, 81, 344])).
% 86.18/86.40 tff(349,plain,
% 86.18/86.40 (node22(c_e_h_2, c_i, s1, s2)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[348, 337])).
% 86.18/86.40 tff(350,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(351,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(352,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[351, 350])).
% 86.18/86.40 tff(353,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[352, 107, 349, 326, 325])).
% 86.18/86.40 tff(354,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1) | node20(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(355,plain,
% 86.18/86.40 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[354, 324])).
% 86.18/86.40 tff(356,plain,
% 86.18/86.40 (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[355, 112])).
% 86.18/86.40 tff(357,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s2)), introduced(assumption)).
% 86.18/86.40 tff(358,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s2)), introduced(assumption)).
% 86.18/86.40 tff(359,plain,
% 86.18/86.40 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X)))),
% 86.18/86.40 inference(bind,[status(th)],[])).
% 86.18/86.40 tff(360,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.18/86.40 inference(quant_intro,[status(thm)],[359])).
% 86.18/86.40 tff(361,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(362,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_22')).
% 86.18/86.40 tff(363,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[362, 361])).
% 86.18/86.40 tff(364,plain,(
% 86.18/86.40 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.18/86.40 inference(skolemize,[status(sab)],[363])).
% 86.18/86.40 tff(365,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[364, 360])).
% 86.18/86.40 tff(366,plain,
% 86.18/86.40 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(367,plain,
% 86.18/86.40 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(368,plain,
% 86.18/86.40 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[367, 366])).
% 86.18/86.40 tff(369,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[368, 365, 358, 357])).
% 86.18/86.40 tff(370,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(371,plain,
% 86.18/86.40 (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[370, 356])).
% 86.18/86.40 tff(372,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s3)), introduced(assumption)).
% 86.18/86.40 tff(373,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s2)), introduced(assumption)).
% 86.18/86.40 tff(374,assumption,(node15(c_e_h_2, c_e, s1, s2)), introduced(assumption)).
% 86.18/86.40 tff(375,assumption,(m_and_h_gate_v_out(c_e_h_2, c_c, s0)), introduced(assumption)).
% 86.18/86.40 tff(376,plain,
% 86.18/86.40 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(377,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[376, 94, 375])).
% 86.18/86.40 tff(378,plain,(~m_and_h_gate_v_out(c_e_h_2, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(379,plain,
% 86.18/86.40 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X)))),
% 86.18/86.40 inference(bind,[status(th)],[])).
% 86.18/86.40 tff(380,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 86.18/86.40 inference(quant_intro,[status(thm)],[379])).
% 86.18/86.40 tff(381,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(382,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_20')).
% 86.18/86.40 tff(383,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[382, 381])).
% 86.18/86.40 tff(384,plain,(
% 86.18/86.40 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 86.18/86.40 inference(skolemize,[status(sab)],[383])).
% 86.18/86.40 tff(385,plain,
% 86.18/86.40 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[384, 380])).
% 86.18/86.40 tff(386,plain,
% 86.18/86.40 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(387,plain,
% 86.18/86.40 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(388,plain,
% 86.18/86.40 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[387, 386])).
% 86.18/86.40 tff(389,plain,
% 86.18/86.40 (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[388, 385, 378])).
% 86.18/86.40 tff(390,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s1)), introduced(assumption)).
% 86.18/86.40 tff(391,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s0)), introduced(assumption)).
% 86.18/86.40 tff(392,plain,
% 86.18/86.40 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(393,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[392, 13, 391])).
% 86.18/86.40 tff(394,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(395,assumption,(node18(c_e_h_2, c_e, s0, s1)), introduced(assumption)).
% 86.18/86.40 tff(396,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(397,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(398,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1))),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[397, 396])).
% 86.18/86.40 tff(399,plain,
% 86.18/86.40 ($false),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[398, 124, 390, 395, 394])).
% 86.18/86.40 tff(400,plain,((~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 86.18/86.40 tff(401,plain,
% 86.18/86.40 (~node18(c_e_h_2, c_e, s0, s1)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[400, 390])).
% 86.18/86.40 tff(402,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))),
% 86.18/86.40 inference(rewrite,[status(thm)],[])).
% 86.18/86.40 tff(403,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))),
% 86.18/86.40 inference(quant_inst,[status(thm)],[])).
% 86.18/86.40 tff(404,plain,
% 86.18/86.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1)),
% 86.18/86.40 inference(modus_ponens,[status(thm)],[403, 402])).
% 86.18/86.40 tff(405,plain,
% 86.18/86.40 (node19(c_e_h_2, c_e, s0, s1)),
% 86.18/86.40 inference(unit_resolution,[status(thm)],[404, 141, 71])).
% 86.18/86.40 tff(406,plain,
% 86.18/86.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(407,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(quant_inst,[status(thm)],[])).
% 86.18/86.41 tff(408,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1))),
% 86.18/86.41 inference(modus_ponens,[status(thm)],[407, 406])).
% 86.18/86.41 tff(409,plain,
% 86.18/86.41 (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1)),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[408, 156, 405])).
% 86.18/86.41 tff(410,plain,
% 86.18/86.41 (node17(c_e_h_2, c_e, s0)),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[409, 401])).
% 86.18/86.41 tff(411,plain,
% 86.18/86.41 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0)))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(412,plain,
% 86.18/86.41 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0)))),
% 86.18/86.41 inference(quant_inst,[status(thm)],[])).
% 86.18/86.41 tff(413,plain,
% 86.18/86.41 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0))),
% 86.18/86.41 inference(modus_ponens,[status(thm)],[412, 411])).
% 86.18/86.41 tff(414,plain,
% 86.18/86.41 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0))),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[413, 245, 389])).
% 86.18/86.41 tff(415,plain,
% 86.18/86.41 (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[414, 410])).
% 86.18/86.41 tff(416,plain,
% 86.18/86.41 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(417,plain,
% 86.18/86.41 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))),
% 86.18/86.41 inference(quant_inst,[status(thm)],[])).
% 86.18/86.41 tff(418,plain,
% 86.18/86.41 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 86.18/86.41 inference(modus_ponens,[status(thm)],[417, 416])).
% 86.18/86.41 tff(419,plain,
% 86.18/86.41 ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[418, 228, 389])).
% 86.18/86.41 tff(420,plain,
% 86.18/86.41 (~node16(c_e_h_2, c_e, s0)),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[419, 415])).
% 86.18/86.41 tff(421,assumption,(node15(c_e_h_2, c_e, s0, s1)), introduced(assumption)).
% 86.18/86.41 tff(422,plain,
% 86.18/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(423,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 86.18/86.41 inference(quant_inst,[status(thm)],[])).
% 86.18/86.41 tff(424,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0)),
% 86.18/86.41 inference(modus_ponens,[status(thm)],[423, 422])).
% 86.18/86.41 tff(425,plain,
% 86.18/86.41 ($false),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[424, 173, 390, 421, 394])).
% 86.18/86.41 tff(426,plain,((~node15(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 86.18/86.41 tff(427,plain,
% 86.18/86.41 (~node15(c_e_h_2, c_e, s0, s1)),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[426, 390])).
% 86.18/86.41 tff(428,plain,
% 86.18/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(429,plain,
% 86.18/86.41 ((node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1))) <=> (node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(430,plain,
% 86.18/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1))))),
% 86.18/86.41 inference(monotonicity,[status(thm)],[429])).
% 86.18/86.41 tff(431,plain,
% 86.18/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(transitivity,[status(thm)],[430, 428])).
% 86.18/86.41 tff(432,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(quant_inst,[status(thm)],[])).
% 86.18/86.41 tff(433,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0) | (~node19(c_e_h_2, c_e, s0, s1))),
% 86.18/86.41 inference(modus_ponens,[status(thm)],[432, 431])).
% 86.18/86.41 tff(434,plain,
% 86.18/86.41 (node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | node16(c_e_h_2, c_e, s0)),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[433, 189, 405])).
% 86.18/86.41 tff(435,plain,
% 86.18/86.41 (node14(c_e_h_2, c_e, s0, s1)),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[434, 427, 420])).
% 86.18/86.41 tff(436,plain,
% 86.18/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(437,plain,
% 86.18/86.41 (((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(438,plain,
% 86.18/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1))))),
% 86.18/86.41 inference(monotonicity,[status(thm)],[437])).
% 86.18/86.41 tff(439,plain,
% 86.18/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)))),
% 86.18/86.41 inference(transitivity,[status(thm)],[438, 436])).
% 86.18/86.41 tff(440,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 86.18/86.41 inference(quant_inst,[status(thm)],[])).
% 86.18/86.41 tff(441,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1))),
% 86.18/86.41 inference(modus_ponens,[status(thm)],[440, 439])).
% 86.18/86.41 tff(442,plain,
% 86.18/86.41 ($false),
% 86.18/86.41 inference(unit_resolution,[status(thm)],[441, 283, 390, 435, 389])).
% 86.18/86.41 tff(443,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 86.18/86.41 tff(444,plain,
% 86.18/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 86.18/86.41 inference(rewrite,[status(thm)],[])).
% 86.18/86.41 tff(445,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 86.18/86.41 inference(quant_inst,[status(thm)],[])).
% 86.18/86.41 tff(446,plain,
% 86.18/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[445, 444])).
% 86.23/86.41 tff(447,plain,
% 86.23/86.41 ($false),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[446, 173, 443, 373, 374])).
% 86.23/86.41 tff(448,plain,((~node15(c_e_h_2, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 86.23/86.41 tff(449,plain,
% 86.23/86.41 (~node15(c_e_h_2, c_e, s1, s2)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[448, 373])).
% 86.23/86.41 tff(450,assumption,(m_and_h_gate_v_out(c_e_h_2, c_c, s1)), introduced(assumption)).
% 86.23/86.41 tff(451,assumption,(node22(c_e_h_2, c_c, s0, s1)), introduced(assumption)).
% 86.23/86.41 tff(452,plain,
% 86.23/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(453,plain,
% 86.23/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(454,plain,
% 86.23/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0)),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[453, 452])).
% 86.23/86.41 tff(455,plain,
% 86.23/86.41 ($false),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[454, 107, 451, 450, 378])).
% 86.23/86.41 tff(456,plain,((~node22(c_e_h_2, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 86.23/86.41 tff(457,plain,
% 86.23/86.41 (~node22(c_e_h_2, c_c, s0, s1)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[456, 450])).
% 86.23/86.41 tff(458,assumption,(m_mutex_h_half_v_out(c_e_h_2, c_a, s0)), introduced(assumption)).
% 86.23/86.41 tff(459,plain,
% 86.23/86.41 (^[I0: $i, I1: $i] : refl((~m_mutex_h_half_v_out(I0, I1, s0)) <=> (~m_mutex_h_half_v_out(I0, I1, s0)))),
% 86.23/86.41 inference(bind,[status(th)],[])).
% 86.23/86.41 tff(460,plain,
% 86.23/86.41 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 86.23/86.41 inference(quant_intro,[status(thm)],[459])).
% 86.23/86.41 tff(461,plain,
% 86.23/86.41 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(462,axiom,(![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_mutex_h_half_1')).
% 86.23/86.41 tff(463,plain,
% 86.23/86.41 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[462, 461])).
% 86.23/86.41 tff(464,plain,(
% 86.23/86.41 ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 86.23/86.41 inference(skolemize,[status(sab)],[463])).
% 86.23/86.41 tff(465,plain,
% 86.23/86.41 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[464, 460])).
% 86.23/86.41 tff(466,plain,
% 86.23/86.41 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(467,plain,
% 86.23/86.41 ($false),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[466, 465, 458])).
% 86.23/86.41 tff(468,plain,(~m_mutex_h_half_v_out(c_e_h_2, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.41 tff(469,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_c, s0)), introduced(assumption)).
% 86.23/86.41 tff(470,assumption,(~m_mutex_h_half_v_out(c_e_h_2, c_a, s0)), introduced(assumption)).
% 86.23/86.41 tff(471,plain,
% 86.23/86.41 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)) <=> ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)))),
% 86.23/86.41 inference(bind,[status(th)],[])).
% 86.23/86.41 tff(472,plain,
% 86.23/86.41 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 86.23/86.41 inference(quant_intro,[status(thm)],[471])).
% 86.23/86.41 tff(473,plain,
% 86.23/86.41 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(474,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_11')).
% 86.23/86.41 tff(475,plain,
% 86.23/86.41 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[474, 473])).
% 86.23/86.41 tff(476,plain,(
% 86.23/86.41 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 86.23/86.41 inference(skolemize,[status(sab)],[475])).
% 86.23/86.41 tff(477,plain,
% 86.23/86.41 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[476, 472])).
% 86.23/86.41 tff(478,plain,
% 86.23/86.41 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(479,plain,
% 86.23/86.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(480,plain,
% 86.23/86.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0)),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[479, 478])).
% 86.23/86.41 tff(481,plain,
% 86.23/86.41 ($false),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[480, 477, 470, 469])).
% 86.23/86.41 tff(482,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.41 tff(483,plain,
% 86.23/86.41 (~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[482, 468])).
% 86.23/86.41 tff(484,plain,
% 86.23/86.41 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s0))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(485,plain,
% 86.23/86.41 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s0))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(486,plain,
% 86.23/86.41 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s0)),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[485, 484])).
% 86.23/86.41 tff(487,plain,
% 86.23/86.41 (~node20(c_e_h_2, c_c, s0)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[486, 37, 483])).
% 86.23/86.41 tff(488,assumption,(~node20(c_e_h_2, c_c, s0)), introduced(assumption)).
% 86.23/86.41 tff(489,assumption,(node21(c_e_h_2, c_c, s0, s1)), introduced(assumption)).
% 86.23/86.41 tff(490,plain,
% 86.23/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1)))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(491,plain,
% 86.23/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1)))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(492,plain,
% 86.23/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1))),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[491, 490])).
% 86.23/86.41 tff(493,plain,
% 86.23/86.41 ($false),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[492, 51, 489, 488, 450])).
% 86.23/86.41 tff(494,plain,((~node21(c_e_h_2, c_c, s0, s1)) | node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 86.23/86.41 tff(495,plain,
% 86.23/86.41 ((~node21(c_e_h_2, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[494, 487])).
% 86.23/86.41 tff(496,plain,
% 86.23/86.41 (~node21(c_e_h_2, c_c, s0, s1)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[495, 450])).
% 86.23/86.41 tff(497,plain,
% 86.23/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(498,plain,
% 86.23/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(499,plain,
% 86.23/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1)),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[498, 497])).
% 86.23/86.41 tff(500,plain,
% 86.23/86.41 (node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[499, 81, 71])).
% 86.23/86.41 tff(501,plain,
% 86.23/86.41 ($false),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[500, 496, 457])).
% 86.23/86.41 tff(502,plain,(~m_and_h_gate_v_out(c_e_h_2, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.41 tff(503,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_c, s1)), introduced(assumption)).
% 86.23/86.41 tff(504,assumption,(m_c_h_element_v_in1(c_e_h_2, c_e, s1)), introduced(assumption)).
% 86.23/86.41 tff(505,plain,
% 86.23/86.41 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(506,plain,
% 86.23/86.41 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(507,plain,
% 86.23/86.41 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1)),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[506, 505])).
% 86.23/86.41 tff(508,plain,
% 86.23/86.41 ($false),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[507, 385, 504, 503])).
% 86.23/86.41 tff(509,plain,(m_and_h_gate_v_out(c_e_h_2, c_c, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 86.23/86.41 tff(510,plain,
% 86.23/86.41 (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[509, 502])).
% 86.23/86.41 tff(511,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s1)), introduced(assumption)).
% 86.23/86.41 tff(512,assumption,(~node15(c_e_h_2, c_e, s1, s2)), introduced(assumption)).
% 86.23/86.41 tff(513,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s1)), introduced(assumption)).
% 86.23/86.41 tff(514,plain,
% 86.23/86.41 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(515,plain,
% 86.23/86.41 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(516,plain,
% 86.23/86.41 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[515, 514])).
% 86.23/86.41 tff(517,plain,
% 86.23/86.41 ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[516, 228, 513])).
% 86.23/86.41 tff(518,plain,
% 86.23/86.41 (~node16(c_e_h_2, c_e, s1)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[517, 511])).
% 86.23/86.41 tff(519,plain,
% 86.23/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(520,plain,
% 86.23/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))),
% 86.23/86.41 inference(quant_inst,[status(thm)],[])).
% 86.23/86.41 tff(521,plain,
% 86.23/86.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2)),
% 86.23/86.41 inference(modus_ponens,[status(thm)],[520, 519])).
% 86.23/86.41 tff(522,plain,
% 86.23/86.41 (node19(c_e_h_2, c_e, s1, s2)),
% 86.23/86.41 inference(unit_resolution,[status(thm)],[521, 141, 344])).
% 86.23/86.41 tff(523,plain,
% 86.23/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | node14(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | node14(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(524,plain,
% 86.23/86.41 ((node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2))) <=> (node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | node14(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.41 inference(rewrite,[status(thm)],[])).
% 86.23/86.41 tff(525,plain,
% 86.23/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | node14(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2))))),
% 86.23/86.41 inference(monotonicity,[status(thm)],[524])).
% 86.23/86.41 tff(526,plain,
% 86.23/86.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | node14(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(transitivity,[status(thm)],[525, 523])).
% 86.23/86.42 tff(527,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(528,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | node14(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2))),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[527, 526])).
% 86.23/86.42 tff(529,plain,
% 86.23/86.42 (node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | node14(c_e_h_2, c_e, s1, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[528, 189, 522])).
% 86.23/86.42 tff(530,plain,
% 86.23/86.42 (node14(c_e_h_2, c_e, s1, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[529, 518, 512])).
% 86.23/86.42 tff(531,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(532,plain,
% 86.23/86.42 (((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(533,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2))))),
% 86.23/86.42 inference(monotonicity,[status(thm)],[532])).
% 86.23/86.42 tff(534,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(transitivity,[status(thm)],[533, 531])).
% 86.23/86.42 tff(535,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(536,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node14(c_e_h_2, c_e, s1, s2))),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[535, 534])).
% 86.23/86.42 tff(537,plain,
% 86.23/86.42 ($false),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[536, 283, 373, 530, 511])).
% 86.23/86.42 tff(538,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | node15(c_e_h_2, c_e, s1, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.42 tff(539,plain,
% 86.23/86.42 (m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[538, 511, 373, 512])).
% 86.23/86.42 tff(540,assumption,(node17(c_e_h_2, c_e, s1)), introduced(assumption)).
% 86.23/86.42 tff(541,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(542,plain,
% 86.23/86.42 ((m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(543,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1))))),
% 86.23/86.42 inference(monotonicity,[status(thm)],[542])).
% 86.23/86.42 tff(544,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)))),
% 86.23/86.42 inference(transitivity,[status(thm)],[543, 541])).
% 86.23/86.42 tff(545,plain,
% 86.23/86.42 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(546,plain,
% 86.23/86.42 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[545, 544])).
% 86.23/86.42 tff(547,plain,
% 86.23/86.42 (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[546, 245, 540])).
% 86.23/86.42 tff(548,plain,
% 86.23/86.42 ($false),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[547, 539, 511])).
% 86.23/86.42 tff(549,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | node15(c_e_h_2, c_e, s1, s2)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.42 tff(550,plain,
% 86.23/86.42 ((~node17(c_e_h_2, c_e, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | node15(c_e_h_2, c_e, s1, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[549, 510])).
% 86.23/86.42 tff(551,plain,
% 86.23/86.42 (~node17(c_e_h_2, c_e, s1)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[550, 373, 449])).
% 86.23/86.42 tff(552,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(553,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(554,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2))),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[553, 552])).
% 86.23/86.42 tff(555,plain,
% 86.23/86.42 (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[554, 156, 522])).
% 86.23/86.42 tff(556,plain,
% 86.23/86.42 (node18(c_e_h_2, c_e, s1, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[555, 551])).
% 86.23/86.42 tff(557,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(558,plain,
% 86.23/86.42 (((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(559,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2))))),
% 86.23/86.42 inference(monotonicity,[status(thm)],[558])).
% 86.23/86.42 tff(560,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(transitivity,[status(thm)],[559, 557])).
% 86.23/86.42 tff(561,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(562,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2))),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[561, 560])).
% 86.23/86.42 tff(563,plain,
% 86.23/86.42 ($false),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[562, 124, 443, 373, 556])).
% 86.23/86.42 tff(564,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.42 tff(565,assumption,(node18(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 86.23/86.42 tff(566,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s2)), introduced(assumption)).
% 86.23/86.42 tff(567,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(568,plain,
% 86.23/86.42 (((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~node18(c_e_h_2, c_e, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(569,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~node18(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3))))),
% 86.23/86.42 inference(monotonicity,[status(thm)],[568])).
% 86.23/86.42 tff(570,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~node18(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.42 inference(transitivity,[status(thm)],[569, 567])).
% 86.23/86.42 tff(571,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(572,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node18(c_e_h_2, c_e, s2, s3))),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[571, 570])).
% 86.23/86.42 tff(573,plain,
% 86.23/86.42 ($false),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[572, 124, 372, 566, 565])).
% 86.23/86.42 tff(574,plain,((~node18(c_e_h_2, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.42 tff(575,plain,
% 86.23/86.42 (~node18(c_e_h_2, c_e, s2, s3)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[574, 372, 564])).
% 86.23/86.42 tff(576,plain,
% 86.23/86.42 (succ(s2, s3) <=> succ(s2, s3)),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(577,axiom,(succ(s2, s3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound3')).
% 86.23/86.42 tff(578,plain,
% 86.23/86.42 (succ(s2, s3)),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[577, 576])).
% 86.23/86.42 tff(579,plain,
% 86.23/86.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(580,plain,
% 86.23/86.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(581,plain,
% 86.23/86.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[580, 579])).
% 86.23/86.42 tff(582,plain,
% 86.23/86.42 (trans(s2, s3)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[581, 578, 64])).
% 86.23/86.42 tff(583,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_e, s2, s3))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(584,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_e, s2, s3))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(585,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_e, s2, s3)),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[584, 583])).
% 86.23/86.42 tff(586,plain,
% 86.23/86.42 (node19(c_e_h_2, c_e, s2, s3)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[585, 141, 582])).
% 86.23/86.42 tff(587,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(588,plain,
% 86.23/86.42 ((node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3))) <=> (node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(589,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.42 inference(monotonicity,[status(thm)],[588])).
% 86.23/86.42 tff(590,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3))),
% 86.23/86.42 inference(transitivity,[status(thm)],[589, 587])).
% 86.23/86.42 tff(591,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(592,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3)),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[591, 590])).
% 86.23/86.42 tff(593,plain,
% 86.23/86.42 (node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[592, 156, 586])).
% 86.23/86.42 tff(594,plain,
% 86.23/86.42 (node17(c_e_h_2, c_e, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[593, 575])).
% 86.23/86.42 tff(595,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s2)), introduced(assumption)).
% 86.23/86.42 tff(596,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(597,plain,
% 86.23/86.42 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(598,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))))),
% 86.23/86.42 inference(monotonicity,[status(thm)],[597])).
% 86.23/86.42 tff(599,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 86.23/86.42 inference(transitivity,[status(thm)],[598, 596])).
% 86.23/86.42 tff(600,plain,
% 86.23/86.42 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(601,plain,
% 86.23/86.42 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[600, 599])).
% 86.23/86.42 tff(602,plain,
% 86.23/86.42 ((~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[601, 209, 595])).
% 86.23/86.42 tff(603,plain,
% 86.23/86.42 (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[602, 594])).
% 86.23/86.42 tff(604,assumption,(node15(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 86.23/86.42 tff(605,plain,
% 86.23/86.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(606,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(607,plain,
% 86.23/86.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2)),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[606, 605])).
% 86.23/86.42 tff(608,plain,
% 86.23/86.42 ($false),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[607, 173, 372, 566, 604])).
% 86.23/86.42 tff(609,plain,((~node15(c_e_h_2, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.42 tff(610,plain,
% 86.23/86.42 (~node15(c_e_h_2, c_e, s2, s3)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[609, 372, 564])).
% 86.23/86.42 tff(611,assumption,(node17(c_e_h_2, c_e, s2)), introduced(assumption)).
% 86.23/86.42 tff(612,assumption,(node16(c_e_h_2, c_e, s2)), introduced(assumption)).
% 86.23/86.42 tff(613,plain,
% 86.23/86.42 (m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[601, 209, 611])).
% 86.23/86.42 tff(614,plain,
% 86.23/86.42 (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[613, 595])).
% 86.23/86.42 tff(615,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(616,plain,
% 86.23/86.42 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(617,plain,
% 86.23/86.42 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[616, 615])).
% 86.23/86.42 tff(618,plain,
% 86.23/86.42 (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[617, 228, 612])).
% 86.23/86.42 tff(619,plain,
% 86.23/86.42 ($false),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[618, 614, 595])).
% 86.23/86.42 tff(620,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node16(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 86.23/86.42 tff(621,plain,
% 86.23/86.42 (m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 86.23/86.42 inference(unit_resolution,[status(thm)],[620, 612, 611])).
% 86.23/86.42 tff(622,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(623,plain,
% 86.23/86.42 ((m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(rewrite,[status(thm)],[])).
% 86.23/86.42 tff(624,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 86.23/86.42 inference(monotonicity,[status(thm)],[623])).
% 86.23/86.42 tff(625,plain,
% 86.23/86.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 86.23/86.42 inference(transitivity,[status(thm)],[624, 622])).
% 86.23/86.42 tff(626,plain,
% 86.23/86.42 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))),
% 86.23/86.42 inference(quant_inst,[status(thm)],[])).
% 86.23/86.42 tff(627,plain,
% 86.23/86.42 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 86.23/86.42 inference(modus_ponens,[status(thm)],[626, 625])).
% 86.23/86.42 tff(628,plain,
% 86.23/86.42 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[627, 245, 611])).
% 86.23/86.43 tff(629,plain,
% 86.23/86.43 (m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[628, 621])).
% 86.23/86.43 tff(630,plain,
% 86.23/86.43 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(631,plain,
% 86.23/86.43 (((~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(632,plain,
% 86.23/86.43 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2))))),
% 86.23/86.43 inference(monotonicity,[status(thm)],[631])).
% 86.23/86.43 tff(633,plain,
% 86.23/86.43 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)))),
% 86.23/86.43 inference(transitivity,[status(thm)],[632, 630])).
% 86.23/86.43 tff(634,plain,
% 86.23/86.43 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(635,plain,
% 86.23/86.43 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2))),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[634, 633])).
% 86.23/86.43 tff(636,plain,
% 86.23/86.43 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[635, 263, 612])).
% 86.23/86.43 tff(637,plain,
% 86.23/86.43 ($false),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[636, 629, 621])).
% 86.23/86.43 tff(638,plain,((~node16(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 86.23/86.43 tff(639,plain,
% 86.23/86.43 (~node16(c_e_h_2, c_e, s2)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[638, 594])).
% 86.23/86.43 tff(640,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(641,plain,
% 86.23/86.43 ((node16(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3) | node15(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3))) <=> (node16(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(642,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3) | node15(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.43 inference(monotonicity,[status(thm)],[641])).
% 86.23/86.43 tff(643,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3) | node15(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3))),
% 86.23/86.43 inference(transitivity,[status(thm)],[642, 640])).
% 86.23/86.43 tff(644,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3) | node15(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(645,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3)),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[644, 643])).
% 86.23/86.43 tff(646,plain,
% 86.23/86.43 (node16(c_e_h_2, c_e, s2) | node15(c_e_h_2, c_e, s2, s3) | node14(c_e_h_2, c_e, s2, s3)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[645, 189, 586])).
% 86.23/86.43 tff(647,plain,
% 86.23/86.43 (node14(c_e_h_2, c_e, s2, s3)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[646, 639, 610])).
% 86.23/86.43 tff(648,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s2)), introduced(assumption)).
% 86.23/86.43 tff(649,assumption,(node14(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 86.23/86.43 tff(650,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(651,plain,
% 86.23/86.43 (((~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(652,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3))))),
% 86.23/86.43 inference(monotonicity,[status(thm)],[651])).
% 86.23/86.43 tff(653,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)))),
% 86.23/86.43 inference(transitivity,[status(thm)],[652, 650])).
% 86.23/86.43 tff(654,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(655,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3))),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[654, 653])).
% 86.23/86.43 tff(656,plain,
% 86.23/86.43 ($false),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[655, 283, 372, 649, 648])).
% 86.23/86.43 tff(657,plain,((~node14(c_e_h_2, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.43 tff(658,plain,
% 86.23/86.43 ($false),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[657, 647, 603, 372])).
% 86.23/86.43 tff(659,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.43 tff(660,plain,
% 86.23/86.43 (~m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[659, 371])).
% 86.23/86.43 tff(661,assumption,(node18(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 86.23/86.43 tff(662,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s3)), introduced(assumption)).
% 86.23/86.43 tff(663,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(664,plain,
% 86.23/86.43 (((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~node18(c_e_h_2, c_e, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(665,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~node18(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4))))),
% 86.23/86.43 inference(monotonicity,[status(thm)],[664])).
% 86.23/86.43 tff(666,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~node18(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(transitivity,[status(thm)],[665, 663])).
% 86.23/86.43 tff(667,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~node18(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(668,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[667, 666])).
% 86.23/86.43 tff(669,plain,
% 86.23/86.43 ($false),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[668, 124, 3, 662, 661])).
% 86.23/86.43 tff(670,plain,((~node18(c_e_h_2, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.43 tff(671,plain,
% 86.23/86.43 ((~node18(c_e_h_2, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[670, 660])).
% 86.23/86.43 tff(672,plain,
% 86.23/86.43 (~node18(c_e_h_2, c_e, s3, s4)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[671, 3])).
% 86.23/86.43 tff(673,plain,
% 86.23/86.43 (succ(s3, s4) <=> succ(s3, s4)),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(674,axiom,(succ(s3, s4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound4')).
% 86.23/86.43 tff(675,plain,
% 86.23/86.43 (succ(s3, s4)),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[674, 673])).
% 86.23/86.43 tff(676,plain,
% 86.23/86.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(677,plain,
% 86.23/86.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(678,plain,
% 86.23/86.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[677, 676])).
% 86.23/86.43 tff(679,plain,
% 86.23/86.43 (trans(s3, s4)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[678, 675, 64])).
% 86.23/86.43 tff(680,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(681,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(682,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_e, s3, s4)),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[681, 680])).
% 86.23/86.43 tff(683,plain,
% 86.23/86.43 (node19(c_e_h_2, c_e, s3, s4)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[682, 141, 679])).
% 86.23/86.43 tff(684,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(685,plain,
% 86.23/86.43 ((node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4))) <=> (node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(686,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(monotonicity,[status(thm)],[685])).
% 86.23/86.43 tff(687,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(transitivity,[status(thm)],[686, 684])).
% 86.23/86.43 tff(688,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(689,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s3) | (~node19(c_e_h_2, c_e, s3, s4)) | node18(c_e_h_2, c_e, s3, s4)),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[688, 687])).
% 86.23/86.43 tff(690,plain,
% 86.23/86.43 (node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[689, 156, 683])).
% 86.23/86.43 tff(691,plain,
% 86.23/86.43 (node17(c_e_h_2, c_e, s3)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[690, 672])).
% 86.23/86.43 tff(692,assumption,(node15(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 86.23/86.43 tff(693,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(694,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(695,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[694, 693])).
% 86.23/86.43 tff(696,plain,
% 86.23/86.43 ($false),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[695, 173, 3, 662, 692])).
% 86.23/86.43 tff(697,plain,((~node15(c_e_h_2, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.43 tff(698,plain,
% 86.23/86.43 ((~node15(c_e_h_2, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[697, 660])).
% 86.23/86.43 tff(699,plain,
% 86.23/86.43 (~node15(c_e_h_2, c_e, s3, s4)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[698, 3])).
% 86.23/86.43 tff(700,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s3)), introduced(assumption)).
% 86.23/86.43 tff(701,assumption,(node14(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 86.23/86.43 tff(702,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(703,plain,
% 86.23/86.43 (((~node14(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(704,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4))))),
% 86.23/86.43 inference(monotonicity,[status(thm)],[703])).
% 86.23/86.43 tff(705,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(transitivity,[status(thm)],[704, 702])).
% 86.23/86.43 tff(706,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)))),
% 86.23/86.43 inference(quant_inst,[status(thm)],[])).
% 86.23/86.43 tff(707,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(modus_ponens,[status(thm)],[706, 705])).
% 86.23/86.43 tff(708,plain,
% 86.23/86.43 ($false),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[707, 283, 3, 701, 700])).
% 86.23/86.43 tff(709,plain,((~node14(c_e_h_2, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 86.23/86.43 tff(710,plain,
% 86.23/86.43 (~node14(c_e_h_2, c_e, s3, s4)),
% 86.23/86.43 inference(unit_resolution,[status(thm)],[709, 3, 700])).
% 86.23/86.43 tff(711,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node15(c_e_h_2, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node15(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(712,plain,
% 86.23/86.43 ((node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4))) <=> (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node15(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(rewrite,[status(thm)],[])).
% 86.23/86.43 tff(713,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node15(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.43 inference(monotonicity,[status(thm)],[712])).
% 86.23/86.43 tff(714,plain,
% 86.23/86.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node15(c_e_h_2, c_e, s3, s4))),
% 86.23/86.43 inference(transitivity,[status(thm)],[713, 711])).
% 86.23/86.43 tff(715,plain,
% 86.23/86.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))),
% 86.23/86.44 inference(quant_inst,[status(thm)],[])).
% 86.23/86.44 tff(716,plain,
% 86.23/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node15(c_e_h_2, c_e, s3, s4)),
% 86.23/86.44 inference(modus_ponens,[status(thm)],[715, 714])).
% 86.23/86.44 tff(717,plain,
% 86.23/86.44 (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4)),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[716, 189, 683])).
% 86.23/86.44 tff(718,plain,
% 86.23/86.44 (node16(c_e_h_2, c_e, s3)),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[717, 710, 699])).
% 86.23/86.44 tff(719,assumption,(node17(c_e_h_2, c_e, s3)), introduced(assumption)).
% 86.23/86.44 tff(720,assumption,(node16(c_e_h_2, c_e, s3)), introduced(assumption)).
% 86.23/86.44 tff(721,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s3)), introduced(assumption)).
% 86.23/86.44 tff(722,plain,
% 86.23/86.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 86.23/86.44 inference(rewrite,[status(thm)],[])).
% 86.23/86.44 tff(723,plain,
% 86.23/86.44 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 86.23/86.44 inference(rewrite,[status(thm)],[])).
% 86.23/86.44 tff(724,plain,
% 86.23/86.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))))),
% 86.23/86.44 inference(monotonicity,[status(thm)],[723])).
% 86.23/86.44 tff(725,plain,
% 86.23/86.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 86.23/86.44 inference(transitivity,[status(thm)],[724, 722])).
% 86.23/86.44 tff(726,plain,
% 86.23/86.44 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)))),
% 86.23/86.44 inference(quant_inst,[status(thm)],[])).
% 86.23/86.44 tff(727,plain,
% 86.23/86.44 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 86.23/86.44 inference(modus_ponens,[status(thm)],[726, 725])).
% 86.23/86.44 tff(728,plain,
% 86.23/86.44 (m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[727, 209, 719])).
% 86.23/86.44 tff(729,plain,
% 86.23/86.44 (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[728, 721])).
% 86.23/86.44 tff(730,plain,
% 86.23/86.44 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3))),
% 86.23/86.44 inference(rewrite,[status(thm)],[])).
% 86.23/86.44 tff(731,plain,
% 86.23/86.44 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3))),
% 86.23/86.44 inference(quant_inst,[status(thm)],[])).
% 86.23/86.44 tff(732,plain,
% 86.23/86.44 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 86.23/86.44 inference(modus_ponens,[status(thm)],[731, 730])).
% 86.23/86.44 tff(733,plain,
% 86.23/86.44 (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[732, 228, 720])).
% 86.23/86.44 tff(734,plain,
% 86.23/86.44 ($false),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[733, 729, 721])).
% 86.23/86.44 tff(735,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node16(c_e_h_2, c_e, s3)) | (~node17(c_e_h_2, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 86.23/86.44 tff(736,plain,
% 86.23/86.44 (m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[735, 720, 719])).
% 86.23/86.44 tff(737,plain,
% 86.23/86.44 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~node17(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~node17(c_e_h_2, c_e, s3)))),
% 86.23/86.44 inference(rewrite,[status(thm)],[])).
% 86.23/86.44 tff(738,plain,
% 86.23/86.44 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~node17(c_e_h_2, c_e, s3)))),
% 86.23/86.44 inference(quant_inst,[status(thm)],[])).
% 86.23/86.44 tff(739,plain,
% 86.23/86.44 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~node17(c_e_h_2, c_e, s3))),
% 86.23/86.44 inference(modus_ponens,[status(thm)],[738, 737])).
% 86.23/86.44 tff(740,plain,
% 86.23/86.44 (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3))),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[739, 245, 719])).
% 86.23/86.44 tff(741,plain,
% 86.23/86.44 (m_c_h_element_v_in1(c_e_h_2, c_e, s3)),
% 86.23/86.44 inference(unit_resolution,[status(thm)],[740, 736])).
% 86.23/86.44 tff(742,plain,
% 86.23/86.44 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 86.23/86.44 inference(rewrite,[status(thm)],[])).
% 86.23/86.44 tff(743,plain,
% 86.23/86.44 (((~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3))) <=> ((~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 86.23/86.44 inference(rewrite,[status(thm)],[])).
% 86.23/86.44 tff(744,plain,
% 86.23/86.44 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))))),
% 86.25/86.44 inference(monotonicity,[status(thm)],[743])).
% 86.25/86.44 tff(745,plain,
% 86.25/86.44 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 86.25/86.44 inference(transitivity,[status(thm)],[744, 742])).
% 86.25/86.44 tff(746,plain,
% 86.25/86.44 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(747,plain,
% 86.25/86.44 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[746, 745])).
% 86.25/86.44 tff(748,plain,
% 86.25/86.44 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[747, 263, 720])).
% 86.25/86.44 tff(749,plain,
% 86.25/86.44 ($false),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[748, 741, 736])).
% 86.25/86.44 tff(750,plain,((~node16(c_e_h_2, c_e, s3)) | (~node17(c_e_h_2, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.44 tff(751,plain,
% 86.25/86.44 ($false),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[750, 718, 691])).
% 86.25/86.44 tff(752,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.44 tff(753,plain,
% 86.25/86.44 (m_c_h_element_v_in1(c_e_h_2, c_e, s3)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[752, 3])).
% 86.25/86.44 tff(754,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s3)), introduced(assumption)).
% 86.25/86.44 tff(755,assumption,(node22(c_e_h_2, c_i, s2, s3)), introduced(assumption)).
% 86.25/86.44 tff(756,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(757,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(758,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[757, 756])).
% 86.25/86.44 tff(759,plain,
% 86.25/86.44 ($false),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[758, 107, 754, 356, 755])).
% 86.25/86.44 tff(760,plain,((~node22(c_e_h_2, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.44 tff(761,plain,
% 86.25/86.44 (~node22(c_e_h_2, c_i, s2, s3)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[760, 754])).
% 86.25/86.44 tff(762,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(763,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(764,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[763, 762])).
% 86.25/86.44 tff(765,plain,
% 86.25/86.44 (node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[764, 81, 582])).
% 86.25/86.44 tff(766,plain,
% 86.25/86.44 (node21(c_e_h_2, c_i, s2, s3)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[765, 761])).
% 86.25/86.44 tff(767,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s2)), introduced(assumption)).
% 86.25/86.44 tff(768,assumption,(node18(c_e_h_2, c_h, s1, s2)), introduced(assumption)).
% 86.25/86.44 tff(769,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node18(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node18(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(770,plain,
% 86.25/86.44 (((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~node18(c_e_h_2, c_h, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node18(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(771,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~node18(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node18(c_e_h_2, c_h, s1, s2))))),
% 86.25/86.44 inference(monotonicity,[status(thm)],[770])).
% 86.25/86.44 tff(772,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~node18(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node18(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.44 inference(transitivity,[status(thm)],[771, 769])).
% 86.25/86.44 tff(773,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~node18(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(774,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node18(c_e_h_2, c_h, s1, s2))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[773, 772])).
% 86.25/86.44 tff(775,plain,
% 86.25/86.44 ($false),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[774, 124, 316, 767, 768])).
% 86.25/86.44 tff(776,plain,((~node18(c_e_h_2, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.44 tff(777,plain,
% 86.25/86.44 (~node18(c_e_h_2, c_h, s1, s2)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[776, 767])).
% 86.25/86.44 tff(778,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_h, s1, s2))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(779,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_h, s1, s2))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(780,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_h, s1, s2)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[779, 778])).
% 86.25/86.44 tff(781,plain,
% 86.25/86.44 (node19(c_e_h_2, c_h, s1, s2)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[780, 141, 344])).
% 86.25/86.44 tff(782,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(783,plain,
% 86.25/86.44 ((node17(c_e_h_2, c_h, s1) | node18(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2))) <=> (node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(784,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s1) | node18(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.44 inference(monotonicity,[status(thm)],[783])).
% 86.25/86.44 tff(785,plain,
% 86.25/86.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s1) | node18(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2))),
% 86.25/86.44 inference(transitivity,[status(thm)],[784, 782])).
% 86.25/86.44 tff(786,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s1) | node18(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(787,plain,
% 86.25/86.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node18(c_e_h_2, c_h, s1, s2)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[786, 785])).
% 86.25/86.44 tff(788,plain,
% 86.25/86.44 (node17(c_e_h_2, c_h, s1) | node18(c_e_h_2, c_h, s1, s2)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[787, 156, 781])).
% 86.25/86.44 tff(789,plain,
% 86.25/86.44 (node17(c_e_h_2, c_h, s1)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[788, 777])).
% 86.25/86.44 tff(790,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s1)), introduced(assumption)).
% 86.25/86.44 tff(791,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s0)), introduced(assumption)).
% 86.25/86.44 tff(792,plain,
% 86.25/86.44 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(793,plain,
% 86.25/86.44 ($false),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[792, 94, 791])).
% 86.25/86.44 tff(794,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.44 tff(795,plain,
% 86.25/86.44 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)) <=> ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)))),
% 86.25/86.44 inference(bind,[status(th)],[])).
% 86.25/86.44 tff(796,plain,
% 86.25/86.44 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 86.25/86.44 inference(quant_intro,[status(thm)],[795])).
% 86.25/86.44 tff(797,plain,
% 86.25/86.44 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(798,axiom,(![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_40')).
% 86.25/86.44 tff(799,plain,
% 86.25/86.44 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[798, 797])).
% 86.25/86.44 tff(800,plain,(
% 86.25/86.44 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 86.25/86.44 inference(skolemize,[status(sab)],[799])).
% 86.25/86.44 tff(801,plain,
% 86.25/86.44 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[800, 796])).
% 86.25/86.44 tff(802,plain,
% 86.25/86.44 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(803,plain,
% 86.25/86.44 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(804,plain,
% 86.25/86.44 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[803, 802])).
% 86.25/86.44 tff(805,plain,
% 86.25/86.44 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[804, 801, 794])).
% 86.25/86.44 tff(806,assumption,(node5(c_e_h_2, c_j, s0, s1)), introduced(assumption)).
% 86.25/86.44 tff(807,assumption,(~node3(c_e_h_1, c_e_h_2, s0)), introduced(assumption)).
% 86.25/86.44 tff(808,plain,
% 86.25/86.44 (^[I0: $i, X: $i, J0: $i] : refl(((~m_cell_v_left(I0, J0)) | node3(I0, J0, X)) <=> ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X)))),
% 86.25/86.44 inference(bind,[status(th)],[])).
% 86.25/86.44 tff(809,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 86.25/86.44 inference(quant_intro,[status(thm)],[808])).
% 86.25/86.44 tff(810,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(811,axiom,(![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_79')).
% 86.25/86.44 tff(812,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[811, 810])).
% 86.25/86.44 tff(813,plain,(
% 86.25/86.44 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 86.25/86.44 inference(skolemize,[status(sab)],[812])).
% 86.25/86.44 tff(814,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[813, 809])).
% 86.25/86.44 tff(815,plain,
% 86.25/86.44 (m_cell_v_left(c_e_h_1, c_e_h_2) <=> m_cell_v_left(c_e_h_1, c_e_h_2)),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(816,axiom,(m_cell_v_left(c_e_h_1, c_e_h_2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_1')).
% 86.25/86.44 tff(817,plain,
% 86.25/86.44 (m_cell_v_left(c_e_h_1, c_e_h_2)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[816, 815])).
% 86.25/86.44 tff(818,plain,
% 86.25/86.44 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s0))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(819,plain,
% 86.25/86.44 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s0))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(820,plain,
% 86.25/86.44 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s0)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[819, 818])).
% 86.25/86.44 tff(821,plain,
% 86.25/86.44 ($false),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[820, 817, 814, 807])).
% 86.25/86.44 tff(822,plain,(node3(c_e_h_1, c_e_h_2, s0)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.44 tff(823,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s0)), introduced(assumption)).
% 86.25/86.44 tff(824,plain,
% 86.25/86.44 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(825,plain,
% 86.25/86.44 ($false),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[824, 94, 823])).
% 86.25/86.44 tff(826,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.44 tff(827,plain,
% 86.25/86.44 (^[I0: $i, X: $i, J0: $i] : refl(((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) <=> ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)))),
% 86.25/86.44 inference(bind,[status(th)],[])).
% 86.25/86.44 tff(828,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 86.25/86.44 inference(quant_intro,[status(thm)],[827])).
% 86.25/86.44 tff(829,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(830,plain,
% 86.25/86.44 (^[I0: $i, X: $i, J0: $i] : rewrite((((~m_cell_v_ack(J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) | (~node3(I0, J0, X))) <=> ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)))),
% 86.25/86.44 inference(bind,[status(th)],[])).
% 86.25/86.44 tff(831,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : (((~m_cell_v_ack(J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) | (~node3(I0, J0, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 86.25/86.44 inference(quant_intro,[status(thm)],[830])).
% 86.25/86.44 tff(832,axiom,(![I0: $i, X: $i, J0: $i] : (((~m_cell_v_ack(J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) | (~node3(I0, J0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_78')).
% 86.25/86.44 tff(833,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[832, 831])).
% 86.25/86.44 tff(834,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[833, 829])).
% 86.25/86.44 tff(835,plain,(
% 86.25/86.44 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 86.25/86.44 inference(skolemize,[status(sab)],[834])).
% 86.25/86.44 tff(836,plain,
% 86.25/86.44 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[835, 828])).
% 86.25/86.44 tff(837,plain,
% 86.25/86.44 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(838,plain,
% 86.25/86.44 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(839,plain,
% 86.25/86.44 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[838, 837])).
% 86.25/86.44 tff(840,plain,
% 86.25/86.44 ((~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[839, 836])).
% 86.25/86.44 tff(841,plain,
% 86.25/86.44 (~m_cell_v_ack(c_e_h_2, s0)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[840, 826, 822])).
% 86.25/86.44 tff(842,plain,
% 86.25/86.44 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X)) <=> ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X)))),
% 86.25/86.44 inference(bind,[status(th)],[])).
% 86.25/86.44 tff(843,plain,
% 86.25/86.44 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 86.25/86.44 inference(quant_intro,[status(thm)],[842])).
% 86.25/86.44 tff(844,plain,
% 86.25/86.44 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(845,axiom,(![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_42')).
% 86.25/86.44 tff(846,plain,
% 86.25/86.44 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[845, 844])).
% 86.25/86.44 tff(847,plain,(
% 86.25/86.44 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 86.25/86.44 inference(skolemize,[status(sab)],[846])).
% 86.25/86.44 tff(848,plain,
% 86.25/86.44 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[847, 843])).
% 86.25/86.44 tff(849,plain,
% 86.25/86.44 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)) | m_cell_v_ack(c_e_h_2, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)) | m_cell_v_ack(c_e_h_2, s0))),
% 86.25/86.44 inference(rewrite,[status(thm)],[])).
% 86.25/86.44 tff(850,plain,
% 86.25/86.44 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)) | m_cell_v_ack(c_e_h_2, s0))),
% 86.25/86.44 inference(quant_inst,[status(thm)],[])).
% 86.25/86.44 tff(851,plain,
% 86.25/86.44 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)) | m_cell_v_ack(c_e_h_2, s0)),
% 86.25/86.44 inference(modus_ponens,[status(thm)],[850, 849])).
% 86.25/86.44 tff(852,plain,
% 86.25/86.44 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)),
% 86.25/86.44 inference(unit_resolution,[status(thm)],[851, 848, 841])).
% 86.25/86.44 tff(853,plain,
% 86.25/86.44 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y))) <=> (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y))))),
% 86.25/86.44 inference(bind,[status(th)],[])).
% 86.25/86.44 tff(854,plain,
% 86.25/86.44 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 86.25/86.44 inference(quant_intro,[status(thm)],[853])).
% 86.25/86.44 tff(855,plain,
% 86.25/86.44 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(856,plain,
% 86.25/86.45 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) <=> (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~m_or_h_gate_v_out(I0, I1, Y)))), (((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> ((m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~m_or_h_gate_v_out(I0, I1, Y))) | (~node5(I0, I1, X, Y))))), rewrite(((m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~m_or_h_gate_v_out(I0, I1, Y))) | (~node5(I0, I1, X, Y))) <=> (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))), (((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))))),
% 86.25/86.45 inference(bind,[status(th)],[])).
% 86.25/86.45 tff(857,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : ((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 86.25/86.45 inference(quant_intro,[status(thm)],[856])).
% 86.25/86.45 tff(858,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) | (~node5(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_or_h_gate_5')).
% 86.25/86.45 tff(859,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[858, 857])).
% 86.25/86.45 tff(860,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[859, 855])).
% 86.25/86.45 tff(861,plain,(
% 86.25/86.45 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 86.25/86.45 inference(skolemize,[status(sab)],[860])).
% 86.25/86.45 tff(862,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[861, 854])).
% 86.25/86.45 tff(863,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(864,plain,
% 86.25/86.45 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1))) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(865,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0)))),
% 86.25/86.45 inference(monotonicity,[status(thm)],[864])).
% 86.25/86.45 tff(866,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0))),
% 86.25/86.45 inference(transitivity,[status(thm)],[865, 863])).
% 86.25/86.45 tff(867,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(868,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0)),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[867, 866])).
% 86.25/86.45 tff(869,plain,
% 86.25/86.45 ($false),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[868, 862, 790, 852, 806, 805])).
% 86.25/86.45 tff(870,plain,((~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.45 tff(871,plain,
% 86.25/86.45 (~node5(c_e_h_2, c_j, s0, s1)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[870, 790])).
% 86.25/86.45 tff(872,plain,
% 86.25/86.45 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))) <=> (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))))),
% 86.25/86.45 inference(bind,[status(th)],[])).
% 86.25/86.45 tff(873,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 86.25/86.45 inference(quant_intro,[status(thm)],[872])).
% 86.25/86.45 tff(874,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(875,plain,
% 86.25/86.45 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node5(I0, I1, X, Y) | node6(I0, I1, X, Y)) | (~trans(X, Y))) <=> (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))))),
% 86.25/86.45 inference(bind,[status(th)],[])).
% 86.25/86.45 tff(876,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node5(I0, I1, X, Y) | node6(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 86.25/86.45 inference(quant_intro,[status(thm)],[875])).
% 86.25/86.45 tff(877,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node5(I0, I1, X, Y) | node6(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_or_h_gate_8')).
% 86.25/86.45 tff(878,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[877, 876])).
% 86.25/86.45 tff(879,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[878, 874])).
% 86.25/86.45 tff(880,plain,(
% 86.25/86.45 ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 86.25/86.45 inference(skolemize,[status(sab)],[879])).
% 86.25/86.45 tff(881,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[880, 873])).
% 86.25/86.45 tff(882,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(883,plain,
% 86.25/86.45 ((node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(884,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1)))),
% 86.25/86.45 inference(monotonicity,[status(thm)],[883])).
% 86.25/86.45 tff(885,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1))),
% 86.25/86.45 inference(transitivity,[status(thm)],[884, 882])).
% 86.25/86.45 tff(886,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1) | (~trans(s0, s1)))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(887,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1)),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[886, 885])).
% 86.25/86.45 tff(888,plain,
% 86.25/86.45 (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[887, 881, 71])).
% 86.25/86.45 tff(889,plain,
% 86.25/86.45 (node6(c_e_h_2, c_j, s0, s1)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[888, 871])).
% 86.25/86.45 tff(890,plain,
% 86.25/86.45 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) <=> ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)))),
% 86.25/86.45 inference(bind,[status(th)],[])).
% 86.25/86.45 tff(891,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 86.25/86.45 inference(quant_intro,[status(thm)],[890])).
% 86.25/86.45 tff(892,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(893,plain,
% 86.25/86.45 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) | (~node6(I0, I1, X, Y))) <=> ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)))),
% 86.25/86.45 inference(bind,[status(th)],[])).
% 86.25/86.45 tff(894,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) | (~node6(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 86.25/86.45 inference(quant_intro,[status(thm)],[893])).
% 86.25/86.45 tff(895,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) | (~node6(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_or_h_gate_7')).
% 86.25/86.45 tff(896,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[895, 894])).
% 86.25/86.45 tff(897,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[896, 892])).
% 86.25/86.45 tff(898,plain,(
% 86.25/86.45 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 86.25/86.45 inference(skolemize,[status(sab)],[897])).
% 86.25/86.45 tff(899,plain,
% 86.25/86.45 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[898, 891])).
% 86.25/86.45 tff(900,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~node6(c_e_h_2, c_j, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~node6(c_e_h_2, c_j, s0, s1)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(901,plain,
% 86.25/86.45 (((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0)) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~node6(c_e_h_2, c_j, s0, s1)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(902,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~node6(c_e_h_2, c_j, s0, s1))))),
% 86.25/86.45 inference(monotonicity,[status(thm)],[901])).
% 86.25/86.45 tff(903,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~node6(c_e_h_2, c_j, s0, s1)))),
% 86.25/86.45 inference(transitivity,[status(thm)],[902, 900])).
% 86.25/86.45 tff(904,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(905,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~node6(c_e_h_2, c_j, s0, s1))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[904, 903])).
% 86.25/86.45 tff(906,plain,
% 86.25/86.45 ($false),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[905, 899, 790, 302, 889])).
% 86.25/86.45 tff(907,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.45 tff(908,plain,
% 86.25/86.45 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(909,plain,
% 86.25/86.45 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(910,plain,
% 86.25/86.45 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1)),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[909, 908])).
% 86.25/86.45 tff(911,plain,
% 86.25/86.45 (~m_c_h_element_v_in2(c_e_h_2, c_h, s1)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[910, 309, 907])).
% 86.25/86.45 tff(912,plain,
% 86.25/86.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(913,plain,
% 86.25/86.45 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~node17(c_e_h_2, c_h, s1))) <=> ((~node17(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(914,plain,
% 86.25/86.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~node17(c_e_h_2, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1))))),
% 86.25/86.45 inference(monotonicity,[status(thm)],[913])).
% 86.25/86.45 tff(915,plain,
% 86.25/86.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~node17(c_e_h_2, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)))),
% 86.25/86.45 inference(transitivity,[status(thm)],[914, 912])).
% 86.25/86.45 tff(916,plain,
% 86.25/86.45 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~node17(c_e_h_2, c_h, s1)))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(917,plain,
% 86.25/86.45 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[916, 915])).
% 86.25/86.45 tff(918,plain,
% 86.25/86.45 ((~node17(c_e_h_2, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1))),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[917, 209, 911])).
% 86.25/86.45 tff(919,plain,
% 86.25/86.45 (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[918, 789])).
% 86.25/86.45 tff(920,plain,
% 86.25/86.45 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | m_c_h_element_v_in2(c_e_h_2, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | m_c_h_element_v_in2(c_e_h_2, c_h, s1))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(921,plain,
% 86.25/86.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | m_c_h_element_v_in2(c_e_h_2, c_h, s1))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(922,plain,
% 86.25/86.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | m_c_h_element_v_in2(c_e_h_2, c_h, s1)),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[921, 920])).
% 86.25/86.45 tff(923,plain,
% 86.25/86.45 ((~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[922, 228, 911])).
% 86.25/86.45 tff(924,plain,
% 86.25/86.45 (~node16(c_e_h_2, c_h, s1)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[923, 919])).
% 86.25/86.45 tff(925,assumption,(node15(c_e_h_2, c_h, s1, s2)), introduced(assumption)).
% 86.25/86.45 tff(926,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(927,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(928,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1)),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[927, 926])).
% 86.25/86.45 tff(929,plain,
% 86.25/86.45 ($false),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[928, 173, 316, 767, 925])).
% 86.25/86.45 tff(930,plain,((~node15(c_e_h_2, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.45 tff(931,plain,
% 86.25/86.45 (~node15(c_e_h_2, c_h, s1, s2)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[930, 767])).
% 86.25/86.45 tff(932,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | node15(c_e_h_2, c_h, s1, s2) | node14(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s1) | node15(c_e_h_2, c_h, s1, s2) | node14(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(933,plain,
% 86.25/86.45 ((node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2))) <=> (node16(c_e_h_2, c_h, s1) | node15(c_e_h_2, c_h, s1, s2) | node14(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(934,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | node15(c_e_h_2, c_h, s1, s2) | node14(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2))))),
% 86.25/86.45 inference(monotonicity,[status(thm)],[933])).
% 86.25/86.45 tff(935,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s1) | node15(c_e_h_2, c_h, s1, s2) | node14(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.45 inference(transitivity,[status(thm)],[934, 932])).
% 86.25/86.45 tff(936,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(937,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s1) | node15(c_e_h_2, c_h, s1, s2) | node14(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[936, 935])).
% 86.25/86.45 tff(938,plain,
% 86.25/86.45 (node16(c_e_h_2, c_h, s1) | node15(c_e_h_2, c_h, s1, s2) | node14(c_e_h_2, c_h, s1, s2)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[937, 189, 781])).
% 86.25/86.45 tff(939,plain,
% 86.25/86.45 (node14(c_e_h_2, c_h, s1, s2)),
% 86.25/86.45 inference(unit_resolution,[status(thm)],[938, 931, 924])).
% 86.25/86.45 tff(940,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node14(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node14(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(941,plain,
% 86.25/86.45 (((~node14(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node14(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.45 inference(rewrite,[status(thm)],[])).
% 86.25/86.45 tff(942,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node14(c_e_h_2, c_h, s1, s2))))),
% 86.25/86.45 inference(monotonicity,[status(thm)],[941])).
% 86.25/86.45 tff(943,plain,
% 86.25/86.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node14(c_e_h_2, c_h, s1, s2)))),
% 86.25/86.45 inference(transitivity,[status(thm)],[942, 940])).
% 86.25/86.45 tff(944,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)))),
% 86.25/86.45 inference(quant_inst,[status(thm)],[])).
% 86.25/86.45 tff(945,plain,
% 86.25/86.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node14(c_e_h_2, c_h, s1, s2))),
% 86.25/86.45 inference(modus_ponens,[status(thm)],[944, 943])).
% 86.25/86.46 tff(946,plain,
% 86.25/86.46 ($false),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[945, 283, 767, 919, 939])).
% 86.25/86.46 tff(947,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.46 tff(948,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(949,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(950,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[949, 948])).
% 86.25/86.46 tff(951,plain,
% 86.25/86.46 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[950, 23, 947])).
% 86.25/86.46 tff(952,plain,
% 86.25/86.46 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s2))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(953,plain,
% 86.25/86.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s2))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(954,plain,
% 86.25/86.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s2)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[953, 952])).
% 86.25/86.46 tff(955,plain,
% 86.25/86.46 (~node20(c_e_h_2, c_i, s2)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[954, 37, 951])).
% 86.25/86.46 tff(956,plain,
% 86.25/86.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node21(c_e_h_2, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node21(c_e_h_2, c_i, s2, s3)))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(957,plain,
% 86.25/86.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node21(c_e_h_2, c_i, s2, s3)))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(958,plain,
% 86.25/86.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node21(c_e_h_2, c_i, s2, s3))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[957, 956])).
% 86.25/86.46 tff(959,plain,
% 86.25/86.46 ($false),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[958, 51, 754, 955, 766])).
% 86.25/86.46 tff(960,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.46 tff(961,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(962,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(963,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[962, 961])).
% 86.25/86.46 tff(964,plain,
% 86.25/86.46 (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[963, 365, 960])).
% 86.25/86.46 tff(965,plain,
% 86.25/86.46 ((~node17(c_e_h_2, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[727, 209, 964])).
% 86.25/86.46 tff(966,plain,
% 86.25/86.46 ($false),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[965, 691, 753])).
% 86.25/86.46 tff(967,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.46 tff(968,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)), introduced(assumption)).
% 86.25/86.46 tff(969,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s4)), introduced(assumption)).
% 86.25/86.46 tff(970,plain,
% 86.25/86.46 (^[I0: $i, X: $i] : refl((m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)) <=> (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(971,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[970])).
% 86.25/86.46 tff(972,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(973,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_57')).
% 86.25/86.46 tff(974,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[973, 972])).
% 86.25/86.46 tff(975,plain,(
% 86.25/86.46 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 86.25/86.46 inference(skolemize,[status(sab)],[974])).
% 86.25/86.46 tff(976,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[975, 971])).
% 86.25/86.46 tff(977,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(978,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(979,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[978, 977])).
% 86.25/86.46 tff(980,plain,
% 86.25/86.46 ($false),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[979, 976, 969, 968])).
% 86.25/86.46 tff(981,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s4) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.46 tff(982,plain,
% 86.25/86.46 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[981, 967])).
% 86.25/86.46 tff(983,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)), introduced(assumption)).
% 86.25/86.46 tff(984,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(985,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(986,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[985, 984])).
% 86.25/86.46 tff(987,plain,
% 86.25/86.46 ($false),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[986, 976, 983, 662])).
% 86.25/86.46 tff(988,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.46 tff(989,plain,
% 86.25/86.46 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[988, 660])).
% 86.25/86.46 tff(990,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)), introduced(assumption)).
% 86.25/86.46 tff(991,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(992,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(993,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[992, 991])).
% 86.25/86.46 tff(994,plain,
% 86.25/86.46 ($false),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[993, 976, 990, 566])).
% 86.25/86.46 tff(995,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.46 tff(996,plain,
% 86.25/86.46 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[995, 564])).
% 86.25/86.46 tff(997,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(998,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(999,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[998, 997])).
% 86.25/86.46 tff(1000,plain,
% 86.25/86.46 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[999, 976, 443])).
% 86.25/86.46 tff(1001,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), introduced(assumption)).
% 86.25/86.46 tff(1002,assumption,(node10(c_e_h_2, c_m, s0, s1)), introduced(assumption)).
% 86.25/86.46 tff(1003,assumption,(m_cell_v_token(c_e_h_2, s0)), introduced(assumption)).
% 86.25/86.46 tff(1004,plain,
% 86.25/86.46 (^[X: $i] : refl((~m_cell_v_token(c_e_h_2, X)) <=> (~m_cell_v_token(c_e_h_2, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1005,plain,
% 86.25/86.46 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1004])).
% 86.25/86.46 tff(1006,plain,
% 86.25/86.46 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1007,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_2, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_6')).
% 86.25/86.46 tff(1008,plain,
% 86.25/86.46 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 86.25/86.46 tff(1009,plain,(
% 86.25/86.46 ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1008])).
% 86.25/86.46 tff(1010,plain,
% 86.25/86.46 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1009, 1005])).
% 86.25/86.46 tff(1011,plain,
% 86.25/86.46 ((~![X: $i] : (~m_cell_v_token(c_e_h_2, X))) | (~m_cell_v_token(c_e_h_2, s0))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1012,plain,
% 86.25/86.46 ($false),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1011, 1010, 1003])).
% 86.25/86.46 tff(1013,plain,(~m_cell_v_token(c_e_h_2, s0)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.46 tff(1014,plain,
% 86.25/86.46 (^[I0: $i, X: $i] : refl((m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) <=> (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1015,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1014])).
% 86.25/86.46 tff(1016,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1017,plain,
% 86.25/86.46 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_h_init_v_init_h_out(I0, c_n, X) | m_cell_v_token(I0, X)) <=> (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1018,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_init_h_out(I0, c_n, X) | m_cell_v_token(I0, X)) <=> ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1017])).
% 86.25/86.46 tff(1019,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_init_h_out(I0, c_n, X) | m_cell_v_token(I0, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_61')).
% 86.25/86.46 tff(1020,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 86.25/86.46 tff(1021,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1020, 1016])).
% 86.25/86.46 tff(1022,plain,(
% 86.25/86.46 ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1021])).
% 86.25/86.46 tff(1023,plain,
% 86.25/86.46 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1022, 1015])).
% 86.25/86.46 tff(1024,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))) <=> ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1025,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1026,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 86.25/86.46 tff(1027,plain,
% 86.25/86.46 (m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1026, 1023, 1013])).
% 86.25/86.46 tff(1028,plain,
% 86.25/86.46 (^[I0: $i, I1: $i] : refl(((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)) <=> ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1029,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1028])).
% 86.25/86.46 tff(1030,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1031,plain,
% 86.25/86.46 (^[I0: $i, I1: $i] : rewrite((m_and_h_gate_h_init_v_out(I0, I1, s0) | (~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) <=> ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1032,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, s0) | (~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1031])).
% 86.25/86.46 tff(1033,axiom,(![I0: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, s0) | (~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_h_init_1')).
% 86.25/86.46 tff(1034,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 86.25/86.46 tff(1035,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1034, 1030])).
% 86.25/86.46 tff(1036,plain,(
% 86.25/86.46 ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1035])).
% 86.25/86.46 tff(1037,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1036, 1029])).
% 86.25/86.46 tff(1038,plain,
% 86.25/86.46 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1039,plain,
% 86.25/86.46 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1040,plain,
% 86.25/86.46 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1039, 1038])).
% 86.25/86.46 tff(1041,plain,
% 86.25/86.46 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1040, 1037, 1027])).
% 86.25/86.46 tff(1042,plain,
% 86.25/86.46 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1043,plain,
% 86.25/86.46 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1042])).
% 86.25/86.46 tff(1044,plain,
% 86.25/86.46 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1045,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_54')).
% 86.25/86.46 tff(1046,plain,
% 86.25/86.46 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 86.25/86.46 tff(1047,plain,(
% 86.25/86.46 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1046])).
% 86.25/86.46 tff(1048,plain,
% 86.25/86.46 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1047, 1043])).
% 86.25/86.46 tff(1049,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1050,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1051,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 86.25/86.46 tff(1052,plain,
% 86.25/86.46 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1051, 1048, 1041])).
% 86.25/86.46 tff(1053,plain,
% 86.25/86.46 (^[I0: $i, X: $i, I1: $i] : refl(((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)) <=> ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1054,plain,
% 86.25/86.46 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1053])).
% 86.25/86.46 tff(1055,plain,
% 86.25/86.46 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1056,plain,
% 86.25/86.46 (^[I0: $i, X: $i, I1: $i] : rewrite((m_and_h_gate_h_init_v_in2(I0, I1, X) | (~node9(I0, I1, X))) <=> ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1057,plain,
% 86.25/86.46 (![I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_in2(I0, I1, X) | (~node9(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1056])).
% 86.25/86.46 tff(1058,axiom,(![I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_in2(I0, I1, X) | (~node9(I0, I1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_h_init_4')).
% 86.25/86.46 tff(1059,plain,
% 86.25/86.46 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 86.25/86.46 tff(1060,plain,
% 86.25/86.46 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1059, 1055])).
% 86.25/86.46 tff(1061,plain,(
% 86.25/86.46 ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1060])).
% 86.25/86.46 tff(1062,plain,
% 86.25/86.46 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1061, 1054])).
% 86.25/86.46 tff(1063,plain,
% 86.25/86.46 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1064,plain,
% 86.25/86.46 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1065,plain,
% 86.25/86.46 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 86.25/86.46 tff(1066,plain,
% 86.25/86.46 (~node9(c_e_h_2, c_m, s0)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1065, 1062, 1052])).
% 86.25/86.46 tff(1067,plain,
% 86.25/86.46 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))) <=> (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1068,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1067])).
% 86.25/86.46 tff(1069,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1070,plain,
% 86.25/86.46 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | node9(I0, I1, X)) | (~node10(I0, I1, X, Y))) <=> (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1071,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | node9(I0, I1, X)) | (~node10(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1070])).
% 86.25/86.46 tff(1072,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | node9(I0, I1, X)) | (~node10(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_h_init_6')).
% 86.25/86.46 tff(1073,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 86.25/86.46 tff(1074,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1073, 1069])).
% 86.25/86.46 tff(1075,plain,(
% 86.25/86.46 ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1074])).
% 86.25/86.46 tff(1076,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1075, 1068])).
% 86.25/86.46 tff(1077,plain,
% 86.25/86.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1078,plain,
% 86.25/86.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1079,plain,
% 86.25/86.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 86.25/86.46 tff(1080,plain,
% 86.25/86.46 ($false),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1079, 1076, 1066, 1001, 1002])).
% 86.25/86.46 tff(1081,plain,((~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.46 tff(1082,plain,
% 86.25/86.46 (~node10(c_e_h_2, c_m, s0, s1)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1081, 1001])).
% 86.25/86.46 tff(1083,plain,
% 86.25/86.46 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1084,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1083])).
% 86.25/86.46 tff(1085,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1086,plain,
% 86.25/86.46 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) | (~trans(X, Y))) <=> ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1087,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1086])).
% 86.25/86.46 tff(1088,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_h_init_9')).
% 86.25/86.46 tff(1089,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 86.25/86.46 tff(1090,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1089, 1085])).
% 86.25/86.46 tff(1091,plain,(
% 86.25/86.46 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1090])).
% 86.25/86.46 tff(1092,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1091, 1084])).
% 86.25/86.46 tff(1093,plain,
% 86.25/86.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1094,plain,
% 86.25/86.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1095,plain,
% 86.25/86.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 86.25/86.46 tff(1096,plain,
% 86.25/86.46 (node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1095, 1092, 71])).
% 86.25/86.46 tff(1097,plain,
% 86.25/86.46 (node11(c_e_h_2, c_m, s0, s1)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1096, 1082])).
% 86.25/86.46 tff(1098,plain,
% 86.25/86.46 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X)) <=> ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1099,plain,
% 86.25/86.46 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1098])).
% 86.25/86.46 tff(1100,plain,
% 86.25/86.46 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1101,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_56')).
% 86.25/86.46 tff(1102,plain,
% 86.25/86.46 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 86.25/86.46 tff(1103,plain,(
% 86.25/86.46 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1102])).
% 86.25/86.46 tff(1104,plain,
% 86.25/86.46 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1103, 1099])).
% 86.25/86.46 tff(1105,plain,
% 86.25/86.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1106,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1107,plain,
% 86.25/86.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 86.25/86.46 tff(1108,plain,
% 86.25/86.46 ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1107, 1104])).
% 86.25/86.46 tff(1109,plain,
% 86.25/86.46 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1108, 1013])).
% 86.25/86.46 tff(1110,plain,
% 86.25/86.46 (^[I0: $i, I1: $i] : refl(((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) <=> ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1111,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1110])).
% 86.25/86.46 tff(1112,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1113,axiom,(![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_h_init_2')).
% 86.25/86.46 tff(1114,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 86.25/86.46 tff(1115,plain,(
% 86.25/86.46 ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 86.25/86.46 inference(skolemize,[status(sab)],[1114])).
% 86.25/86.46 tff(1116,plain,
% 86.25/86.46 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1115, 1111])).
% 86.25/86.46 tff(1117,plain,
% 86.25/86.46 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1118,plain,
% 86.25/86.46 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0))),
% 86.25/86.46 inference(quant_inst,[status(thm)],[])).
% 86.25/86.46 tff(1119,plain,
% 86.25/86.46 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 86.25/86.46 tff(1120,plain,
% 86.25/86.46 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 86.25/86.46 inference(unit_resolution,[status(thm)],[1119, 1116, 1109])).
% 86.25/86.46 tff(1121,plain,
% 86.25/86.46 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) <=> ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1122,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1121])).
% 86.25/86.46 tff(1123,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 86.25/86.46 inference(rewrite,[status(thm)],[])).
% 86.25/86.46 tff(1124,plain,
% 86.25/86.46 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) | (~node11(I0, I1, X, Y))) <=> ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.46 inference(bind,[status(th)],[])).
% 86.25/86.46 tff(1125,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) | (~node11(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 86.25/86.46 inference(quant_intro,[status(thm)],[1124])).
% 86.25/86.46 tff(1126,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) | (~node11(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_h_init_8')).
% 86.25/86.46 tff(1127,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 86.25/86.46 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 86.25/86.46 tff(1128,plain,
% 86.25/86.46 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1127, 1123])).
% 86.25/86.47 tff(1129,plain,(
% 86.25/86.47 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 86.25/86.47 inference(skolemize,[status(sab)],[1128])).
% 86.25/86.47 tff(1130,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1129, 1122])).
% 86.25/86.47 tff(1131,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1132,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1133,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 86.25/86.47 tff(1134,plain,
% 86.25/86.47 ($false),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1133, 1130, 1120, 1001, 1097])).
% 86.25/86.47 tff(1135,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.47 tff(1136,plain,
% 86.25/86.47 (^[I0: $i, X: $i] : refl((m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 86.25/86.47 inference(bind,[status(th)],[])).
% 86.25/86.47 tff(1137,plain,
% 86.25/86.47 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.47 inference(quant_intro,[status(thm)],[1136])).
% 86.25/86.47 tff(1138,plain,
% 86.25/86.47 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1139,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_59')).
% 86.25/86.47 tff(1140,plain,
% 86.25/86.47 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 86.25/86.47 tff(1141,plain,(
% 86.25/86.47 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.47 inference(skolemize,[status(sab)],[1140])).
% 86.25/86.47 tff(1142,plain,
% 86.25/86.47 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1141, 1137])).
% 86.25/86.47 tff(1143,plain,
% 86.25/86.47 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1144,plain,
% 86.25/86.47 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1145,plain,
% 86.25/86.47 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 86.25/86.47 tff(1146,plain,
% 86.25/86.47 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1145, 1142, 1135])).
% 86.25/86.47 tff(1147,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)), introduced(assumption)).
% 86.25/86.47 tff(1148,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)), introduced(assumption)).
% 86.25/86.47 tff(1149,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), introduced(assumption)).
% 86.25/86.47 tff(1150,assumption,(node11(c_e_h_2, c_n, s1, s2)), introduced(assumption)).
% 86.25/86.47 tff(1151,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), introduced(assumption)).
% 86.25/86.47 tff(1152,plain,
% 86.25/86.47 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) <=> (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X))))),
% 86.25/86.47 inference(bind,[status(th)],[])).
% 86.25/86.47 tff(1153,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.47 inference(quant_intro,[status(thm)],[1152])).
% 86.25/86.47 tff(1154,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1155,plain,
% 86.25/86.47 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) <=> (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))), (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))) <=> ((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))))), rewrite(((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))) <=> (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))), (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))) <=> (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))))),
% 86.25/86.47 inference(bind,[status(th)],[])).
% 86.25/86.47 tff(1156,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.47 inference(quant_intro,[status(thm)],[1155])).
% 86.25/86.47 tff(1157,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_h_init_7')).
% 86.25/86.47 tff(1158,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 86.25/86.47 tff(1159,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1158, 1154])).
% 86.25/86.47 tff(1160,plain,(
% 86.25/86.47 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.47 inference(skolemize,[status(sab)],[1159])).
% 86.25/86.47 tff(1161,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1160, 1153])).
% 86.25/86.47 tff(1162,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1163,plain,
% 86.25/86.47 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1164,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1))))),
% 86.25/86.47 inference(monotonicity,[status(thm)],[1163])).
% 86.25/86.47 tff(1165,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)))),
% 86.25/86.47 inference(transitivity,[status(thm)],[1164, 1162])).
% 86.25/86.47 tff(1166,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1167,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 86.25/86.47 tff(1168,plain,
% 86.25/86.47 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1))),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1167, 1161, 1041])).
% 86.25/86.47 tff(1169,plain,
% 86.25/86.47 (~node11(c_e_h_2, c_n, s0, s1)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1168, 1151])).
% 86.25/86.47 tff(1170,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1171,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1172,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1)),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 86.25/86.47 tff(1173,plain,
% 86.25/86.47 (node10(c_e_h_2, c_n, s0, s1)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1172, 1092, 71, 1169])).
% 86.25/86.47 tff(1174,plain,
% 86.25/86.47 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1175,plain,
% 86.25/86.47 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1176,plain,
% 86.25/86.47 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0)),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 86.25/86.47 tff(1177,plain,
% 86.25/86.47 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1176, 976, 394])).
% 86.25/86.47 tff(1178,plain,
% 86.25/86.47 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1179,plain,
% 86.25/86.47 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1180,plain,
% 86.25/86.47 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 86.25/86.47 tff(1181,plain,
% 86.25/86.47 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1180, 1142, 1120])).
% 86.25/86.47 tff(1182,plain,
% 86.25/86.47 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) <=> ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)))),
% 86.25/86.47 inference(bind,[status(th)],[])).
% 86.25/86.47 tff(1183,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 86.25/86.47 inference(quant_intro,[status(thm)],[1182])).
% 86.25/86.47 tff(1184,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1185,plain,
% 86.25/86.47 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(trans(monotonicity(rewrite((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) <=> ((~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))), (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) <=> (((~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))))), rewrite((((~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) <=> ((~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))), (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) <=> ((~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)))), ((((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node10(I0, I1, X, Y))) <=> (((~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))))), rewrite((((~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))) <=> ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))), ((((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node10(I0, I1, X, Y))) <=> ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))))),
% 86.25/86.47 inference(bind,[status(th)],[])).
% 86.25/86.47 tff(1186,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node10(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 86.25/86.47 inference(quant_intro,[status(thm)],[1185])).
% 86.25/86.47 tff(1187,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node10(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_h_init_5')).
% 86.25/86.47 tff(1188,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 86.25/86.47 tff(1189,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1188, 1184])).
% 86.25/86.47 tff(1190,plain,(
% 86.25/86.47 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 86.25/86.47 inference(skolemize,[status(sab)],[1189])).
% 86.25/86.47 tff(1191,plain,
% 86.25/86.47 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1190, 1183])).
% 86.25/86.47 tff(1192,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1193,plain,
% 86.25/86.47 (((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1194,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1))))),
% 86.25/86.47 inference(monotonicity,[status(thm)],[1193])).
% 86.25/86.47 tff(1195,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)))),
% 86.25/86.47 inference(transitivity,[status(thm)],[1194, 1192])).
% 86.25/86.47 tff(1196,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1197,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 86.25/86.47 tff(1198,plain,
% 86.25/86.47 ($false),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1197, 1191, 1181, 1151, 1177, 1173])).
% 86.25/86.47 tff(1199,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.47 tff(1200,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1201,plain,
% 86.25/86.47 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1202,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2))))),
% 86.25/86.47 inference(monotonicity,[status(thm)],[1201])).
% 86.25/86.47 tff(1203,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2)))),
% 86.25/86.47 inference(transitivity,[status(thm)],[1202, 1200])).
% 86.25/86.47 tff(1204,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1205,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) | (~node11(c_e_h_2, c_n, s1, s2))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 86.25/86.47 tff(1206,plain,
% 86.25/86.47 ($false),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1205, 1161, 1199, 1149, 1150])).
% 86.25/86.47 tff(1207,plain,((~node11(c_e_h_2, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.47 tff(1208,plain,
% 86.25/86.47 (~node11(c_e_h_2, c_n, s1, s2)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1207, 1149])).
% 86.25/86.47 tff(1209,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1210,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1211,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2)),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 86.25/86.47 tff(1212,plain,
% 86.25/86.47 (node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1211, 1092, 344])).
% 86.25/86.47 tff(1213,plain,
% 86.25/86.47 (node10(c_e_h_2, c_n, s1, s2)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1212, 1208])).
% 86.25/86.47 tff(1214,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1215,plain,
% 86.25/86.47 (((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1216,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1))))),
% 86.25/86.47 inference(monotonicity,[status(thm)],[1215])).
% 86.25/86.47 tff(1217,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)))),
% 86.25/86.47 inference(transitivity,[status(thm)],[1216, 1214])).
% 86.25/86.47 tff(1218,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1219,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 86.25/86.47 tff(1220,plain,
% 86.25/86.47 ($false),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1219, 1191, 1149, 1213, 1148, 1147])).
% 86.25/86.47 tff(1221,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.47 tff(1222,plain,
% 86.25/86.47 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1))),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1221, 1146])).
% 86.25/86.47 tff(1223,plain,
% 86.25/86.47 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1222, 1000])).
% 86.25/86.47 tff(1224,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), introduced(assumption)).
% 86.25/86.47 tff(1225,assumption,(node10(c_e_h_2, c_m, s1, s2)), introduced(assumption)).
% 86.25/86.47 tff(1226,plain,
% 86.25/86.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1227,plain,
% 86.25/86.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1228,plain,
% 86.25/86.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 86.25/86.47 tff(1229,plain,
% 86.25/86.47 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1228, 1048, 1199])).
% 86.25/86.47 tff(1230,plain,
% 86.25/86.47 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1231,plain,
% 86.25/86.47 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1232,plain,
% 86.25/86.47 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 86.25/86.47 tff(1233,plain,
% 86.25/86.47 (~node9(c_e_h_2, c_m, s1)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1232, 1062, 1229])).
% 86.25/86.47 tff(1234,plain,
% 86.25/86.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))),
% 86.25/86.47 inference(rewrite,[status(thm)],[])).
% 86.25/86.47 tff(1235,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))),
% 86.25/86.47 inference(quant_inst,[status(thm)],[])).
% 86.25/86.47 tff(1236,plain,
% 86.25/86.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2))),
% 86.25/86.47 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 86.25/86.47 tff(1237,plain,
% 86.25/86.47 ($false),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1236, 1076, 1224, 1233, 1225])).
% 86.25/86.47 tff(1238,plain,((~node10(c_e_h_2, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.47 tff(1239,plain,
% 86.25/86.47 (~node10(c_e_h_2, c_m, s1, s2)),
% 86.25/86.47 inference(unit_resolution,[status(thm)],[1238, 1224])).
% 86.25/86.48 tff(1240,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1241,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1242,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 86.25/86.48 tff(1243,plain,
% 86.25/86.48 (node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1242, 1092, 344])).
% 86.25/86.48 tff(1244,plain,
% 86.25/86.48 (node11(c_e_h_2, c_m, s1, s2)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1243, 1239])).
% 86.25/86.48 tff(1245,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1246,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1247,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 86.25/86.48 tff(1248,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1247, 1130, 1135, 1224, 1244])).
% 86.25/86.48 tff(1249,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1250,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)), introduced(assumption)).
% 86.25/86.48 tff(1251,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), introduced(assumption)).
% 86.25/86.48 tff(1252,plain,
% 86.25/86.48 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1253,plain,
% 86.25/86.48 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1254,plain,
% 86.25/86.48 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 86.25/86.48 tff(1255,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1254, 1142, 1251, 1250])).
% 86.25/86.48 tff(1256,plain,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1257,plain,
% 86.25/86.48 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1256, 1249])).
% 86.25/86.48 tff(1258,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), introduced(assumption)).
% 86.25/86.48 tff(1259,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)), introduced(assumption)).
% 86.25/86.48 tff(1260,assumption,(node11(c_e_h_2, c_n, s2, s3)), introduced(assumption)).
% 86.25/86.48 tff(1261,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node11(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node11(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1262,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node11(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1263,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node11(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 86.25/86.48 tff(1264,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1263, 1161, 1259, 1258, 1260])).
% 86.25/86.48 tff(1265,plain,((~node11(c_e_h_2, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1266,plain,
% 86.25/86.48 (~node11(c_e_h_2, c_n, s2, s3)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1265, 1259, 1258])).
% 86.25/86.48 tff(1267,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)), introduced(assumption)).
% 86.25/86.48 tff(1268,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)), introduced(assumption)).
% 86.25/86.48 tff(1269,assumption,(node10(c_e_h_2, c_n, s2, s3)), introduced(assumption)).
% 86.25/86.48 tff(1270,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1271,plain,
% 86.25/86.48 (((~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1272,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3))))),
% 86.25/86.48 inference(monotonicity,[status(thm)],[1271])).
% 86.25/86.48 tff(1273,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3)))),
% 86.25/86.48 inference(transitivity,[status(thm)],[1272, 1270])).
% 86.25/86.48 tff(1274,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1275,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~node10(c_e_h_2, c_n, s2, s3))),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 86.25/86.48 tff(1276,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1275, 1191, 1259, 1267, 1268, 1269])).
% 86.25/86.48 tff(1277,plain,((~node10(c_e_h_2, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1278,plain,
% 86.25/86.48 (~node10(c_e_h_2, c_n, s2, s3)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1277, 1259, 1268, 1267])).
% 86.25/86.48 tff(1279,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1280,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1281,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 86.25/86.48 tff(1282,plain,
% 86.25/86.48 (node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1281, 1092, 582])).
% 86.25/86.48 tff(1283,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1282, 1278, 1266])).
% 86.25/86.48 tff(1284,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1285,plain,
% 86.25/86.48 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1284, 1257])).
% 86.25/86.48 tff(1286,plain,
% 86.25/86.48 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2))),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1285, 1223])).
% 86.25/86.48 tff(1287,plain,
% 86.25/86.48 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1286, 996])).
% 86.25/86.48 tff(1288,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), introduced(assumption)).
% 86.25/86.48 tff(1289,assumption,(node11(c_e_h_2, c_m, s2, s3)), introduced(assumption)).
% 86.25/86.48 tff(1290,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1291,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1292,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 86.25/86.48 tff(1293,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1292, 1130, 1288, 1249, 1289])).
% 86.25/86.48 tff(1294,plain,((~node11(c_e_h_2, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1295,plain,
% 86.25/86.48 (~node11(c_e_h_2, c_m, s2, s3)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1294, 1288])).
% 86.25/86.48 tff(1296,plain,
% 86.25/86.48 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1297,plain,
% 86.25/86.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1298,plain,
% 86.25/86.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 86.25/86.48 tff(1299,plain,
% 86.25/86.48 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1298, 1048, 1223])).
% 86.25/86.48 tff(1300,plain,
% 86.25/86.48 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1301,plain,
% 86.25/86.48 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1302,plain,
% 86.25/86.48 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1301, 1300])).
% 86.25/86.48 tff(1303,plain,
% 86.25/86.48 (~node9(c_e_h_2, c_m, s2)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1302, 1062, 1299])).
% 86.25/86.48 tff(1304,assumption,(~node9(c_e_h_2, c_m, s2)), introduced(assumption)).
% 86.25/86.48 tff(1305,assumption,(node10(c_e_h_2, c_m, s2, s3)), introduced(assumption)).
% 86.25/86.48 tff(1306,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1307,plain,
% 86.25/86.48 ((node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1308,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3))))),
% 86.25/86.48 inference(monotonicity,[status(thm)],[1307])).
% 86.25/86.48 tff(1309,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 86.25/86.48 inference(transitivity,[status(thm)],[1308, 1306])).
% 86.25/86.48 tff(1310,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1311,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3))),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 86.25/86.48 tff(1312,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1311, 1076, 1288, 1305, 1304])).
% 86.25/86.48 tff(1313,plain,((~node10(c_e_h_2, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1314,plain,
% 86.25/86.48 ((~node10(c_e_h_2, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1313, 1303])).
% 86.25/86.48 tff(1315,plain,
% 86.25/86.48 (~node10(c_e_h_2, c_m, s2, s3)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1314, 1288])).
% 86.25/86.48 tff(1316,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1317,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1318,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 86.25/86.48 tff(1319,plain,
% 86.25/86.48 (node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1318, 1092, 582])).
% 86.25/86.48 tff(1320,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1319, 1315, 1295])).
% 86.25/86.48 tff(1321,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1322,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), introduced(assumption)).
% 86.25/86.48 tff(1323,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)), introduced(assumption)).
% 86.25/86.48 tff(1324,plain,
% 86.25/86.48 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1325,plain,
% 86.25/86.48 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1326,plain,
% 86.25/86.48 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 86.25/86.48 tff(1327,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1326, 1142, 1323, 1322])).
% 86.25/86.48 tff(1328,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1329,plain,
% 86.25/86.48 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1328, 1321])).
% 86.25/86.48 tff(1330,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)), introduced(assumption)).
% 86.25/86.48 tff(1331,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)), introduced(assumption)).
% 86.25/86.48 tff(1332,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)), introduced(assumption)).
% 86.25/86.48 tff(1333,assumption,(node10(c_e_h_2, c_n, s3, s4)), introduced(assumption)).
% 86.25/86.48 tff(1334,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1335,plain,
% 86.25/86.48 (((~node10(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1336,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4))))),
% 86.25/86.48 inference(monotonicity,[status(thm)],[1335])).
% 86.25/86.48 tff(1337,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4)))),
% 86.25/86.48 inference(transitivity,[status(thm)],[1336, 1334])).
% 86.25/86.48 tff(1338,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1339,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4))),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 86.25/86.48 tff(1340,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1339, 1191, 1332, 1331, 1330, 1333])).
% 86.25/86.48 tff(1341,plain,((~node10(c_e_h_2, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1342,plain,
% 86.25/86.48 (~node10(c_e_h_2, c_n, s3, s4)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1341, 1332, 1331, 1330])).
% 86.25/86.48 tff(1343,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)), introduced(assumption)).
% 86.25/86.48 tff(1344,assumption,(node11(c_e_h_2, c_n, s3, s4)), introduced(assumption)).
% 86.25/86.48 tff(1345,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1346,plain,
% 86.25/86.48 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1347,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4))))),
% 86.25/86.48 inference(monotonicity,[status(thm)],[1346])).
% 86.25/86.48 tff(1348,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 86.25/86.48 inference(transitivity,[status(thm)],[1347, 1345])).
% 86.25/86.48 tff(1349,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1350,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~node11(c_e_h_2, c_n, s3, s4))),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 86.25/86.48 tff(1351,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1350, 1161, 1332, 1343, 1344])).
% 86.25/86.48 tff(1352,plain,((~node11(c_e_h_2, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1353,plain,
% 86.25/86.48 (~node11(c_e_h_2, c_n, s3, s4)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1352, 1332, 1343])).
% 86.25/86.48 tff(1354,plain,
% 86.25/86.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4))),
% 86.25/86.48 inference(rewrite,[status(thm)],[])).
% 86.25/86.48 tff(1355,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4))),
% 86.25/86.48 inference(quant_inst,[status(thm)],[])).
% 86.25/86.48 tff(1356,plain,
% 86.25/86.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4)),
% 86.25/86.48 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 86.25/86.48 tff(1357,plain,
% 86.25/86.48 (node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4)),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1356, 1092, 679])).
% 86.25/86.48 tff(1358,plain,
% 86.25/86.48 ($false),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1357, 1353, 1342])).
% 86.25/86.48 tff(1359,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.48 tff(1360,plain,
% 86.25/86.48 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3))),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1359, 1329])).
% 86.25/86.48 tff(1361,plain,
% 86.25/86.48 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3))),
% 86.25/86.48 inference(unit_resolution,[status(thm)],[1360, 1287])).
% 86.25/86.49 tff(1362,plain,
% 86.25/86.49 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1361, 989])).
% 86.25/86.49 tff(1363,plain,
% 86.25/86.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1364,plain,
% 86.25/86.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1365,plain,
% 86.25/86.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 86.25/86.49 tff(1366,plain,
% 86.25/86.49 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1365, 1048, 1287])).
% 86.25/86.49 tff(1367,plain,
% 86.25/86.49 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1368,plain,
% 86.25/86.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1369,plain,
% 86.25/86.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 86.25/86.49 tff(1370,plain,
% 86.25/86.49 (~node9(c_e_h_2, c_m, s3)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1369, 1062, 1366])).
% 86.25/86.49 tff(1371,assumption,(~node9(c_e_h_2, c_m, s3)), introduced(assumption)).
% 86.25/86.49 tff(1372,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)), introduced(assumption)).
% 86.25/86.49 tff(1373,assumption,(node10(c_e_h_2, c_m, s3, s4)), introduced(assumption)).
% 86.25/86.49 tff(1374,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1375,plain,
% 86.25/86.49 ((node9(c_e_h_2, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node10(c_e_h_2, c_m, s3, s4))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1376,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node10(c_e_h_2, c_m, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4))))),
% 86.25/86.49 inference(monotonicity,[status(thm)],[1375])).
% 86.25/86.49 tff(1377,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node10(c_e_h_2, c_m, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 86.25/86.49 inference(transitivity,[status(thm)],[1376, 1374])).
% 86.25/86.49 tff(1378,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1379,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3) | (~node10(c_e_h_2, c_m, s3, s4))),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 86.25/86.49 tff(1380,plain,
% 86.25/86.49 ($false),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1379, 1076, 1372, 1373, 1371])).
% 86.25/86.49 tff(1381,plain,((~node10(c_e_h_2, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.49 tff(1382,plain,
% 86.25/86.49 (~node10(c_e_h_2, c_m, s3, s4)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1381, 1372, 1371])).
% 86.25/86.49 tff(1383,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1384,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1385,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 86.25/86.49 tff(1386,plain,
% 86.25/86.49 (node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1385, 1092, 679])).
% 86.25/86.49 tff(1387,plain,
% 86.25/86.49 (node11(c_e_h_2, c_m, s3, s4)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1386, 1382])).
% 86.25/86.49 tff(1388,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1389,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1390,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 86.25/86.49 tff(1391,plain,
% 86.25/86.49 ($false),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1390, 1130, 1372, 1321, 1387])).
% 86.25/86.49 tff(1392,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.49 tff(1393,plain,
% 86.25/86.49 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1392, 1370])).
% 86.25/86.49 tff(1394,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)), introduced(assumption)).
% 86.25/86.49 tff(1395,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)), introduced(assumption)).
% 86.25/86.49 tff(1396,plain,
% 86.25/86.49 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1397,plain,
% 86.25/86.49 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1398,plain,
% 86.25/86.49 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 86.25/86.49 tff(1399,plain,
% 86.25/86.49 ($false),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1398, 1142, 1395, 1394])).
% 86.25/86.49 tff(1400,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.49 tff(1401,plain,
% 86.25/86.49 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1400, 1393])).
% 86.25/86.49 tff(1402,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)), introduced(assumption)).
% 86.25/86.49 tff(1403,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)), introduced(assumption)).
% 86.25/86.49 tff(1404,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1405,plain,
% 86.25/86.49 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1406,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 86.25/86.49 inference(monotonicity,[status(thm)],[1405])).
% 86.25/86.49 tff(1407,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 86.25/86.49 inference(transitivity,[status(thm)],[1406, 1404])).
% 86.25/86.49 tff(1408,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1409,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 86.25/86.49 tff(1410,plain,
% 86.25/86.49 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~node11(c_e_h_2, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1409, 1161])).
% 86.25/86.49 tff(1411,plain,
% 86.25/86.49 (~node11(c_e_h_2, c_n, s4, s5)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1410, 1403, 1402])).
% 86.25/86.49 tff(1412,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)), introduced(assumption)).
% 86.25/86.49 tff(1413,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)), introduced(assumption)).
% 86.25/86.49 tff(1414,assumption,(node10(c_e_h_2, c_n, s4, s5)), introduced(assumption)).
% 86.25/86.49 tff(1415,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1416,plain,
% 86.25/86.49 (((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1417,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5))))),
% 86.25/86.49 inference(monotonicity,[status(thm)],[1416])).
% 86.25/86.49 tff(1418,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 86.25/86.49 inference(transitivity,[status(thm)],[1417, 1415])).
% 86.25/86.49 tff(1419,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1420,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5))),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1419, 1418])).
% 86.25/86.49 tff(1421,plain,
% 86.25/86.49 ($false),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1420, 1191, 1403, 1412, 1413, 1414])).
% 86.25/86.49 tff(1422,plain,((~node10(c_e_h_2, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.49 tff(1423,plain,
% 86.25/86.49 (~node10(c_e_h_2, c_n, s4, s5)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1422, 1403, 1413, 1412])).
% 86.25/86.49 tff(1424,assumption,(~node10(c_e_h_2, c_n, s4, s5)), introduced(assumption)).
% 86.25/86.49 tff(1425,assumption,(~node11(c_e_h_2, c_n, s4, s5)), introduced(assumption)).
% 86.25/86.49 tff(1426,plain,
% 86.25/86.49 (succ(s4, s5) <=> succ(s4, s5)),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1427,axiom,(succ(s4, s5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound5')).
% 86.25/86.49 tff(1428,plain,
% 86.25/86.49 (succ(s4, s5)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 86.25/86.49 tff(1429,plain,
% 86.25/86.49 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1430,plain,
% 86.25/86.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1431,plain,
% 86.25/86.49 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 86.25/86.49 tff(1432,plain,
% 86.25/86.49 (trans(s4, s5)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1431, 1428, 64])).
% 86.25/86.49 tff(1433,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1434,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1435,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 86.25/86.49 tff(1436,plain,
% 86.25/86.49 ($false),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1435, 1092, 1432, 1425, 1424])).
% 86.25/86.49 tff(1437,plain,(node11(c_e_h_2, c_n, s4, s5) | node10(c_e_h_2, c_n, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.49 tff(1438,plain,
% 86.25/86.49 ($false),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1437, 1423, 1411])).
% 86.25/86.49 tff(1439,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.49 tff(1440,plain,
% 86.25/86.49 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1439, 1401])).
% 86.25/86.49 tff(1441,plain,
% 86.25/86.49 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4))),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1440, 1362])).
% 86.25/86.49 tff(1442,plain,
% 86.25/86.49 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1441, 982])).
% 86.25/86.49 tff(1443,plain,
% 86.25/86.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1444,plain,
% 86.25/86.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1445,plain,
% 86.25/86.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 86.25/86.49 tff(1446,plain,
% 86.25/86.49 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1445, 1048, 1442])).
% 86.25/86.49 tff(1447,plain,
% 86.25/86.49 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1448,plain,
% 86.25/86.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1449,plain,
% 86.25/86.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 86.25/86.49 tff(1450,plain,
% 86.25/86.49 (~node9(c_e_h_2, c_m, s5)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1449, 1062, 1446])).
% 86.25/86.49 tff(1451,plain,
% 86.25/86.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1452,plain,
% 86.25/86.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1453,plain,
% 86.25/86.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 86.25/86.49 tff(1454,plain,
% 86.25/86.49 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1453, 1048, 1362])).
% 86.25/86.49 tff(1455,plain,
% 86.25/86.49 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1456,plain,
% 86.25/86.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1457,plain,
% 86.25/86.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 86.25/86.49 tff(1458,plain,
% 86.25/86.49 (~node9(c_e_h_2, c_m, s4)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1457, 1062, 1454])).
% 86.25/86.49 tff(1459,assumption,(~node9(c_e_h_2, c_m, s4)), introduced(assumption)).
% 86.25/86.49 tff(1460,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), introduced(assumption)).
% 86.25/86.49 tff(1461,assumption,(node10(c_e_h_2, c_m, s4, s5)), introduced(assumption)).
% 86.25/86.49 tff(1462,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_2, c_m, s4, s5)) | node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_2, c_m, s4, s5)) | node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1463,plain,
% 86.25/86.49 ((node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node10(c_e_h_2, c_m, s4, s5))) <=> ((~node10(c_e_h_2, c_m, s4, s5)) | node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)))),
% 86.25/86.49 inference(rewrite,[status(thm)],[])).
% 86.25/86.49 tff(1464,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node10(c_e_h_2, c_m, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_2, c_m, s4, s5)) | node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))))),
% 86.25/86.49 inference(monotonicity,[status(thm)],[1463])).
% 86.25/86.49 tff(1465,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node10(c_e_h_2, c_m, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_2, c_m, s4, s5)) | node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)))),
% 86.25/86.49 inference(transitivity,[status(thm)],[1464, 1462])).
% 86.25/86.49 tff(1466,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node10(c_e_h_2, c_m, s4, s5)))),
% 86.25/86.49 inference(quant_inst,[status(thm)],[])).
% 86.25/86.49 tff(1467,plain,
% 86.25/86.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_2, c_m, s4, s5)) | node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 86.25/86.49 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 86.25/86.49 tff(1468,plain,
% 86.25/86.49 ($false),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1467, 1076, 1460, 1461, 1459])).
% 86.25/86.49 tff(1469,plain,((~node10(c_e_h_2, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.49 tff(1470,plain,
% 86.25/86.49 (~node10(c_e_h_2, c_m, s4, s5)),
% 86.25/86.49 inference(unit_resolution,[status(thm)],[1469, 1460, 1459])).
% 86.25/86.49 tff(1471,plain,
% 86.25/86.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1472,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1473,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 86.25/86.50 tff(1474,plain,
% 86.25/86.50 (node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1473, 1092, 1432])).
% 86.25/86.50 tff(1475,plain,
% 86.25/86.50 (node11(c_e_h_2, c_m, s4, s5)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1474, 1470])).
% 86.25/86.50 tff(1476,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1477,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1478,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 86.25/86.50 tff(1479,plain,
% 86.25/86.50 ($false),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1478, 1130, 1395, 1460, 1475])).
% 86.25/86.50 tff(1480,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4) | node9(c_e_h_2, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.50 tff(1481,plain,
% 86.25/86.50 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1480, 1393])).
% 86.25/86.50 tff(1482,plain,
% 86.25/86.50 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1481, 1458])).
% 86.25/86.50 tff(1483,assumption,(~node9(c_e_h_2, c_m, s5)), introduced(assumption)).
% 86.25/86.50 tff(1484,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), introduced(assumption)).
% 86.25/86.50 tff(1485,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), introduced(assumption)).
% 86.25/86.50 tff(1486,assumption,(node11(c_e_h_2, c_m, s5, s6)), introduced(assumption)).
% 86.25/86.50 tff(1487,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1488,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1489,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 86.25/86.50 tff(1490,plain,
% 86.25/86.50 ($false),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1489, 1130, 1485, 1484, 1486])).
% 86.25/86.50 tff(1491,plain,((~node11(c_e_h_2, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.50 tff(1492,plain,
% 86.25/86.50 (~node11(c_e_h_2, c_m, s5, s6)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1491, 1485, 1484])).
% 86.25/86.50 tff(1493,plain,
% 86.25/86.50 (succ(s5, s6) <=> succ(s5, s6)),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1494,axiom,(succ(s5, s6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound6')).
% 86.25/86.50 tff(1495,plain,
% 86.25/86.50 (succ(s5, s6)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 86.25/86.50 tff(1496,plain,
% 86.25/86.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1497,plain,
% 86.25/86.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1498,plain,
% 86.25/86.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 86.25/86.50 tff(1499,plain,
% 86.25/86.50 (trans(s5, s6)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1498, 1495, 64])).
% 86.25/86.50 tff(1500,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1501,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1502,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 86.25/86.50 tff(1503,plain,
% 86.25/86.50 (node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1502, 1092, 1499])).
% 86.25/86.50 tff(1504,plain,
% 86.25/86.50 (node10(c_e_h_2, c_m, s5, s6)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1503, 1492])).
% 86.25/86.50 tff(1505,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)) | node9(c_e_h_2, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)) | node9(c_e_h_2, c_m, s5))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1506,plain,
% 86.25/86.50 ((node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)) | node9(c_e_h_2, c_m, s5))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1507,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)) | node9(c_e_h_2, c_m, s5)))),
% 86.25/86.50 inference(monotonicity,[status(thm)],[1506])).
% 86.25/86.50 tff(1508,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)) | node9(c_e_h_2, c_m, s5))),
% 86.25/86.50 inference(transitivity,[status(thm)],[1507, 1505])).
% 86.25/86.50 tff(1509,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1510,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)) | node9(c_e_h_2, c_m, s5)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 86.25/86.50 tff(1511,plain,
% 86.25/86.50 ($false),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1510, 1076, 1485, 1504, 1483])).
% 86.25/86.50 tff(1512,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | node9(c_e_h_2, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.50 tff(1513,plain,
% 86.25/86.50 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | node9(c_e_h_2, c_m, s5)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1512, 1482])).
% 86.25/86.50 tff(1514,plain,
% 86.25/86.50 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1513, 1450])).
% 86.25/86.50 tff(1515,plain,
% 86.25/86.50 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 86.25/86.50 inference(bind,[status(th)],[])).
% 86.25/86.50 tff(1516,plain,
% 86.25/86.50 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.50 inference(quant_intro,[status(thm)],[1515])).
% 86.25/86.50 tff(1517,plain,
% 86.25/86.50 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1518,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_74')).
% 86.25/86.50 tff(1519,plain,
% 86.25/86.50 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 86.25/86.50 tff(1520,plain,(
% 86.25/86.50 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.50 inference(skolemize,[status(sab)],[1519])).
% 86.25/86.50 tff(1521,plain,
% 86.25/86.50 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1520, 1516])).
% 86.25/86.50 tff(1522,plain,
% 86.25/86.50 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1523,plain,
% 86.25/86.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1524,plain,
% 86.25/86.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 86.25/86.50 tff(1525,plain,
% 86.25/86.50 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s6)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1524, 1521, 1514])).
% 86.25/86.50 tff(1526,plain,
% 86.25/86.50 (^[I0: $i, X: $i, I1: $i] : refl(((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)) <=> ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)))),
% 86.25/86.50 inference(bind,[status(th)],[])).
% 86.25/86.50 tff(1527,plain,
% 86.25/86.50 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 86.25/86.50 inference(quant_intro,[status(thm)],[1526])).
% 86.25/86.50 tff(1528,plain,
% 86.25/86.50 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1529,plain,
% 86.25/86.50 (^[I0: $i, X: $i, I1: $i] : rewrite((m_and_h_gate_v_in2(I0, I1, X) | (~node20(I0, I1, X))) <=> ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)))),
% 86.25/86.50 inference(bind,[status(th)],[])).
% 86.25/86.50 tff(1530,plain,
% 86.25/86.50 (![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in2(I0, I1, X) | (~node20(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 86.25/86.50 inference(quant_intro,[status(thm)],[1529])).
% 86.25/86.50 tff(1531,axiom,(![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in2(I0, I1, X) | (~node20(I0, I1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_3')).
% 86.25/86.50 tff(1532,plain,
% 86.25/86.50 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 86.25/86.50 tff(1533,plain,
% 86.25/86.50 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1532, 1528])).
% 86.25/86.50 tff(1534,plain,(
% 86.25/86.50 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 86.25/86.50 inference(skolemize,[status(sab)],[1533])).
% 86.25/86.50 tff(1535,plain,
% 86.25/86.50 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1534, 1527])).
% 86.25/86.50 tff(1536,plain,
% 86.25/86.50 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s6))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1537,plain,
% 86.25/86.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s6))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1538,plain,
% 86.25/86.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s6)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 86.25/86.50 tff(1539,plain,
% 86.25/86.50 (~node20(c_e_h_2, c_r, s6)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1538, 1535, 1525])).
% 86.25/86.50 tff(1540,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node21(c_e_h_2, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node21(c_e_h_2, c_r, s6, s7)))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1541,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node21(c_e_h_2, c_r, s6, s7)))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1542,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node21(c_e_h_2, c_r, s6, s7))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 86.25/86.50 tff(1543,plain,
% 86.25/86.50 ($false),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1542, 51, 1539, 1, 2])).
% 86.25/86.50 tff(1544,plain,((~node21(c_e_h_2, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.50 tff(1545,plain,
% 86.25/86.50 (~node21(c_e_h_2, c_r, s6, s7)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1544, 1])).
% 86.25/86.50 tff(1546,plain,
% 86.25/86.50 (succ(s6, s7) <=> succ(s6, s7)),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1547,axiom,(succ(s6, s7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound7')).
% 86.25/86.50 tff(1548,plain,
% 86.25/86.50 (succ(s6, s7)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 86.25/86.50 tff(1549,plain,
% 86.25/86.50 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1550,plain,
% 86.25/86.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1551,plain,
% 86.25/86.50 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 86.25/86.50 tff(1552,plain,
% 86.25/86.50 (trans(s6, s7)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1551, 1548, 64])).
% 86.25/86.50 tff(1553,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1554,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1555,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 86.25/86.50 tff(1556,plain,
% 86.25/86.50 (node21(c_e_h_2, c_r, s6, s7) | node22(c_e_h_2, c_r, s6, s7)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1555, 81, 1552])).
% 86.25/86.50 tff(1557,plain,
% 86.25/86.50 (node22(c_e_h_2, c_r, s6, s7)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1556, 1545])).
% 86.25/86.50 tff(1558,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s6)), introduced(assumption)).
% 86.25/86.50 tff(1559,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s3)), introduced(assumption)).
% 86.25/86.50 tff(1560,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s2)), introduced(assumption)).
% 86.25/86.50 tff(1561,assumption,(node18(c_e_h_2, c_h, s2, s3)), introduced(assumption)).
% 86.25/86.50 tff(1562,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1563,plain,
% 86.25/86.50 (((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~node18(c_e_h_2, c_h, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1564,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~node18(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3))))),
% 86.25/86.50 inference(monotonicity,[status(thm)],[1563])).
% 86.25/86.50 tff(1565,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~node18(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(transitivity,[status(thm)],[1564, 1562])).
% 86.25/86.50 tff(1566,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~node18(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1567,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 86.25/86.50 tff(1568,plain,
% 86.25/86.50 ($false),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1567, 124, 1559, 947, 1561])).
% 86.25/86.50 tff(1569,plain,((~node18(c_e_h_2, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.50 tff(1570,plain,
% 86.25/86.50 (~node18(c_e_h_2, c_h, s2, s3)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1569, 1559])).
% 86.25/86.50 tff(1571,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_h, s2, s3))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1572,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_h, s2, s3))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1573,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_h, s2, s3)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 86.25/86.50 tff(1574,plain,
% 86.25/86.50 (node19(c_e_h_2, c_h, s2, s3)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1573, 141, 582])).
% 86.25/86.50 tff(1575,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1576,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1577,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 86.25/86.50 tff(1578,plain,
% 86.25/86.50 (node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1577, 156, 1574])).
% 86.25/86.50 tff(1579,plain,
% 86.25/86.50 (node17(c_e_h_2, c_h, s2)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1578, 1570])).
% 86.25/86.50 tff(1580,plain,
% 86.25/86.50 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1581,plain,
% 86.25/86.50 ((m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | (~node17(c_e_h_2, c_h, s2))) <=> ((~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1582,plain,
% 86.25/86.50 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | (~node17(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2))))),
% 86.25/86.50 inference(monotonicity,[status(thm)],[1581])).
% 86.25/86.50 tff(1583,plain,
% 86.25/86.50 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | (~node17(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)))),
% 86.25/86.50 inference(transitivity,[status(thm)],[1582, 1580])).
% 86.25/86.50 tff(1584,plain,
% 86.25/86.50 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | (~node17(c_e_h_2, c_h, s2)))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1585,plain,
% 86.25/86.50 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 86.25/86.50 tff(1586,plain,
% 86.25/86.50 (m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2))),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1585, 245, 1579])).
% 86.25/86.50 tff(1587,plain,
% 86.25/86.50 (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1586, 1560])).
% 86.25/86.50 tff(1588,assumption,(node15(c_e_h_2, c_h, s2, s3)), introduced(assumption)).
% 86.25/86.50 tff(1589,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1590,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1591,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2)),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 86.25/86.50 tff(1592,plain,
% 86.25/86.50 ($false),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1591, 173, 1559, 947, 1588])).
% 86.25/86.50 tff(1593,plain,((~node15(c_e_h_2, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.50 tff(1594,plain,
% 86.25/86.50 (~node15(c_e_h_2, c_h, s2, s3)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1593, 1559])).
% 86.25/86.50 tff(1595,assumption,(node14(c_e_h_2, c_h, s2, s3)), introduced(assumption)).
% 86.25/86.50 tff(1596,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1597,plain,
% 86.25/86.50 (((~node14(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(rewrite,[status(thm)],[])).
% 86.25/86.50 tff(1598,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3))))),
% 86.25/86.50 inference(monotonicity,[status(thm)],[1597])).
% 86.25/86.50 tff(1599,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.50 inference(transitivity,[status(thm)],[1598, 1596])).
% 86.25/86.50 tff(1600,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)))),
% 86.25/86.50 inference(quant_inst,[status(thm)],[])).
% 86.25/86.50 tff(1601,plain,
% 86.25/86.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3))),
% 86.25/86.50 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 86.25/86.50 tff(1602,plain,
% 86.25/86.50 ($false),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1601, 283, 1559, 1560, 1595])).
% 86.25/86.50 tff(1603,plain,((~node14(c_e_h_2, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.50 tff(1604,plain,
% 86.25/86.50 (~node14(c_e_h_2, c_h, s2, s3)),
% 86.25/86.50 inference(unit_resolution,[status(thm)],[1603, 1560, 1559])).
% 86.25/86.50 tff(1605,plain,
% 86.25/86.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1606,plain,
% 86.25/86.51 ((node16(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3) | node15(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3))) <=> (node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1607,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3) | node15(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3))))),
% 86.25/86.51 inference(monotonicity,[status(thm)],[1606])).
% 86.25/86.51 tff(1608,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3) | node15(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.51 inference(transitivity,[status(thm)],[1607, 1605])).
% 86.25/86.51 tff(1609,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3) | node15(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1610,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3))),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 86.25/86.51 tff(1611,plain,
% 86.25/86.51 (node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1610, 189, 1574])).
% 86.25/86.51 tff(1612,plain,
% 86.25/86.51 (node16(c_e_h_2, c_h, s2)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1611, 1604, 1594])).
% 86.25/86.51 tff(1613,plain,
% 86.25/86.51 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1614,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1615,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 86.25/86.51 tff(1616,plain,
% 86.25/86.51 ($false),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1615, 228, 1560, 1612, 1587])).
% 86.25/86.51 tff(1617,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.51 tff(1618,plain,
% 86.25/86.51 (m_c_h_element_v_in1(c_e_h_2, c_h, s2)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1617, 1559])).
% 86.25/86.51 tff(1619,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s1)), introduced(assumption)).
% 86.25/86.51 tff(1620,assumption,(node22(c_e_h_2, c_l, s0, s1)), introduced(assumption)).
% 86.25/86.51 tff(1621,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1622,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1623,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 86.25/86.51 tff(1624,plain,
% 86.25/86.51 ($false),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1623, 107, 1620, 794, 1619])).
% 86.25/86.51 tff(1625,plain,((~node22(c_e_h_2, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.51 tff(1626,plain,
% 86.25/86.51 (~node22(c_e_h_2, c_l, s0, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1625, 1619])).
% 86.25/86.51 tff(1627,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1628,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1629,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 86.25/86.51 tff(1630,plain,
% 86.25/86.51 (node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1629, 81, 71])).
% 86.25/86.51 tff(1631,plain,
% 86.25/86.51 (node21(c_e_h_2, c_l, s0, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1630, 1626])).
% 86.25/86.51 tff(1632,plain,
% 86.25/86.51 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 86.25/86.51 inference(bind,[status(th)],[])).
% 86.25/86.51 tff(1633,plain,
% 86.25/86.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.51 inference(quant_intro,[status(thm)],[1632])).
% 86.25/86.51 tff(1634,plain,
% 86.25/86.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1635,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_50')).
% 86.25/86.51 tff(1636,plain,
% 86.25/86.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 86.25/86.51 tff(1637,plain,(
% 86.25/86.51 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.51 inference(skolemize,[status(sab)],[1636])).
% 86.25/86.51 tff(1638,plain,
% 86.25/86.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1637, 1633])).
% 86.25/86.51 tff(1639,plain,
% 86.25/86.51 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1640,plain,
% 86.25/86.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1641,plain,
% 86.25/86.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1640, 1639])).
% 86.25/86.51 tff(1642,plain,
% 86.25/86.51 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1641, 1638, 1120])).
% 86.25/86.51 tff(1643,plain,
% 86.25/86.51 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s0))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1644,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s0))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1645,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s0)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 86.25/86.51 tff(1646,plain,
% 86.25/86.51 (~node20(c_e_h_2, c_l, s0)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1645, 1535, 1642])).
% 86.25/86.51 tff(1647,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1)))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1648,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1)))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1649,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1))),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1648, 1647])).
% 86.25/86.51 tff(1650,plain,
% 86.25/86.51 ($false),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1649, 51, 1646, 1631, 1619])).
% 86.25/86.51 tff(1651,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.51 tff(1652,plain,
% 86.25/86.51 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1653,plain,
% 86.25/86.51 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1654,plain,
% 86.25/86.51 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 86.25/86.51 tff(1655,plain,
% 86.25/86.51 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1654, 801, 1651])).
% 86.25/86.51 tff(1656,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s0)), introduced(assumption)).
% 86.25/86.51 tff(1657,plain,
% 86.25/86.51 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1658,plain,
% 86.25/86.51 ($false),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1657, 13, 1656])).
% 86.25/86.51 tff(1659,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.51 tff(1660,plain,
% 86.25/86.51 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X)) <=> ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X)))),
% 86.25/86.51 inference(bind,[status(th)],[])).
% 86.25/86.51 tff(1661,plain,
% 86.25/86.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 86.25/86.51 inference(quant_intro,[status(thm)],[1660])).
% 86.25/86.51 tff(1662,plain,
% 86.25/86.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1663,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_68')).
% 86.25/86.51 tff(1664,plain,
% 86.25/86.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 86.25/86.51 tff(1665,plain,(
% 86.25/86.51 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 86.25/86.51 inference(skolemize,[status(sab)],[1664])).
% 86.25/86.51 tff(1666,plain,
% 86.25/86.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1665, 1661])).
% 86.25/86.51 tff(1667,plain,
% 86.25/86.51 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1668,plain,
% 86.25/86.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1669,plain,
% 86.25/86.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)) | m_c_h_element_v_out(c_e_h_1, c_f, s0)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 86.25/86.51 tff(1670,plain,
% 86.25/86.51 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1669, 1666, 1659])).
% 86.25/86.51 tff(1671,plain,
% 86.25/86.51 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s0))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1672,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s0))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1673,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s0)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 86.25/86.51 tff(1674,plain,
% 86.25/86.51 (~node20(c_e_h_1, c_q, s0)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1673, 37, 1670])).
% 86.25/86.51 tff(1675,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s1)), introduced(assumption)).
% 86.25/86.51 tff(1676,assumption,(node22(c_e_h_1, c_q, s0, s1)), introduced(assumption)).
% 86.25/86.51 tff(1677,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1678,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1679,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 86.25/86.51 tff(1680,plain,
% 86.25/86.51 ($false),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1679, 107, 1676, 1675, 826])).
% 86.25/86.51 tff(1681,plain,((~node22(c_e_h_1, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.51 tff(1682,plain,
% 86.25/86.51 (~node22(c_e_h_1, c_q, s0, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1681, 1675])).
% 86.25/86.51 tff(1683,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1684,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1685,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 86.25/86.51 tff(1686,plain,
% 86.25/86.51 (node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1685, 81, 71])).
% 86.25/86.51 tff(1687,plain,
% 86.25/86.51 (node21(c_e_h_1, c_q, s0, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1686, 1682])).
% 86.25/86.51 tff(1688,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1)))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1689,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1)))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1690,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1))),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 86.25/86.51 tff(1691,plain,
% 86.25/86.51 ($false),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1690, 51, 1687, 1675, 1674])).
% 86.25/86.51 tff(1692,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.51 tff(1693,plain,
% 86.25/86.51 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s1))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1694,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s1))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1695,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s1)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 86.25/86.51 tff(1696,plain,
% 86.25/86.51 (node3(c_e_h_1, c_e_h_2, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1695, 817, 814])).
% 86.25/86.51 tff(1697,plain,
% 86.25/86.51 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s1)) | (~node3(c_e_h_1, c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s1)) | (~node3(c_e_h_1, c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1698,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s1)) | (~node3(c_e_h_1, c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1699,plain,
% 86.25/86.51 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s1)) | (~node3(c_e_h_1, c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 86.25/86.51 tff(1700,plain,
% 86.25/86.51 ((~m_cell_v_ack(c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1699, 836, 1696])).
% 86.25/86.51 tff(1701,plain,
% 86.25/86.51 (~m_cell_v_ack(c_e_h_2, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1700, 1692])).
% 86.25/86.51 tff(1702,plain,
% 86.25/86.51 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)) | m_cell_v_ack(c_e_h_2, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)) | m_cell_v_ack(c_e_h_2, s1))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1703,plain,
% 86.25/86.51 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)) | m_cell_v_ack(c_e_h_2, s1))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1704,plain,
% 86.25/86.51 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)) | m_cell_v_ack(c_e_h_2, s1)),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 86.25/86.51 tff(1705,plain,
% 86.25/86.51 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1704, 848, 1701])).
% 86.25/86.51 tff(1706,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)), introduced(assumption)).
% 86.25/86.51 tff(1707,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s2)), introduced(assumption)).
% 86.25/86.51 tff(1708,assumption,(node6(c_e_h_2, c_j, s1, s2)), introduced(assumption)).
% 86.25/86.51 tff(1709,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1710,plain,
% 86.25/86.51 (((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1711,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2))))),
% 86.25/86.51 inference(monotonicity,[status(thm)],[1710])).
% 86.25/86.51 tff(1712,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 86.25/86.51 inference(transitivity,[status(thm)],[1711, 1709])).
% 86.25/86.51 tff(1713,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))),
% 86.25/86.51 inference(quant_inst,[status(thm)],[])).
% 86.25/86.51 tff(1714,plain,
% 86.25/86.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2))),
% 86.25/86.51 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 86.25/86.51 tff(1715,plain,
% 86.25/86.51 ($false),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1714, 899, 907, 1707, 1708])).
% 86.25/86.51 tff(1716,plain,((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.51 tff(1717,plain,
% 86.25/86.51 (~node6(c_e_h_2, c_j, s1, s2)),
% 86.25/86.51 inference(unit_resolution,[status(thm)],[1716, 1707])).
% 86.25/86.51 tff(1718,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1719,plain,
% 86.25/86.51 ((node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2))),
% 86.25/86.51 inference(rewrite,[status(thm)],[])).
% 86.25/86.51 tff(1720,plain,
% 86.25/86.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2)))),
% 86.25/86.52 inference(monotonicity,[status(thm)],[1719])).
% 86.25/86.52 tff(1721,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2))),
% 86.25/86.52 inference(transitivity,[status(thm)],[1720, 1718])).
% 86.25/86.52 tff(1722,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2)))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1723,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2)),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 86.25/86.52 tff(1724,plain,
% 86.25/86.52 (node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1723, 881, 344])).
% 86.25/86.52 tff(1725,plain,
% 86.25/86.52 (node5(c_e_h_2, c_j, s1, s2)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1724, 1717])).
% 86.25/86.52 tff(1726,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)), introduced(assumption)).
% 86.25/86.52 tff(1727,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1728,plain,
% 86.25/86.52 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1729,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2))))),
% 86.25/86.52 inference(monotonicity,[status(thm)],[1728])).
% 86.25/86.52 tff(1730,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)))),
% 86.25/86.52 inference(transitivity,[status(thm)],[1729, 1727])).
% 86.25/86.52 tff(1731,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1732,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2))),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 86.25/86.52 tff(1733,plain,
% 86.25/86.52 ($false),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1732, 862, 1726, 1707, 1725, 1706])).
% 86.25/86.52 tff(1734,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.52 tff(1735,plain,
% 86.25/86.52 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1734, 1705])).
% 86.25/86.52 tff(1736,plain,
% 86.25/86.52 (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1735, 1655])).
% 86.25/86.52 tff(1737,plain,
% 86.25/86.52 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1738,plain,
% 86.25/86.52 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1739,plain,
% 86.25/86.52 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2)),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 86.25/86.52 tff(1740,plain,
% 86.25/86.52 (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1739, 309, 1736])).
% 86.25/86.52 tff(1741,plain,
% 86.25/86.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1742,plain,
% 86.25/86.52 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2))) <=> ((~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1743,plain,
% 86.25/86.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2))))),
% 86.25/86.52 inference(monotonicity,[status(thm)],[1742])).
% 86.25/86.52 tff(1744,plain,
% 86.25/86.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)))),
% 86.25/86.52 inference(transitivity,[status(thm)],[1743, 1741])).
% 86.25/86.52 tff(1745,plain,
% 86.25/86.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1746,plain,
% 86.25/86.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2))),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 86.25/86.52 tff(1747,plain,
% 86.25/86.52 ((~node17(c_e_h_2, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2))),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1746, 209, 1740])).
% 86.25/86.52 tff(1748,plain,
% 86.25/86.52 ($false),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1747, 1579, 1618])).
% 86.25/86.52 tff(1749,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.52 tff(1750,plain,
% 86.25/86.52 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1751,plain,
% 86.25/86.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1752,plain,
% 86.25/86.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3)),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 86.25/86.52 tff(1753,plain,
% 86.25/86.52 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1752, 23, 1749])).
% 86.25/86.52 tff(1754,plain,
% 86.25/86.52 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1755,plain,
% 86.25/86.52 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1756,plain,
% 86.25/86.52 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3)),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 86.25/86.52 tff(1757,plain,
% 86.25/86.52 (~node20(c_e_h_2, c_i, s3)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1756, 37, 1753])).
% 86.25/86.52 tff(1758,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s4)), introduced(assumption)).
% 86.25/86.52 tff(1759,assumption,(node22(c_e_h_2, c_i, s3, s4)), introduced(assumption)).
% 86.25/86.52 tff(1760,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1761,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1762,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 86.25/86.52 tff(1763,plain,
% 86.25/86.52 ($false),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1762, 107, 960, 1758, 1759])).
% 86.25/86.52 tff(1764,plain,((~node22(c_e_h_2, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4))), inference(lemma,lemma(discharge,[]))).
% 86.25/86.52 tff(1765,plain,
% 86.25/86.52 (~node22(c_e_h_2, c_i, s3, s4)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1764, 1758])).
% 86.25/86.52 tff(1766,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1767,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1768,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4)),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 86.25/86.52 tff(1769,plain,
% 86.25/86.52 (node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1768, 81, 679])).
% 86.25/86.52 tff(1770,plain,
% 86.25/86.52 (node21(c_e_h_2, c_i, s3, s4)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1769, 1765])).
% 86.25/86.52 tff(1771,assumption,(~node20(c_e_h_2, c_i, s3)), introduced(assumption)).
% 86.25/86.52 tff(1772,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1773,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1774,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4))),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 86.25/86.52 tff(1775,plain,
% 86.25/86.52 ($false),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1774, 51, 1758, 1771, 1770])).
% 86.25/86.52 tff(1776,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | node20(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.52 tff(1777,plain,
% 86.25/86.52 (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1776, 1757])).
% 86.25/86.52 tff(1778,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s4)), introduced(assumption)).
% 86.25/86.52 tff(1779,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s4)), introduced(assumption)).
% 86.25/86.52 tff(1780,plain,
% 86.25/86.52 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1781,plain,
% 86.25/86.52 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1782,plain,
% 86.25/86.52 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 86.25/86.52 tff(1783,plain,
% 86.25/86.52 ($false),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1782, 365, 1779, 1778])).
% 86.25/86.52 tff(1784,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 86.25/86.52 tff(1785,plain,
% 86.25/86.52 (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1784, 1777])).
% 86.25/86.52 tff(1786,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s5)), introduced(assumption)).
% 86.25/86.52 tff(1787,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1788,plain,
% 86.25/86.52 (((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))),
% 86.25/86.52 inference(rewrite,[status(thm)],[])).
% 86.25/86.52 tff(1789,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))))),
% 86.25/86.52 inference(monotonicity,[status(thm)],[1788])).
% 86.25/86.52 tff(1790,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))),
% 86.25/86.52 inference(transitivity,[status(thm)],[1789, 1787])).
% 86.25/86.52 tff(1791,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)))),
% 86.25/86.52 inference(quant_inst,[status(thm)],[])).
% 86.25/86.52 tff(1792,plain,
% 86.25/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.25/86.52 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 86.25/86.52 tff(1793,plain,
% 86.25/86.52 (m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1792, 124])).
% 86.25/86.52 tff(1794,plain,
% 86.25/86.52 (~node18(c_e_h_2, c_e, s4, s5)),
% 86.25/86.52 inference(unit_resolution,[status(thm)],[1793, 1786, 969])).
% 86.25/86.52 tff(1795,assumption,(~node19(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 86.25/86.52 tff(1796,plain,
% 86.25/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_e, s4, s5))),
% 86.34/86.52 inference(rewrite,[status(thm)],[])).
% 86.34/86.52 tff(1797,plain,
% 86.34/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_e, s4, s5))),
% 86.34/86.52 inference(quant_inst,[status(thm)],[])).
% 86.34/86.52 tff(1798,plain,
% 86.34/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_e, s4, s5)),
% 86.34/86.52 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 86.34/86.52 tff(1799,plain,
% 86.34/86.52 ($false),
% 86.34/86.52 inference(unit_resolution,[status(thm)],[1798, 141, 1432, 1795])).
% 86.34/86.52 tff(1800,plain,(node19(c_e_h_2, c_e, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.52 tff(1801,plain,
% 86.34/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4))),
% 86.34/86.52 inference(rewrite,[status(thm)],[])).
% 86.34/86.52 tff(1802,plain,
% 86.34/86.52 ((node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5))) <=> ((~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4))),
% 86.34/86.52 inference(rewrite,[status(thm)],[])).
% 86.34/86.52 tff(1803,plain,
% 86.34/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4)))),
% 86.34/86.52 inference(monotonicity,[status(thm)],[1802])).
% 86.34/86.52 tff(1804,plain,
% 86.34/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4))),
% 86.34/86.52 inference(transitivity,[status(thm)],[1803, 1801])).
% 86.34/86.52 tff(1805,plain,
% 86.34/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))),
% 86.34/86.52 inference(quant_inst,[status(thm)],[])).
% 86.34/86.52 tff(1806,plain,
% 86.34/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s4, s5)) | node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4)),
% 86.34/86.52 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 86.34/86.52 tff(1807,plain,
% 86.34/86.52 (node18(c_e_h_2, c_e, s4, s5) | node17(c_e_h_2, c_e, s4)),
% 86.34/86.52 inference(unit_resolution,[status(thm)],[1806, 156, 1800])).
% 86.34/86.52 tff(1808,plain,
% 86.34/86.52 (node17(c_e_h_2, c_e, s4)),
% 86.34/86.52 inference(unit_resolution,[status(thm)],[1807, 1794])).
% 86.34/86.52 tff(1809,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s4)), introduced(assumption)).
% 86.34/86.52 tff(1810,assumption,(node14(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 86.34/86.52 tff(1811,plain,
% 86.34/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))),
% 86.34/86.52 inference(rewrite,[status(thm)],[])).
% 86.34/86.52 tff(1812,plain,
% 86.34/86.52 (((~node14(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))),
% 86.34/86.52 inference(rewrite,[status(thm)],[])).
% 86.34/86.52 tff(1813,plain,
% 86.34/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))))),
% 86.34/86.52 inference(monotonicity,[status(thm)],[1812])).
% 86.34/86.52 tff(1814,plain,
% 86.34/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))),
% 86.34/86.52 inference(transitivity,[status(thm)],[1813, 1811])).
% 86.34/86.52 tff(1815,plain,
% 86.34/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))),
% 86.34/86.52 inference(quant_inst,[status(thm)],[])).
% 86.34/86.52 tff(1816,plain,
% 86.34/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~node14(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.34/86.52 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 86.34/86.52 tff(1817,plain,
% 86.34/86.52 ($false),
% 86.34/86.52 inference(unit_resolution,[status(thm)],[1816, 283, 1786, 1810, 1809])).
% 86.34/86.52 tff(1818,plain,((~node14(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.52 tff(1819,plain,
% 86.34/86.52 (~node14(c_e_h_2, c_e, s4, s5)),
% 86.34/86.52 inference(unit_resolution,[status(thm)],[1818, 1786, 1809])).
% 86.34/86.52 tff(1820,assumption,(node15(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 86.34/86.52 tff(1821,plain,
% 86.34/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 86.34/86.52 inference(rewrite,[status(thm)],[])).
% 86.34/86.52 tff(1822,plain,
% 86.34/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 86.34/86.52 inference(quant_inst,[status(thm)],[])).
% 86.34/86.52 tff(1823,plain,
% 86.34/86.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4)),
% 86.34/86.52 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 86.34/86.52 tff(1824,plain,
% 86.34/86.52 ($false),
% 86.34/86.52 inference(unit_resolution,[status(thm)],[1823, 173, 1786, 969, 1820])).
% 86.34/86.52 tff(1825,plain,((~node15(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.52 tff(1826,plain,
% 86.34/86.52 (~node15(c_e_h_2, c_e, s4, s5)),
% 86.34/86.52 inference(unit_resolution,[status(thm)],[1825, 1786, 969])).
% 86.34/86.52 tff(1827,plain,
% 86.34/86.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1828,plain,
% 86.34/86.53 ((node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5))) <=> (node14(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1829,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(monotonicity,[status(thm)],[1828])).
% 86.34/86.53 tff(1830,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(transitivity,[status(thm)],[1829, 1827])).
% 86.34/86.53 tff(1831,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1832,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)) | node15(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 86.34/86.53 tff(1833,plain,
% 86.34/86.53 (node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | node16(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1832, 189, 1800])).
% 86.34/86.53 tff(1834,plain,
% 86.34/86.53 (node16(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1833, 1826, 1819])).
% 86.34/86.53 tff(1835,assumption,(node16(c_e_h_2, c_e, s4)), introduced(assumption)).
% 86.34/86.53 tff(1836,assumption,(node17(c_e_h_2, c_e, s4)), introduced(assumption)).
% 86.34/86.53 tff(1837,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s4)), introduced(assumption)).
% 86.34/86.53 tff(1838,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1839,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1840,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 86.34/86.53 tff(1841,plain,
% 86.34/86.53 (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1840, 228, 1835])).
% 86.34/86.53 tff(1842,plain,
% 86.34/86.53 (m_c_h_element_v_in1(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1841, 1837])).
% 86.34/86.53 tff(1843,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1844,plain,
% 86.34/86.53 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1845,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4))))),
% 86.34/86.53 inference(monotonicity,[status(thm)],[1844])).
% 86.34/86.53 tff(1846,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(transitivity,[status(thm)],[1845, 1843])).
% 86.34/86.53 tff(1847,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1848,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 86.34/86.53 tff(1849,plain,
% 86.34/86.53 (m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1848, 209, 1836])).
% 86.34/86.53 tff(1850,plain,
% 86.34/86.53 ($false),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1849, 1842, 1837])).
% 86.34/86.53 tff(1851,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4)) | (~node16(c_e_h_2, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.53 tff(1852,plain,
% 86.34/86.53 (m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1851, 1836, 1835])).
% 86.34/86.53 tff(1853,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1854,plain,
% 86.34/86.53 (((~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1855,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4))))),
% 86.34/86.53 inference(monotonicity,[status(thm)],[1854])).
% 86.34/86.53 tff(1856,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(transitivity,[status(thm)],[1855, 1853])).
% 86.34/86.53 tff(1857,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1858,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node16(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 86.34/86.53 tff(1859,plain,
% 86.34/86.53 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1858, 263, 1835])).
% 86.34/86.53 tff(1860,plain,
% 86.34/86.53 (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1859, 1852])).
% 86.34/86.53 tff(1861,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1862,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4)))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1863,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 86.34/86.53 tff(1864,plain,
% 86.34/86.53 (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1863, 245, 1836])).
% 86.34/86.53 tff(1865,plain,
% 86.34/86.53 ($false),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1864, 1860, 1852])).
% 86.34/86.53 tff(1866,plain,((~node17(c_e_h_2, c_e, s4)) | (~node16(c_e_h_2, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.53 tff(1867,plain,
% 86.34/86.53 ($false),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1866, 1834, 1808])).
% 86.34/86.53 tff(1868,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | m_c_h_element_v_in1(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.53 tff(1869,plain,
% 86.34/86.53 ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1868, 967])).
% 86.34/86.53 tff(1870,plain,
% 86.34/86.53 (m_c_h_element_v_in1(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1869, 1786])).
% 86.34/86.53 tff(1871,plain,
% 86.34/86.53 ((~node18(c_e_h_2, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1793, 967])).
% 86.34/86.53 tff(1872,plain,
% 86.34/86.53 (~node18(c_e_h_2, c_e, s4, s5)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1871, 1786])).
% 86.34/86.53 tff(1873,plain,
% 86.34/86.53 (node17(c_e_h_2, c_e, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1807, 1872])).
% 86.34/86.53 tff(1874,plain,
% 86.34/86.53 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | (~node17(c_e_h_2, c_e, s4))),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1848, 209, 1837])).
% 86.34/86.53 tff(1875,plain,
% 86.34/86.53 ($false),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1874, 1873, 1870])).
% 86.34/86.53 tff(1876,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.53 tff(1877,plain,
% 86.34/86.53 (~m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1876, 1785])).
% 86.34/86.53 tff(1878,plain,
% 86.34/86.53 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)))),
% 86.34/86.53 inference(bind,[status(th)],[])).
% 86.34/86.53 tff(1879,plain,
% 86.34/86.53 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 86.34/86.53 inference(quant_intro,[status(thm)],[1878])).
% 86.34/86.53 tff(1880,plain,
% 86.34/86.53 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1881,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_72')).
% 86.34/86.53 tff(1882,plain,
% 86.34/86.53 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1881, 1880])).
% 86.34/86.53 tff(1883,plain,(
% 86.34/86.53 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 86.34/86.53 inference(skolemize,[status(sab)],[1882])).
% 86.34/86.53 tff(1884,plain,
% 86.34/86.53 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1883, 1879])).
% 86.34/86.53 tff(1885,plain,
% 86.34/86.53 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1886,plain,
% 86.34/86.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1887,plain,
% 86.34/86.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 86.34/86.53 tff(1888,plain,
% 86.34/86.53 (~m_and_h_gate_v_in1(c_e_h_2, c_r, s5)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1887, 1884, 1877])).
% 86.34/86.53 tff(1889,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s5))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1890,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s5))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1891,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s5)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 86.34/86.53 tff(1892,plain,
% 86.34/86.53 (~node20(c_e_h_2, c_r, s5)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1891, 37, 1888])).
% 86.34/86.53 tff(1893,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | node20(c_e_h_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | node20(c_e_h_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1894,plain,
% 86.34/86.53 ((node20(c_e_h_2, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, c_r, s5, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | node20(c_e_h_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1895,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | node20(c_e_h_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6))))),
% 86.34/86.53 inference(monotonicity,[status(thm)],[1894])).
% 86.34/86.53 tff(1896,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | node20(c_e_h_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6)))),
% 86.34/86.53 inference(transitivity,[status(thm)],[1895, 1893])).
% 86.34/86.53 tff(1897,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, c_r, s5, s6)))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1898,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | node20(c_e_h_2, c_r, s5) | (~node21(c_e_h_2, c_r, s5, s6))),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 86.34/86.53 tff(1899,plain,
% 86.34/86.53 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node21(c_e_h_2, c_r, s5, s6))),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1898, 51, 1892])).
% 86.34/86.53 tff(1900,plain,
% 86.34/86.53 (~node21(c_e_h_2, c_r, s5, s6)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1899, 1558])).
% 86.34/86.53 tff(1901,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_r, s5, s6) | node22(c_e_h_2, c_r, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_r, s5, s6) | node22(c_e_h_2, c_r, s5, s6))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1902,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_r, s5, s6) | node22(c_e_h_2, c_r, s5, s6))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1903,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_r, s5, s6) | node22(c_e_h_2, c_r, s5, s6)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 86.34/86.53 tff(1904,plain,
% 86.34/86.53 (node22(c_e_h_2, c_r, s5, s6)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1903, 81, 1499, 1900])).
% 86.34/86.53 tff(1905,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s5)), introduced(assumption)).
% 86.34/86.53 tff(1906,plain,
% 86.34/86.53 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1907,plain,
% 86.34/86.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1908,plain,
% 86.34/86.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 86.34/86.53 tff(1909,plain,
% 86.34/86.53 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1908, 1521, 1393])).
% 86.34/86.53 tff(1910,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s4))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1911,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s4))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1912,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s4)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 86.34/86.53 tff(1913,plain,
% 86.34/86.53 (~node20(c_e_h_2, c_r, s4)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1912, 1535, 1909])).
% 86.34/86.53 tff(1914,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, c_r, s4, s5)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1915,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, c_r, s4, s5)))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1916,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, c_r, s4, s5))),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 86.34/86.53 tff(1917,plain,
% 86.34/86.53 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node21(c_e_h_2, c_r, s4, s5))),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1916, 51, 1913])).
% 86.34/86.53 tff(1918,plain,
% 86.34/86.53 (~node21(c_e_h_2, c_r, s4, s5)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1917, 1905])).
% 86.34/86.53 tff(1919,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_r, s4, s5) | node22(c_e_h_2, c_r, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_r, s4, s5) | node22(c_e_h_2, c_r, s4, s5))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1920,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_r, s4, s5) | node22(c_e_h_2, c_r, s4, s5))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1921,plain,
% 86.34/86.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_r, s4, s5) | node22(c_e_h_2, c_r, s4, s5)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 86.34/86.53 tff(1922,plain,
% 86.34/86.53 (node22(c_e_h_2, c_r, s4, s5)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1921, 81, 1432, 1918])).
% 86.34/86.53 tff(1923,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s4)), introduced(assumption)).
% 86.34/86.53 tff(1924,plain,
% 86.34/86.53 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1925,plain,
% 86.34/86.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1926,plain,
% 86.34/86.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 86.34/86.53 tff(1927,plain,
% 86.34/86.53 ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1926, 1521])).
% 86.34/86.53 tff(1928,plain,
% 86.34/86.53 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s3)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1927, 1321])).
% 86.34/86.53 tff(1929,plain,
% 86.34/86.53 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1930,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3))),
% 86.34/86.53 inference(quant_inst,[status(thm)],[])).
% 86.34/86.53 tff(1931,plain,
% 86.34/86.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s3)),
% 86.34/86.53 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 86.34/86.53 tff(1932,plain,
% 86.34/86.53 (~node20(c_e_h_2, c_r, s3)),
% 86.34/86.53 inference(unit_resolution,[status(thm)],[1931, 1535, 1928])).
% 86.34/86.53 tff(1933,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1934,plain,
% 86.34/86.53 ((node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 86.34/86.53 inference(rewrite,[status(thm)],[])).
% 86.34/86.53 tff(1935,plain,
% 86.34/86.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4))))),
% 86.34/86.54 inference(monotonicity,[status(thm)],[1934])).
% 86.34/86.54 tff(1936,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 86.34/86.54 inference(transitivity,[status(thm)],[1935, 1933])).
% 86.34/86.54 tff(1937,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4)))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1938,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | node20(c_e_h_2, c_r, s3) | (~node21(c_e_h_2, c_r, s3, s4))),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 86.34/86.54 tff(1939,plain,
% 86.34/86.54 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node21(c_e_h_2, c_r, s3, s4))),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1938, 51, 1932])).
% 86.34/86.54 tff(1940,plain,
% 86.34/86.54 (~node21(c_e_h_2, c_r, s3, s4)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1939, 1923])).
% 86.34/86.54 tff(1941,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1942,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1943,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_r, s3, s4) | node22(c_e_h_2, c_r, s3, s4)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1942, 1941])).
% 86.34/86.54 tff(1944,plain,
% 86.34/86.54 (node22(c_e_h_2, c_r, s3, s4)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1943, 81, 679, 1940])).
% 86.34/86.54 tff(1945,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s3)), introduced(assumption)).
% 86.34/86.54 tff(1946,plain,
% 86.34/86.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1947,plain,
% 86.34/86.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1948,plain,
% 86.34/86.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 86.34/86.54 tff(1949,plain,
% 86.34/86.54 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s2)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1948, 1521, 1249])).
% 86.34/86.54 tff(1950,plain,
% 86.34/86.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s2))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1951,plain,
% 86.34/86.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s2))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1952,plain,
% 86.34/86.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s2)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 86.34/86.54 tff(1953,plain,
% 86.34/86.54 (~node20(c_e_h_2, c_r, s2)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1952, 1535, 1949])).
% 86.34/86.54 tff(1954,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | node20(c_e_h_2, c_r, s2) | (~node21(c_e_h_2, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | node20(c_e_h_2, c_r, s2) | (~node21(c_e_h_2, c_r, s2, s3)))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1955,plain,
% 86.34/86.54 ((node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | node20(c_e_h_2, c_r, s2) | (~node21(c_e_h_2, c_r, s2, s3)))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1956,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | node20(c_e_h_2, c_r, s2) | (~node21(c_e_h_2, c_r, s2, s3))))),
% 86.34/86.54 inference(monotonicity,[status(thm)],[1955])).
% 86.34/86.54 tff(1957,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | node20(c_e_h_2, c_r, s2) | (~node21(c_e_h_2, c_r, s2, s3)))),
% 86.34/86.54 inference(transitivity,[status(thm)],[1956, 1954])).
% 86.34/86.54 tff(1958,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3)))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1959,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | node20(c_e_h_2, c_r, s2) | (~node21(c_e_h_2, c_r, s2, s3))),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 86.34/86.54 tff(1960,plain,
% 86.34/86.54 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node21(c_e_h_2, c_r, s2, s3))),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1959, 51, 1953])).
% 86.34/86.54 tff(1961,plain,
% 86.34/86.54 (~node21(c_e_h_2, c_r, s2, s3)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1960, 1945])).
% 86.34/86.54 tff(1962,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1963,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1964,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_r, s2, s3) | node22(c_e_h_2, c_r, s2, s3)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 86.34/86.54 tff(1965,plain,
% 86.34/86.54 (node22(c_e_h_2, c_r, s2, s3)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1964, 81, 582, 1961])).
% 86.34/86.54 tff(1966,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s2)), introduced(assumption)).
% 86.34/86.54 tff(1967,plain,
% 86.34/86.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1968,plain,
% 86.34/86.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1969,plain,
% 86.34/86.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 86.34/86.54 tff(1970,plain,
% 86.34/86.54 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s1)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1969, 1521, 1135])).
% 86.34/86.54 tff(1971,plain,
% 86.34/86.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s1))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1972,plain,
% 86.34/86.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s1))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1973,plain,
% 86.34/86.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s1)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 86.34/86.54 tff(1974,plain,
% 86.34/86.54 (~node20(c_e_h_2, c_r, s1)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1973, 1535, 1970])).
% 86.34/86.54 tff(1975,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2)))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1976,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2)))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1977,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2))),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 86.34/86.54 tff(1978,plain,
% 86.34/86.54 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node21(c_e_h_2, c_r, s1, s2))),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1977, 51, 1974])).
% 86.34/86.54 tff(1979,plain,
% 86.34/86.54 (~node21(c_e_h_2, c_r, s1, s2)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1978, 1966])).
% 86.34/86.54 tff(1980,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1981,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1982,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_r, s1, s2) | node22(c_e_h_2, c_r, s1, s2)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 86.34/86.54 tff(1983,plain,
% 86.34/86.54 (node22(c_e_h_2, c_r, s1, s2)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1982, 81, 344, 1979])).
% 86.34/86.54 tff(1984,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s1)), introduced(assumption)).
% 86.34/86.54 tff(1985,assumption,(node21(c_e_h_2, c_r, s0, s1)), introduced(assumption)).
% 86.34/86.54 tff(1986,plain,
% 86.34/86.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1987,plain,
% 86.34/86.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1988,plain,
% 86.34/86.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 86.34/86.54 tff(1989,plain,
% 86.34/86.54 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s0)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1988, 1521, 1120])).
% 86.34/86.54 tff(1990,plain,
% 86.34/86.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s0))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1991,plain,
% 86.34/86.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s0))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1992,plain,
% 86.34/86.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s0)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 86.34/86.54 tff(1993,plain,
% 86.34/86.54 (~node20(c_e_h_2, c_r, s0)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1992, 1535, 1989])).
% 86.34/86.54 tff(1994,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1995,plain,
% 86.34/86.54 ((node20(c_e_h_2, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(1996,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1))))),
% 86.34/86.54 inference(monotonicity,[status(thm)],[1995])).
% 86.34/86.54 tff(1997,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 86.34/86.54 inference(transitivity,[status(thm)],[1996, 1994])).
% 86.34/86.54 tff(1998,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node21(c_e_h_2, c_r, s0, s1)))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(1999,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | node20(c_e_h_2, c_r, s0) | (~node21(c_e_h_2, c_r, s0, s1))),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 86.34/86.54 tff(2000,plain,
% 86.34/86.54 ($false),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[1999, 51, 1984, 1993, 1985])).
% 86.34/86.54 tff(2001,plain,((~node21(c_e_h_2, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.54 tff(2002,plain,
% 86.34/86.54 (~node21(c_e_h_2, c_r, s0, s1)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2001, 1984])).
% 86.34/86.54 tff(2003,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(2004,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(2005,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 86.34/86.54 tff(2006,plain,
% 86.34/86.54 (node21(c_e_h_2, c_r, s0, s1) | node22(c_e_h_2, c_r, s0, s1)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2005, 81, 71])).
% 86.34/86.54 tff(2007,plain,
% 86.34/86.54 (node22(c_e_h_2, c_r, s0, s1)),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2006, 2002])).
% 86.34/86.54 tff(2008,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s0)), introduced(assumption)).
% 86.34/86.54 tff(2009,plain,
% 86.34/86.54 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(2010,plain,
% 86.34/86.54 ($false),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2009, 94, 2008])).
% 86.34/86.54 tff(2011,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.54 tff(2012,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(2013,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(2014,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s1)) | (~node22(c_e_h_2, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 86.34/86.54 tff(2015,plain,
% 86.34/86.54 ($false),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2014, 107, 2011, 1984, 2007])).
% 86.34/86.54 tff(2016,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.54 tff(2017,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(2018,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(2019,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s2)) | (~node22(c_e_h_2, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s1)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 86.34/86.54 tff(2020,plain,
% 86.34/86.54 ($false),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2019, 107, 2016, 1966, 1983])).
% 86.34/86.54 tff(2021,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.54 tff(2022,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(2023,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(2024,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s3)) | (~node22(c_e_h_2, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 86.34/86.54 tff(2025,plain,
% 86.34/86.54 ($false),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2024, 107, 1945, 2021, 1965])).
% 86.34/86.54 tff(2026,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.54 tff(2027,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(2028,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(2029,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s4)) | (~node22(c_e_h_2, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 86.34/86.54 tff(2030,plain,
% 86.34/86.54 ($false),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2029, 107, 2026, 1923, 1944])).
% 86.34/86.54 tff(2031,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.54 tff(2032,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(2033,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(2034,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s5)) | (~node22(c_e_h_2, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[2033, 2032])).
% 86.34/86.54 tff(2035,plain,
% 86.34/86.54 ($false),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2034, 107, 1905, 2031, 1922])).
% 86.34/86.54 tff(2036,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.54 tff(2037,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 86.34/86.54 inference(rewrite,[status(thm)],[])).
% 86.34/86.54 tff(2038,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 86.34/86.54 inference(quant_inst,[status(thm)],[])).
% 86.34/86.54 tff(2039,plain,
% 86.34/86.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s6)) | (~node22(c_e_h_2, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5)),
% 86.34/86.54 inference(modus_ponens,[status(thm)],[2038, 2037])).
% 86.34/86.54 tff(2040,plain,
% 86.34/86.54 ($false),
% 86.34/86.54 inference(unit_resolution,[status(thm)],[2039, 107, 2036, 1558, 1904])).
% 86.34/86.54 tff(2041,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.54 tff(2042,plain,
% 86.34/86.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node22(c_e_h_2, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node22(c_e_h_2, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2043,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node22(c_e_h_2, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2044,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s7)) | (~node22(c_e_h_2, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 86.34/86.55 tff(2045,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2044, 107, 2041, 1, 1557])).
% 86.34/86.55 tff(2046,plain,(~m_and_h_gate_v_out(c_e_h_2, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2047,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s7)), introduced(assumption)).
% 86.34/86.55 tff(2048,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s8)), introduced(assumption)).
% 86.34/86.55 tff(2049,assumption,(node21(c_e_h_2, c_r, s7, s8)), introduced(assumption)).
% 86.34/86.55 tff(2050,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s5)), introduced(assumption)).
% 86.34/86.55 tff(2051,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)), introduced(assumption)).
% 86.34/86.55 tff(2052,plain,
% 86.34/86.55 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2053,plain,
% 86.34/86.55 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2054,plain,
% 86.34/86.55 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 86.34/86.55 tff(2055,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2054, 976, 2051, 2050])).
% 86.34/86.55 tff(2056,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s5) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2057,plain,
% 86.34/86.55 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2056, 1877])).
% 86.34/86.55 tff(2058,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)), introduced(assumption)).
% 86.34/86.55 tff(2059,plain,
% 86.34/86.55 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2060,plain,
% 86.34/86.55 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2061,plain,
% 86.34/86.55 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 86.34/86.55 tff(2062,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2061, 1142, 2058, 1484])).
% 86.34/86.55 tff(2063,plain,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2064,plain,
% 86.34/86.55 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2063, 1482])).
% 86.34/86.55 tff(2065,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)), introduced(assumption)).
% 86.34/86.55 tff(2066,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)), introduced(assumption)).
% 86.34/86.55 tff(2067,assumption,(node11(c_e_h_2, c_n, s5, s6)), introduced(assumption)).
% 86.34/86.55 tff(2068,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2069,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2070,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 86.34/86.55 tff(2071,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2070, 1161, 2065, 2066, 2067])).
% 86.34/86.55 tff(2072,plain,((~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2073,plain,
% 86.34/86.55 (~node11(c_e_h_2, c_n, s5, s6)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2072, 2066, 2065])).
% 86.34/86.55 tff(2074,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)), introduced(assumption)).
% 86.34/86.55 tff(2075,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)), introduced(assumption)).
% 86.34/86.55 tff(2076,assumption,(node10(c_e_h_2, c_n, s5, s6)), introduced(assumption)).
% 86.34/86.55 tff(2077,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~node10(c_e_h_2, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~node10(c_e_h_2, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2078,plain,
% 86.34/86.55 (((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~node10(c_e_h_2, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2079,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~node10(c_e_h_2, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))),
% 86.34/86.55 inference(monotonicity,[status(thm)],[2078])).
% 86.34/86.55 tff(2080,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~node10(c_e_h_2, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))),
% 86.34/86.55 inference(transitivity,[status(thm)],[2079, 2077])).
% 86.34/86.55 tff(2081,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2082,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~node10(c_e_h_2, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 86.34/86.55 tff(2083,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2082, 1191, 2075, 2074, 2066, 2076])).
% 86.34/86.55 tff(2084,plain,((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2085,plain,
% 86.34/86.55 (~node10(c_e_h_2, c_n, s5, s6)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2084, 2066, 2075, 2074])).
% 86.34/86.55 tff(2086,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2087,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2088,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 86.34/86.55 tff(2089,plain,
% 86.34/86.55 (node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2088, 1092, 1499])).
% 86.34/86.55 tff(2090,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2089, 2085, 2073])).
% 86.34/86.55 tff(2091,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2092,plain,
% 86.34/86.55 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2091, 2064])).
% 86.34/86.55 tff(2093,plain,
% 86.34/86.55 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5))),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2092, 1442])).
% 86.34/86.55 tff(2094,plain,
% 86.34/86.55 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2093, 2057])).
% 86.34/86.55 tff(2095,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)), introduced(assumption)).
% 86.34/86.55 tff(2096,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)), introduced(assumption)).
% 86.34/86.55 tff(2097,plain,
% 86.34/86.55 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2098,plain,
% 86.34/86.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2099,plain,
% 86.34/86.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 86.34/86.55 tff(2100,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2099, 1048, 2096, 2095])).
% 86.34/86.55 tff(2101,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2102,plain,
% 86.34/86.55 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2101, 2094])).
% 86.34/86.55 tff(2103,plain,
% 86.34/86.55 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2104,plain,
% 86.34/86.55 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2105,plain,
% 86.34/86.55 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 86.34/86.55 tff(2106,plain,
% 86.34/86.55 (~node9(c_e_h_2, c_m, s6)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2105, 1062, 2102])).
% 86.34/86.55 tff(2107,assumption,(~node9(c_e_h_2, c_m, s6)), introduced(assumption)).
% 86.34/86.55 tff(2108,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), introduced(assumption)).
% 86.34/86.55 tff(2109,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)), introduced(assumption)).
% 86.34/86.55 tff(2110,assumption,(node11(c_e_h_2, c_m, s6, s7)), introduced(assumption)).
% 86.34/86.55 tff(2111,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node11(c_e_h_2, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node11(c_e_h_2, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2112,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node11(c_e_h_2, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2113,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node11(c_e_h_2, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 86.34/86.55 tff(2114,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2113, 1130, 2109, 2108, 2110])).
% 86.34/86.55 tff(2115,plain,((~node11(c_e_h_2, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2116,plain,
% 86.34/86.55 (~node11(c_e_h_2, c_m, s6, s7)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2115, 2109, 2108])).
% 86.34/86.55 tff(2117,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2118,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2119,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 86.34/86.55 tff(2120,plain,
% 86.34/86.55 (node10(c_e_h_2, c_m, s6, s7) | node11(c_e_h_2, c_m, s6, s7)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2119, 1092, 1552])).
% 86.34/86.55 tff(2121,plain,
% 86.34/86.55 (node10(c_e_h_2, c_m, s6, s7)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2120, 2116])).
% 86.34/86.55 tff(2122,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6) | (~node10(c_e_h_2, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6) | (~node10(c_e_h_2, c_m, s6, s7)))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2123,plain,
% 86.34/86.55 ((node9(c_e_h_2, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6) | (~node10(c_e_h_2, c_m, s6, s7)))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2124,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6) | (~node10(c_e_h_2, c_m, s6, s7))))),
% 86.34/86.55 inference(monotonicity,[status(thm)],[2123])).
% 86.34/86.55 tff(2125,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6) | (~node10(c_e_h_2, c_m, s6, s7)))),
% 86.34/86.55 inference(transitivity,[status(thm)],[2124, 2122])).
% 86.34/86.55 tff(2126,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node10(c_e_h_2, c_m, s6, s7)))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2127,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6) | (~node10(c_e_h_2, c_m, s6, s7))),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 86.34/86.55 tff(2128,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2127, 1076, 2109, 2121, 2107])).
% 86.34/86.55 tff(2129,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2130,plain,
% 86.34/86.55 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | node9(c_e_h_2, c_m, s6)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2129, 1514])).
% 86.34/86.55 tff(2131,plain,
% 86.34/86.55 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2130, 2106])).
% 86.34/86.55 tff(2132,plain,
% 86.34/86.55 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2133,plain,
% 86.34/86.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2134,plain,
% 86.34/86.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 86.34/86.55 tff(2135,plain,
% 86.34/86.55 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s7)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2134, 1521, 2131])).
% 86.34/86.55 tff(2136,plain,
% 86.34/86.55 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s7))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2137,plain,
% 86.34/86.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s7))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2138,plain,
% 86.34/86.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s7)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 86.34/86.55 tff(2139,plain,
% 86.34/86.55 (~node20(c_e_h_2, c_r, s7)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2138, 1535, 2135])).
% 86.34/86.55 tff(2140,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node21(c_e_h_2, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node21(c_e_h_2, c_r, s7, s8)))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2141,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node21(c_e_h_2, c_r, s7, s8)))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2142,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node21(c_e_h_2, c_r, s7, s8))),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 86.34/86.55 tff(2143,plain,
% 86.34/86.55 ($false),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2142, 51, 2139, 2049, 2048])).
% 86.34/86.55 tff(2144,plain,((~node21(c_e_h_2, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.55 tff(2145,plain,
% 86.34/86.55 (~node21(c_e_h_2, c_r, s7, s8)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2144, 2048])).
% 86.34/86.55 tff(2146,plain,
% 86.34/86.55 (succ(s7, s8) <=> succ(s7, s8)),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2147,axiom,(succ(s7, s8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound8')).
% 86.34/86.55 tff(2148,plain,
% 86.34/86.55 (succ(s7, s8)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 86.34/86.55 tff(2149,plain,
% 86.34/86.55 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2150,plain,
% 86.34/86.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2151,plain,
% 86.34/86.55 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 86.34/86.55 tff(2152,plain,
% 86.34/86.55 (trans(s7, s8)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2151, 2148, 64])).
% 86.34/86.55 tff(2153,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2154,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2155,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8)),
% 86.34/86.55 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 86.34/86.55 tff(2156,plain,
% 86.34/86.55 (node21(c_e_h_2, c_r, s7, s8) | node22(c_e_h_2, c_r, s7, s8)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2155, 81, 2152])).
% 86.34/86.55 tff(2157,plain,
% 86.34/86.55 (node22(c_e_h_2, c_r, s7, s8)),
% 86.34/86.55 inference(unit_resolution,[status(thm)],[2156, 2145])).
% 86.34/86.55 tff(2158,plain,
% 86.34/86.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node22(c_e_h_2, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node22(c_e_h_2, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7))),
% 86.34/86.55 inference(rewrite,[status(thm)],[])).
% 86.34/86.55 tff(2159,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node22(c_e_h_2, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7))),
% 86.34/86.55 inference(quant_inst,[status(thm)],[])).
% 86.34/86.55 tff(2160,plain,
% 86.34/86.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | (~node22(c_e_h_2, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7)),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 86.34/86.56 tff(2161,plain,
% 86.34/86.56 ($false),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2160, 107, 2157, 2048, 2047])).
% 86.34/86.56 tff(2162,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s8)) | m_and_h_gate_v_out(c_e_h_2, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.56 tff(2163,plain,
% 86.34/86.56 (~m_and_h_gate_v_out(c_e_h_2, c_r, s8)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2162, 2046])).
% 86.34/86.56 tff(2164,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s5)), introduced(assumption)).
% 86.34/86.56 tff(2165,assumption,(node22(c_e_h_2, c_i, s4, s5)), introduced(assumption)).
% 86.34/86.56 tff(2166,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2167,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2168,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 86.34/86.56 tff(2169,plain,
% 86.34/86.56 ($false),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2168, 107, 2164, 1777, 2165])).
% 86.34/86.56 tff(2170,plain,((~node22(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.56 tff(2171,plain,
% 86.34/86.56 (~node22(c_e_h_2, c_i, s4, s5)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2170, 2164])).
% 86.34/86.56 tff(2172,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s4)), introduced(assumption)).
% 86.34/86.56 tff(2173,assumption,(node18(c_e_h_2, c_h, s3, s4)), introduced(assumption)).
% 86.34/86.56 tff(2174,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s3)), introduced(assumption)).
% 86.34/86.56 tff(2175,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2176,plain,
% 86.34/86.56 (((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~node18(c_e_h_2, c_h, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2177,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~node18(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4))))),
% 86.34/86.56 inference(monotonicity,[status(thm)],[2176])).
% 86.34/86.56 tff(2178,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~node18(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.56 inference(transitivity,[status(thm)],[2177, 2175])).
% 86.34/86.56 tff(2179,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~node18(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2180,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4))),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2179, 2178])).
% 86.34/86.56 tff(2181,plain,
% 86.34/86.56 ($false),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2180, 124, 2174, 2172, 2173])).
% 86.34/86.56 tff(2182,plain,((~node18(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.56 tff(2183,plain,
% 86.34/86.56 ((~node18(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2182, 1749])).
% 86.34/86.56 tff(2184,plain,
% 86.34/86.56 (~node18(c_e_h_2, c_h, s3, s4)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2183, 2172])).
% 86.34/86.56 tff(2185,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_h, s3, s4))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2186,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_h, s3, s4))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2187,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_h, s3, s4)),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2186, 2185])).
% 86.34/86.56 tff(2188,plain,
% 86.34/86.56 (node19(c_e_h_2, c_h, s3, s4)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2187, 141, 679])).
% 86.34/86.56 tff(2189,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s3, s4) | node17(c_e_h_2, c_h, s3) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s3, s4) | node17(c_e_h_2, c_h, s3) | (~node19(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2190,plain,
% 86.34/86.56 ((node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4))) <=> (node18(c_e_h_2, c_h, s3, s4) | node17(c_e_h_2, c_h, s3) | (~node19(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2191,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s3, s4) | node17(c_e_h_2, c_h, s3) | (~node19(c_e_h_2, c_h, s3, s4))))),
% 86.34/86.56 inference(monotonicity,[status(thm)],[2190])).
% 86.34/86.56 tff(2192,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s3, s4) | node17(c_e_h_2, c_h, s3) | (~node19(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.56 inference(transitivity,[status(thm)],[2191, 2189])).
% 86.34/86.56 tff(2193,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2194,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s3, s4) | node17(c_e_h_2, c_h, s3) | (~node19(c_e_h_2, c_h, s3, s4))),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 86.34/86.56 tff(2195,plain,
% 86.34/86.56 (node18(c_e_h_2, c_h, s3, s4) | node17(c_e_h_2, c_h, s3)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2194, 156, 2188])).
% 86.34/86.56 tff(2196,plain,
% 86.34/86.56 (node17(c_e_h_2, c_h, s3)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2195, 2184])).
% 86.34/86.56 tff(2197,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s2)), introduced(assumption)).
% 86.34/86.56 tff(2198,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s1)), introduced(assumption)).
% 86.34/86.56 tff(2199,assumption,(node14(c_e_h_1, c_f, s0, s1)), introduced(assumption)).
% 86.34/86.56 tff(2200,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2201,plain,
% 86.34/86.56 (((~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2202,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1))))),
% 86.34/86.56 inference(monotonicity,[status(thm)],[2201])).
% 86.34/86.56 tff(2203,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))),
% 86.34/86.56 inference(transitivity,[status(thm)],[2202, 2200])).
% 86.34/86.56 tff(2204,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2205,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~node14(c_e_h_1, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2204, 2203])).
% 86.34/86.56 tff(2206,plain,
% 86.34/86.56 (m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2205, 283, 2199])).
% 86.34/86.56 tff(2207,plain,
% 86.34/86.56 (m_c_h_element_v_in1(c_e_h_1, c_f, s0)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2206, 2198])).
% 86.34/86.56 tff(2208,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s0)), introduced(assumption)).
% 86.34/86.56 tff(2209,plain,
% 86.34/86.56 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2210,plain,
% 86.34/86.56 ($false),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2209, 94, 2208])).
% 86.34/86.56 tff(2211,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.56 tff(2212,plain,
% 86.34/86.56 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X)))),
% 86.34/86.56 inference(bind,[status(th)],[])).
% 86.34/86.56 tff(2213,plain,
% 86.34/86.56 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.34/86.56 inference(quant_intro,[status(thm)],[2212])).
% 86.34/86.56 tff(2214,plain,
% 86.34/86.56 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2215,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_26')).
% 86.34/86.56 tff(2216,plain,
% 86.34/86.56 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 86.34/86.56 tff(2217,plain,(
% 86.34/86.56 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.34/86.56 inference(skolemize,[status(sab)],[2216])).
% 86.34/86.56 tff(2218,plain,
% 86.34/86.56 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2217, 2213])).
% 86.34/86.56 tff(2219,plain,
% 86.34/86.56 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2220,plain,
% 86.34/86.56 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2221,plain,
% 86.34/86.56 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0)),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 86.34/86.56 tff(2222,plain,
% 86.34/86.56 (~m_c_h_element_v_in2(c_e_h_1, c_f, s0)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2221, 2218, 2211])).
% 86.34/86.56 tff(2223,plain,
% 86.34/86.56 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2224,plain,
% 86.34/86.56 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s0)) | m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2225,plain,
% 86.34/86.56 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s0)) | m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0))))),
% 86.34/86.56 inference(monotonicity,[status(thm)],[2224])).
% 86.34/86.56 tff(2226,plain,
% 86.34/86.56 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s0)) | m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)))),
% 86.34/86.56 inference(transitivity,[status(thm)],[2225, 2223])).
% 86.34/86.56 tff(2227,plain,
% 86.34/86.56 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s0)) | m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2228,plain,
% 86.34/86.56 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s0) | (~node17(c_e_h_1, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0))),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 86.34/86.56 tff(2229,plain,
% 86.34/86.56 ((~node17(c_e_h_1, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0))),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2228, 209, 2222])).
% 86.34/86.56 tff(2230,plain,
% 86.34/86.56 (~node17(c_e_h_1, c_f, s0)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2229, 2207])).
% 86.34/86.56 tff(2231,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_f, s0, s1))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2232,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_f, s0, s1))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2233,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 86.34/86.56 tff(2234,plain,
% 86.34/86.56 (node19(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2233, 141, 71])).
% 86.34/86.56 tff(2235,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s0) | node18(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s0) | node18(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2236,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s0) | node18(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2237,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s0) | node18(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1))),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 86.34/86.56 tff(2238,plain,
% 86.34/86.56 (node17(c_e_h_1, c_f, s0) | node18(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2237, 156, 2234])).
% 86.34/86.56 tff(2239,plain,
% 86.34/86.56 (node18(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2238, 2230])).
% 86.34/86.56 tff(2240,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node18(c_e_h_1, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node18(c_e_h_1, c_f, s0, s1)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2241,plain,
% 86.34/86.56 (((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~node18(c_e_h_1, c_f, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node18(c_e_h_1, c_f, s0, s1)))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2242,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~node18(c_e_h_1, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node18(c_e_h_1, c_f, s0, s1))))),
% 86.34/86.56 inference(monotonicity,[status(thm)],[2241])).
% 86.34/86.56 tff(2243,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~node18(c_e_h_1, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node18(c_e_h_1, c_f, s0, s1)))),
% 86.34/86.56 inference(transitivity,[status(thm)],[2242, 2240])).
% 86.34/86.56 tff(2244,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~node18(c_e_h_1, c_f, s0, s1)))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2245,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node18(c_e_h_1, c_f, s0, s1))),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 86.34/86.56 tff(2246,plain,
% 86.34/86.56 ($false),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2245, 124, 1659, 2239, 2198])).
% 86.34/86.56 tff(2247,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node14(c_e_h_1, c_f, s0, s1))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.56 tff(2248,plain,
% 86.34/86.56 (~node14(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2247, 2198])).
% 86.34/86.56 tff(2249,assumption,(node18(c_e_h_1, c_f, s0, s1)), introduced(assumption)).
% 86.34/86.56 tff(2250,plain,
% 86.34/86.56 ($false),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2245, 124, 1659, 2249, 2198])).
% 86.34/86.56 tff(2251,plain,((~node18(c_e_h_1, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.56 tff(2252,plain,
% 86.34/86.56 (~node18(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2251, 2198])).
% 86.34/86.56 tff(2253,plain,
% 86.34/86.56 (node17(c_e_h_1, c_f, s0)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2238, 2252])).
% 86.34/86.56 tff(2254,plain,
% 86.34/86.56 (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2229, 2253])).
% 86.34/86.56 tff(2255,plain,
% 86.34/86.56 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | m_c_h_element_v_in2(c_e_h_1, c_f, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | m_c_h_element_v_in2(c_e_h_1, c_f, s0))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2256,plain,
% 86.34/86.56 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | m_c_h_element_v_in2(c_e_h_1, c_f, s0))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2257,plain,
% 86.34/86.56 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | m_c_h_element_v_in2(c_e_h_1, c_f, s0)),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2256, 2255])).
% 86.34/86.56 tff(2258,plain,
% 86.34/86.56 ((~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2257, 228, 2222])).
% 86.34/86.56 tff(2259,plain,
% 86.34/86.56 (~node16(c_e_h_1, c_f, s0)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2258, 2254])).
% 86.34/86.56 tff(2260,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node15(c_e_h_1, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node15(c_e_h_1, c_f, s0, s1))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2261,plain,
% 86.34/86.56 ((node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1))) <=> (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node15(c_e_h_1, c_f, s0, s1))),
% 86.34/86.56 inference(rewrite,[status(thm)],[])).
% 86.34/86.56 tff(2262,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node15(c_e_h_1, c_f, s0, s1)))),
% 86.34/86.56 inference(monotonicity,[status(thm)],[2261])).
% 86.34/86.56 tff(2263,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node15(c_e_h_1, c_f, s0, s1))),
% 86.34/86.56 inference(transitivity,[status(thm)],[2262, 2260])).
% 86.34/86.56 tff(2264,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))),
% 86.34/86.56 inference(quant_inst,[status(thm)],[])).
% 86.34/86.56 tff(2265,plain,
% 86.34/86.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node15(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 86.34/86.56 tff(2266,plain,
% 86.34/86.56 (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2265, 189, 2234])).
% 86.34/86.56 tff(2267,plain,
% 86.34/86.56 (node15(c_e_h_1, c_f, s0, s1)),
% 86.34/86.56 inference(unit_resolution,[status(thm)],[2266, 2259, 2248])).
% 86.34/86.56 tff(2268,plain,
% 86.34/86.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2269,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2270,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2269, 2268])).
% 86.34/86.57 tff(2271,plain,
% 86.34/86.57 ($false),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2270, 173, 1659, 2267, 2198])).
% 86.34/86.57 tff(2272,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.57 tff(2273,plain,
% 86.34/86.57 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2274,plain,
% 86.34/86.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2275,plain,
% 86.34/86.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s1)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 86.34/86.57 tff(2276,plain,
% 86.34/86.57 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2275, 1666, 2272])).
% 86.34/86.57 tff(2277,plain,
% 86.34/86.57 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s1))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2278,plain,
% 86.34/86.57 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s1))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2279,plain,
% 86.34/86.57 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s1)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2278, 2277])).
% 86.34/86.57 tff(2280,plain,
% 86.34/86.57 (~node20(c_e_h_1, c_q, s1)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2279, 37, 2276])).
% 86.34/86.57 tff(2281,assumption,(node21(c_e_h_1, c_q, s1, s2)), introduced(assumption)).
% 86.34/86.57 tff(2282,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2283,plain,
% 86.34/86.57 ((node20(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2284,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2))))),
% 86.34/86.57 inference(monotonicity,[status(thm)],[2283])).
% 86.34/86.57 tff(2285,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 86.34/86.57 inference(transitivity,[status(thm)],[2284, 2282])).
% 86.34/86.57 tff(2286,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2287,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2))),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 86.34/86.57 tff(2288,plain,
% 86.34/86.57 ($false),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2287, 51, 2197, 2281, 2280])).
% 86.34/86.57 tff(2289,plain,((~node21(c_e_h_1, c_q, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.57 tff(2290,plain,
% 86.34/86.57 (~node21(c_e_h_1, c_q, s1, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2289, 2197])).
% 86.34/86.57 tff(2291,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2292,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2293,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 86.34/86.57 tff(2294,plain,
% 86.34/86.57 (node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2293, 81, 344])).
% 86.34/86.57 tff(2295,plain,
% 86.34/86.57 (node22(c_e_h_1, c_q, s1, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2294, 2290])).
% 86.34/86.57 tff(2296,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2297,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2298,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 86.34/86.57 tff(2299,plain,
% 86.34/86.57 ($false),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2298, 107, 1692, 2197, 2295])).
% 86.34/86.57 tff(2300,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.57 tff(2301,plain,
% 86.34/86.57 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s2))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2302,plain,
% 86.34/86.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s2))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2303,plain,
% 86.34/86.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s2)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 86.34/86.57 tff(2304,plain,
% 86.34/86.57 (node3(c_e_h_1, c_e_h_2, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2303, 817, 814])).
% 86.34/86.57 tff(2305,plain,
% 86.34/86.57 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s2)) | (~node3(c_e_h_1, c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s2)) | (~node3(c_e_h_1, c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2306,plain,
% 86.34/86.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s2)) | (~node3(c_e_h_1, c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2307,plain,
% 86.34/86.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s2)) | (~node3(c_e_h_1, c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 86.34/86.57 tff(2308,plain,
% 86.34/86.57 ((~m_cell_v_ack(c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2307, 836, 2304])).
% 86.34/86.57 tff(2309,plain,
% 86.34/86.57 (~m_cell_v_ack(c_e_h_2, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2308, 2300])).
% 86.34/86.57 tff(2310,plain,
% 86.34/86.57 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2311,plain,
% 86.34/86.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2312,plain,
% 86.34/86.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 86.34/86.57 tff(2313,plain,
% 86.34/86.57 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2312, 848, 2309])).
% 86.34/86.57 tff(2314,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s2)), introduced(assumption)).
% 86.34/86.57 tff(2315,plain,
% 86.34/86.57 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2316,plain,
% 86.34/86.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2317,plain,
% 86.34/86.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 86.34/86.57 tff(2318,plain,
% 86.34/86.57 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2317, 1638, 1135])).
% 86.34/86.57 tff(2319,plain,
% 86.34/86.57 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s1))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2320,plain,
% 86.34/86.57 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s1))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2321,plain,
% 86.34/86.57 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s1)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 86.34/86.57 tff(2322,plain,
% 86.34/86.57 (~node20(c_e_h_2, c_l, s1)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2321, 1535, 2318])).
% 86.34/86.57 tff(2323,assumption,(node21(c_e_h_2, c_l, s1, s2)), introduced(assumption)).
% 86.34/86.57 tff(2324,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | node20(c_e_h_2, c_l, s1) | (~node21(c_e_h_2, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | node20(c_e_h_2, c_l, s1) | (~node21(c_e_h_2, c_l, s1, s2)))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2325,plain,
% 86.34/86.57 ((node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | node20(c_e_h_2, c_l, s1) | (~node21(c_e_h_2, c_l, s1, s2)))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2326,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | node20(c_e_h_2, c_l, s1) | (~node21(c_e_h_2, c_l, s1, s2))))),
% 86.34/86.57 inference(monotonicity,[status(thm)],[2325])).
% 86.34/86.57 tff(2327,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | node20(c_e_h_2, c_l, s1) | (~node21(c_e_h_2, c_l, s1, s2)))),
% 86.34/86.57 inference(transitivity,[status(thm)],[2326, 2324])).
% 86.34/86.57 tff(2328,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2)))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2329,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | node20(c_e_h_2, c_l, s1) | (~node21(c_e_h_2, c_l, s1, s2))),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2328, 2327])).
% 86.34/86.57 tff(2330,plain,
% 86.34/86.57 ($false),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2329, 51, 2323, 2322, 2314])).
% 86.34/86.57 tff(2331,plain,((~node21(c_e_h_2, c_l, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.57 tff(2332,plain,
% 86.34/86.57 (~node21(c_e_h_2, c_l, s1, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2331, 2314])).
% 86.34/86.57 tff(2333,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2334,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2335,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 86.34/86.57 tff(2336,plain,
% 86.34/86.57 (node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2335, 81, 344])).
% 86.34/86.57 tff(2337,plain,
% 86.34/86.57 (node22(c_e_h_2, c_l, s1, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2336, 2332])).
% 86.34/86.57 tff(2338,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2339,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2340,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 86.34/86.57 tff(2341,plain,
% 86.34/86.57 ($false),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2340, 107, 2337, 1651, 2314])).
% 86.34/86.57 tff(2342,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.57 tff(2343,plain,
% 86.34/86.57 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2344,plain,
% 86.34/86.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2345,plain,
% 86.34/86.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 86.34/86.57 tff(2346,plain,
% 86.34/86.57 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2345, 801, 2342])).
% 86.34/86.57 tff(2347,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s3)), introduced(assumption)).
% 86.34/86.57 tff(2348,assumption,(node6(c_e_h_2, c_j, s2, s3)), introduced(assumption)).
% 86.34/86.57 tff(2349,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | (~node6(c_e_h_2, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | (~node6(c_e_h_2, c_j, s2, s3)))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2350,plain,
% 86.34/86.57 (((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | (~node6(c_e_h_2, c_j, s2, s3)))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2351,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | (~node6(c_e_h_2, c_j, s2, s3))))),
% 86.34/86.57 inference(monotonicity,[status(thm)],[2350])).
% 86.34/86.57 tff(2352,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | (~node6(c_e_h_2, c_j, s2, s3)))),
% 86.34/86.57 inference(transitivity,[status(thm)],[2351, 2349])).
% 86.34/86.57 tff(2353,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2354,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | (~node6(c_e_h_2, c_j, s2, s3))),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 86.34/86.57 tff(2355,plain,
% 86.34/86.57 ($false),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2354, 899, 2347, 1736, 2348])).
% 86.34/86.57 tff(2356,plain,((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.57 tff(2357,plain,
% 86.34/86.57 (~node6(c_e_h_2, c_j, s2, s3)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2356, 2347])).
% 86.34/86.57 tff(2358,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2359,plain,
% 86.34/86.57 ((node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2360,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3)))),
% 86.34/86.57 inference(monotonicity,[status(thm)],[2359])).
% 86.34/86.57 tff(2361,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3))),
% 86.34/86.57 inference(transitivity,[status(thm)],[2360, 2358])).
% 86.34/86.57 tff(2362,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3)))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2363,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3)),
% 86.34/86.57 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 86.34/86.57 tff(2364,plain,
% 86.34/86.57 (node5(c_e_h_2, c_j, s2, s3) | node6(c_e_h_2, c_j, s2, s3)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2363, 881, 582])).
% 86.34/86.57 tff(2365,plain,
% 86.34/86.57 (node5(c_e_h_2, c_j, s2, s3)),
% 86.34/86.57 inference(unit_resolution,[status(thm)],[2364, 2357])).
% 86.34/86.57 tff(2366,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2367,plain,
% 86.34/86.57 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3))) <=> (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)))),
% 86.34/86.57 inference(rewrite,[status(thm)],[])).
% 86.34/86.57 tff(2368,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3))))),
% 86.34/86.57 inference(monotonicity,[status(thm)],[2367])).
% 86.34/86.57 tff(2369,plain,
% 86.34/86.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)))),
% 86.34/86.57 inference(transitivity,[status(thm)],[2368, 2366])).
% 86.34/86.57 tff(2370,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))),
% 86.34/86.57 inference(quant_inst,[status(thm)],[])).
% 86.34/86.57 tff(2371,plain,
% 86.34/86.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3))),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 86.34/86.58 tff(2372,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2371, 862, 2347, 2365, 2346, 2313])).
% 86.34/86.58 tff(2373,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2374,plain,
% 86.34/86.58 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2375,plain,
% 86.34/86.58 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2376,plain,
% 86.34/86.58 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 86.34/86.58 tff(2377,plain,
% 86.34/86.58 (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2376, 309, 2373])).
% 86.34/86.58 tff(2378,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2379,plain,
% 86.34/86.58 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2380,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(monotonicity,[status(thm)],[2379])).
% 86.34/86.58 tff(2381,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(transitivity,[status(thm)],[2380, 2378])).
% 86.34/86.58 tff(2382,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2383,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2382, 2381])).
% 86.34/86.58 tff(2384,plain,
% 86.34/86.58 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2383, 209, 2377])).
% 86.34/86.58 tff(2385,plain,
% 86.34/86.58 (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2384, 2196])).
% 86.34/86.58 tff(2386,assumption,(node15(c_e_h_2, c_h, s3, s4)), introduced(assumption)).
% 86.34/86.58 tff(2387,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2388,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2389,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 86.34/86.58 tff(2390,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2389, 173, 1749, 2172, 2386])).
% 86.34/86.58 tff(2391,plain,((~node15(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2392,plain,
% 86.34/86.58 (~node15(c_e_h_2, c_h, s3, s4)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2391, 2172])).
% 86.34/86.58 tff(2393,assumption,(node17(c_e_h_2, c_h, s3)), introduced(assumption)).
% 86.34/86.58 tff(2394,assumption,(node16(c_e_h_2, c_h, s3)), introduced(assumption)).
% 86.34/86.58 tff(2395,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s3)), introduced(assumption)).
% 86.34/86.58 tff(2396,plain,
% 86.34/86.58 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2383, 209, 2393])).
% 86.34/86.58 tff(2397,plain,
% 86.34/86.58 (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2396, 2395])).
% 86.34/86.58 tff(2398,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2399,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2400,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2399, 2398])).
% 86.34/86.58 tff(2401,plain,
% 86.34/86.58 (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2400, 228, 2394])).
% 86.34/86.58 tff(2402,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2401, 2397, 2395])).
% 86.34/86.58 tff(2403,plain,(m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node16(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2404,plain,
% 86.34/86.58 (m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2403, 2394, 2393])).
% 86.34/86.58 tff(2405,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2406,plain,
% 86.34/86.58 ((m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2407,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3))))),
% 86.34/86.58 inference(monotonicity,[status(thm)],[2406])).
% 86.34/86.58 tff(2408,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(transitivity,[status(thm)],[2407, 2405])).
% 86.34/86.58 tff(2409,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2410,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 86.34/86.58 tff(2411,plain,
% 86.34/86.58 (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2410, 245, 2393])).
% 86.34/86.58 tff(2412,plain,
% 86.34/86.58 (m_c_h_element_v_in1(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2411, 2404])).
% 86.34/86.58 tff(2413,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2414,plain,
% 86.34/86.58 (((~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2415,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3))))),
% 86.34/86.58 inference(monotonicity,[status(thm)],[2414])).
% 86.34/86.58 tff(2416,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(transitivity,[status(thm)],[2415, 2413])).
% 86.34/86.58 tff(2417,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2418,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~node16(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 86.34/86.58 tff(2419,plain,
% 86.34/86.58 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2418, 263, 2394])).
% 86.34/86.58 tff(2420,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2419, 2412, 2404])).
% 86.34/86.58 tff(2421,plain,((~node16(c_e_h_2, c_h, s3)) | (~node17(c_e_h_2, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2422,plain,
% 86.34/86.58 (~node16(c_e_h_2, c_h, s3)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2421, 2196])).
% 86.34/86.58 tff(2423,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node15(c_e_h_2, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node15(c_e_h_2, c_h, s3, s4))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2424,plain,
% 86.34/86.58 ((node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4))) <=> (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node15(c_e_h_2, c_h, s3, s4))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2425,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node15(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.58 inference(monotonicity,[status(thm)],[2424])).
% 86.34/86.58 tff(2426,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node15(c_e_h_2, c_h, s3, s4))),
% 86.34/86.58 inference(transitivity,[status(thm)],[2425, 2423])).
% 86.34/86.58 tff(2427,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2428,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node15(c_e_h_2, c_h, s3, s4)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2427, 2426])).
% 86.34/86.58 tff(2429,plain,
% 86.34/86.58 (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2428, 189, 2188])).
% 86.34/86.58 tff(2430,plain,
% 86.34/86.58 (node14(c_e_h_2, c_h, s3, s4)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2429, 2422, 2392])).
% 86.34/86.58 tff(2431,assumption,(node14(c_e_h_2, c_h, s3, s4)), introduced(assumption)).
% 86.34/86.58 tff(2432,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s3)), introduced(assumption)).
% 86.34/86.58 tff(2433,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2434,plain,
% 86.34/86.58 (((~node14(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2435,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))))),
% 86.34/86.58 inference(monotonicity,[status(thm)],[2434])).
% 86.34/86.58 tff(2436,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))),
% 86.34/86.58 inference(transitivity,[status(thm)],[2435, 2433])).
% 86.34/86.58 tff(2437,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2438,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2437, 2436])).
% 86.34/86.58 tff(2439,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2438, 283, 2172, 2432, 2431])).
% 86.34/86.58 tff(2440,plain,((~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2441,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2440, 2430, 2385, 2172])).
% 86.34/86.58 tff(2442,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2443,plain,
% 86.34/86.58 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2444,plain,
% 86.34/86.58 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2445,plain,
% 86.34/86.58 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 86.34/86.58 tff(2446,plain,
% 86.34/86.58 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2445, 23, 2442])).
% 86.34/86.58 tff(2447,plain,
% 86.34/86.58 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2448,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2449,plain,
% 86.34/86.58 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 86.34/86.58 tff(2450,plain,
% 86.34/86.58 (~node20(c_e_h_2, c_i, s4)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2449, 37, 2446])).
% 86.34/86.58 tff(2451,assumption,(~node20(c_e_h_2, c_i, s4)), introduced(assumption)).
% 86.34/86.58 tff(2452,assumption,(node21(c_e_h_2, c_i, s4, s5)), introduced(assumption)).
% 86.34/86.58 tff(2453,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5)))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2454,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5)))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2455,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5))),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 86.34/86.58 tff(2456,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2455, 51, 2164, 2452, 2451])).
% 86.34/86.58 tff(2457,plain,((~node21(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | node20(c_e_h_2, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2458,plain,
% 86.34/86.58 (~node21(c_e_h_2, c_i, s4, s5)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2457, 2164, 2450])).
% 86.34/86.58 tff(2459,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2460,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2461,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2460, 2459])).
% 86.34/86.58 tff(2462,plain,
% 86.34/86.58 (node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2461, 81, 1432])).
% 86.34/86.58 tff(2463,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2462, 2458, 2171])).
% 86.34/86.58 tff(2464,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2465,plain,
% 86.34/86.58 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2466,plain,
% 86.34/86.58 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2467,plain,
% 86.34/86.58 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2466, 2465])).
% 86.34/86.58 tff(2468,plain,
% 86.34/86.58 (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2467, 365, 2464])).
% 86.34/86.58 tff(2469,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s6)), introduced(assumption)).
% 86.34/86.58 tff(2470,assumption,(node15(c_e_h_2, c_e, s5, s6)), introduced(assumption)).
% 86.34/86.58 tff(2471,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.34/86.58 inference(rewrite,[status(thm)],[])).
% 86.34/86.58 tff(2472,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 86.34/86.58 inference(quant_inst,[status(thm)],[])).
% 86.34/86.58 tff(2473,plain,
% 86.34/86.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 86.34/86.58 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 86.34/86.58 tff(2474,plain,
% 86.34/86.58 ($false),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2473, 173, 2470, 2050, 2469])).
% 86.34/86.58 tff(2475,plain,((~node15(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.58 tff(2476,plain,
% 86.34/86.58 (~node15(c_e_h_2, c_e, s5, s6)),
% 86.34/86.58 inference(unit_resolution,[status(thm)],[2475, 2469, 2050])).
% 86.34/86.58 tff(2477,assumption,(node18(c_e_h_2, c_e, s5, s6)), introduced(assumption)).
% 86.34/86.58 tff(2478,plain,
% 86.34/86.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~node18(c_e_h_2, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~node18(c_e_h_2, c_e, s5, s6)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2479,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~node18(c_e_h_2, c_e, s5, s6)))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2480,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~node18(c_e_h_2, c_e, s5, s6))),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 86.34/86.59 tff(2481,plain,
% 86.34/86.59 ($false),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2480, 124, 2477, 2050, 2469])).
% 86.34/86.59 tff(2482,plain,((~node18(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.59 tff(2483,plain,
% 86.34/86.59 (~node18(c_e_h_2, c_e, s5, s6)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2482, 2469, 2050])).
% 86.34/86.59 tff(2484,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_2, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_2, c_e, s5, s6))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2485,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_2, c_e, s5, s6))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2486,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_2, c_e, s5, s6)),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2485, 2484])).
% 86.34/86.59 tff(2487,plain,
% 86.34/86.59 (node19(c_e_h_2, c_e, s5, s6)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2486, 141, 1499])).
% 86.34/86.59 tff(2488,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2489,plain,
% 86.34/86.59 ((node17(c_e_h_2, c_e, s5) | node18(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6))) <=> ((~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2490,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s5) | node18(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(monotonicity,[status(thm)],[2489])).
% 86.34/86.59 tff(2491,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s5) | node18(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(transitivity,[status(thm)],[2490, 2488])).
% 86.34/86.59 tff(2492,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s5) | node18(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6)))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2493,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s5, s6)) | node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5)),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 86.34/86.59 tff(2494,plain,
% 86.34/86.59 (node18(c_e_h_2, c_e, s5, s6) | node17(c_e_h_2, c_e, s5)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2493, 156, 2487])).
% 86.34/86.59 tff(2495,plain,
% 86.34/86.59 (node17(c_e_h_2, c_e, s5)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2494, 2483])).
% 86.34/86.59 tff(2496,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s5)), introduced(assumption)).
% 86.34/86.59 tff(2497,plain,
% 86.34/86.59 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2498,plain,
% 86.34/86.59 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2499,plain,
% 86.34/86.59 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5))))),
% 86.34/86.59 inference(monotonicity,[status(thm)],[2498])).
% 86.34/86.59 tff(2500,plain,
% 86.34/86.59 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(transitivity,[status(thm)],[2499, 2497])).
% 86.34/86.59 tff(2501,plain,
% 86.34/86.59 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2502,plain,
% 86.34/86.59 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2501, 2500])).
% 86.34/86.59 tff(2503,plain,
% 86.34/86.59 ((~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2502, 209, 2496])).
% 86.34/86.59 tff(2504,plain,
% 86.34/86.59 (~m_c_h_element_v_in1(c_e_h_2, c_e, s5)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2503, 2495])).
% 86.34/86.59 tff(2505,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s5)), introduced(assumption)).
% 86.34/86.59 tff(2506,assumption,(~node15(c_e_h_2, c_e, s5, s6)), introduced(assumption)).
% 86.34/86.59 tff(2507,assumption,(node17(c_e_h_2, c_e, s5)), introduced(assumption)).
% 86.34/86.59 tff(2508,plain,
% 86.34/86.59 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2509,plain,
% 86.34/86.59 ((m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2510,plain,
% 86.34/86.59 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5))))),
% 86.34/86.59 inference(monotonicity,[status(thm)],[2509])).
% 86.34/86.59 tff(2511,plain,
% 86.34/86.59 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(transitivity,[status(thm)],[2510, 2508])).
% 86.34/86.59 tff(2512,plain,
% 86.34/86.59 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)) | (~node17(c_e_h_2, c_e, s5)))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2513,plain,
% 86.34/86.59 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~node17(c_e_h_2, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 86.34/86.59 tff(2514,plain,
% 86.34/86.59 (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2513, 245, 2507])).
% 86.34/86.59 tff(2515,plain,
% 86.34/86.59 (~m_c_h_element_v_in2(c_e_h_2, c_e, s5)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2514, 2505])).
% 86.34/86.59 tff(2516,plain,
% 86.34/86.59 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_in2(c_e_h_2, c_e, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_in2(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2517,plain,
% 86.34/86.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_in2(c_e_h_2, c_e, s5))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2518,plain,
% 86.34/86.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | m_c_h_element_v_in2(c_e_h_2, c_e, s5)),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 86.34/86.59 tff(2519,plain,
% 86.34/86.59 (~node16(c_e_h_2, c_e, s5)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2518, 228, 2505, 2515])).
% 86.34/86.59 tff(2520,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s5, s6)) | node16(c_e_h_2, c_e, s5) | node15(c_e_h_2, c_e, s5, s6) | node14(c_e_h_2, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s5, s6)) | node16(c_e_h_2, c_e, s5) | node15(c_e_h_2, c_e, s5, s6) | node14(c_e_h_2, c_e, s5, s6))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2521,plain,
% 86.34/86.59 ((node16(c_e_h_2, c_e, s5) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6))) <=> ((~node19(c_e_h_2, c_e, s5, s6)) | node16(c_e_h_2, c_e, s5) | node15(c_e_h_2, c_e, s5, s6) | node14(c_e_h_2, c_e, s5, s6))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2522,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s5) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s5, s6)) | node16(c_e_h_2, c_e, s5) | node15(c_e_h_2, c_e, s5, s6) | node14(c_e_h_2, c_e, s5, s6)))),
% 86.34/86.59 inference(monotonicity,[status(thm)],[2521])).
% 86.34/86.59 tff(2523,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s5) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s5, s6)) | node16(c_e_h_2, c_e, s5) | node15(c_e_h_2, c_e, s5, s6) | node14(c_e_h_2, c_e, s5, s6))),
% 86.34/86.59 inference(transitivity,[status(thm)],[2522, 2520])).
% 86.34/86.59 tff(2524,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s5) | node14(c_e_h_2, c_e, s5, s6) | node15(c_e_h_2, c_e, s5, s6) | (~node19(c_e_h_2, c_e, s5, s6)))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2525,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s5, s6)) | node16(c_e_h_2, c_e, s5) | node15(c_e_h_2, c_e, s5, s6) | node14(c_e_h_2, c_e, s5, s6)),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 86.34/86.59 tff(2526,plain,
% 86.34/86.59 (node16(c_e_h_2, c_e, s5) | node15(c_e_h_2, c_e, s5, s6) | node14(c_e_h_2, c_e, s5, s6)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2525, 189, 2487])).
% 86.34/86.59 tff(2527,plain,
% 86.34/86.59 (node14(c_e_h_2, c_e, s5, s6)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2526, 2519, 2506])).
% 86.34/86.59 tff(2528,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node14(c_e_h_2, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node14(c_e_h_2, c_e, s5, s6)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2529,plain,
% 86.34/86.59 (((~node14(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node14(c_e_h_2, c_e, s5, s6)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2530,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node14(c_e_h_2, c_e, s5, s6))))),
% 86.34/86.59 inference(monotonicity,[status(thm)],[2529])).
% 86.34/86.59 tff(2531,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node14(c_e_h_2, c_e, s5, s6)))),
% 86.34/86.59 inference(transitivity,[status(thm)],[2530, 2528])).
% 86.34/86.59 tff(2532,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2533,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | (~node14(c_e_h_2, c_e, s5, s6))),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2532, 2531])).
% 86.34/86.59 tff(2534,plain,
% 86.34/86.59 ($false),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2533, 283, 2527, 2469, 2505])).
% 86.34/86.59 tff(2535,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s5) | (~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | node15(c_e_h_2, c_e, s5, s6) | (~node17(c_e_h_2, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.59 tff(2536,plain,
% 86.34/86.59 ($false),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2535, 2504, 2495, 2476, 2469])).
% 86.34/86.59 tff(2537,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.59 tff(2538,plain,
% 86.34/86.59 ((~m_c_h_element_v_out(c_e_h_2, c_e, s6)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2537, 1877])).
% 86.34/86.59 tff(2539,plain,
% 86.34/86.59 (~m_c_h_element_v_out(c_e_h_2, c_e, s6)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2538, 2468])).
% 86.34/86.59 tff(2540,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)), introduced(assumption)).
% 86.34/86.59 tff(2541,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s6)), introduced(assumption)).
% 86.34/86.59 tff(2542,plain,
% 86.34/86.59 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2543,plain,
% 86.34/86.59 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2544,plain,
% 86.34/86.59 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6)),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 86.34/86.59 tff(2545,plain,
% 86.34/86.59 ($false),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2544, 976, 2541, 2540])).
% 86.34/86.59 tff(2546,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s6) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 86.34/86.59 tff(2547,plain,
% 86.34/86.59 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2546, 2539])).
% 86.34/86.59 tff(2548,plain,
% 86.34/86.59 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2549,plain,
% 86.34/86.59 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2550,plain,
% 86.34/86.59 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 86.34/86.59 tff(2551,plain,
% 86.34/86.59 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2550, 1142, 1514])).
% 86.34/86.59 tff(2552,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)), introduced(assumption)).
% 86.34/86.59 tff(2553,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)), introduced(assumption)).
% 86.34/86.59 tff(2554,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)), introduced(assumption)).
% 86.34/86.59 tff(2555,assumption,(node10(c_e_h_2, c_n, s6, s7)), introduced(assumption)).
% 86.34/86.59 tff(2556,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2557,plain,
% 86.34/86.59 (((~node10(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2558,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7))))),
% 86.34/86.59 inference(monotonicity,[status(thm)],[2557])).
% 86.34/86.59 tff(2559,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7)))),
% 86.34/86.59 inference(transitivity,[status(thm)],[2558, 2556])).
% 86.34/86.59 tff(2560,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2561,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)) | (~node10(c_e_h_2, c_n, s6, s7))),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 86.34/86.59 tff(2562,plain,
% 86.34/86.59 ($false),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2561, 1191, 2554, 2555, 2553, 2552])).
% 86.34/86.59 tff(2563,plain,((~node10(c_e_h_2, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.59 tff(2564,plain,
% 86.34/86.59 (~node10(c_e_h_2, c_n, s6, s7)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2563, 2554, 2553, 2552])).
% 86.34/86.59 tff(2565,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2566,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7))),
% 86.34/86.59 inference(quant_inst,[status(thm)],[])).
% 86.34/86.59 tff(2567,plain,
% 86.34/86.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7)),
% 86.34/86.59 inference(modus_ponens,[status(thm)],[2566, 2565])).
% 86.34/86.59 tff(2568,plain,
% 86.34/86.59 (node10(c_e_h_2, c_n, s6, s7) | node11(c_e_h_2, c_n, s6, s7)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2567, 1092, 1552])).
% 86.34/86.59 tff(2569,plain,
% 86.34/86.59 (node11(c_e_h_2, c_n, s6, s7)),
% 86.34/86.59 inference(unit_resolution,[status(thm)],[2568, 2564])).
% 86.34/86.59 tff(2570,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2571,plain,
% 86.34/86.59 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~node11(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7)))),
% 86.34/86.59 inference(rewrite,[status(thm)],[])).
% 86.34/86.59 tff(2572,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~node11(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7))))),
% 86.34/86.59 inference(monotonicity,[status(thm)],[2571])).
% 86.34/86.59 tff(2573,plain,
% 86.34/86.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~node11(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7)))),
% 86.34/86.60 inference(transitivity,[status(thm)],[2572, 2570])).
% 86.34/86.60 tff(2574,plain,
% 86.34/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~node11(c_e_h_2, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))),
% 86.34/86.60 inference(quant_inst,[status(thm)],[])).
% 86.34/86.60 tff(2575,plain,
% 86.34/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~node11(c_e_h_2, c_n, s6, s7))),
% 86.34/86.60 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 86.34/86.60 tff(2576,plain,
% 86.34/86.60 ($false),
% 86.34/86.60 inference(unit_resolution,[status(thm)],[2575, 1161, 2096, 2554, 2569])).
% 86.34/86.60 tff(2577,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 86.34/86.60 tff(2578,plain,
% 86.34/86.60 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6))),
% 86.34/86.60 inference(unit_resolution,[status(thm)],[2577, 2551])).
% 86.34/86.60 tff(2579,plain,
% 86.34/86.60 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6))),
% 86.34/86.60 inference(unit_resolution,[status(thm)],[2578, 2094])).
% 86.34/86.60 tff(2580,plain,
% 86.41/86.60 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2579, 2547])).
% 86.41/86.60 tff(2581,plain,
% 86.41/86.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2582,plain,
% 86.41/86.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2583,plain,
% 86.41/86.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7))),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2582, 2581])).
% 86.41/86.60 tff(2584,plain,
% 86.41/86.60 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2583, 1048, 2580])).
% 86.41/86.60 tff(2585,plain,
% 86.41/86.60 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2586,plain,
% 86.41/86.60 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2587,plain,
% 86.41/86.60 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2586, 2585])).
% 86.41/86.60 tff(2588,plain,
% 86.41/86.60 (~node9(c_e_h_2, c_m, s7)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2587, 1062, 2584])).
% 86.41/86.60 tff(2589,assumption,(~node9(c_e_h_2, c_m, s7)), introduced(assumption)).
% 86.41/86.60 tff(2590,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)), introduced(assumption)).
% 86.41/86.60 tff(2591,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)), introduced(assumption)).
% 86.41/86.60 tff(2592,assumption,(node11(c_e_h_2, c_m, s7, s8)), introduced(assumption)).
% 86.41/86.60 tff(2593,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2594,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2595,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2594, 2593])).
% 86.41/86.60 tff(2596,plain,
% 86.41/86.60 ($false),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2595, 1130, 2590, 2591, 2592])).
% 86.41/86.60 tff(2597,plain,((~node11(c_e_h_2, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.60 tff(2598,plain,
% 86.41/86.60 (~node11(c_e_h_2, c_m, s7, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2597, 2591, 2590])).
% 86.41/86.60 tff(2599,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2600,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2601,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 86.41/86.60 tff(2602,plain,
% 86.41/86.60 (node10(c_e_h_2, c_m, s7, s8) | node11(c_e_h_2, c_m, s7, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2601, 1092, 2152])).
% 86.41/86.60 tff(2603,plain,
% 86.41/86.60 (node10(c_e_h_2, c_m, s7, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2602, 2598])).
% 86.41/86.60 tff(2604,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8)))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2605,plain,
% 86.41/86.60 ((node9(c_e_h_2, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node10(c_e_h_2, c_m, s7, s8))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8)))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2606,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node10(c_e_h_2, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8))))),
% 86.41/86.60 inference(monotonicity,[status(thm)],[2605])).
% 86.41/86.60 tff(2607,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node10(c_e_h_2, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8)))),
% 86.41/86.60 inference(transitivity,[status(thm)],[2606, 2604])).
% 86.41/86.60 tff(2608,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | (~node10(c_e_h_2, c_m, s7, s8)))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2609,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | (~node10(c_e_h_2, c_m, s7, s8))),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2608, 2607])).
% 86.41/86.60 tff(2610,plain,
% 86.41/86.60 ($false),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2609, 1076, 2591, 2603, 2589])).
% 86.41/86.60 tff(2611,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.60 tff(2612,plain,
% 86.41/86.60 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)) | node9(c_e_h_2, c_m, s7)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2611, 2131])).
% 86.41/86.60 tff(2613,plain,
% 86.41/86.60 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2612, 2588])).
% 86.41/86.60 tff(2614,plain,
% 86.41/86.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2615,plain,
% 86.41/86.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2616,plain,
% 86.41/86.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2615, 2614])).
% 86.41/86.60 tff(2617,plain,
% 86.41/86.60 ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2616, 1521])).
% 86.41/86.60 tff(2618,plain,
% 86.41/86.60 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2617, 2613])).
% 86.41/86.60 tff(2619,plain,
% 86.41/86.60 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s8))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2620,plain,
% 86.41/86.60 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s8))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2621,plain,
% 86.41/86.60 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s8)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2620, 2619])).
% 86.41/86.60 tff(2622,plain,
% 86.41/86.60 (~node20(c_e_h_2, c_r, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2621, 1535, 2618])).
% 86.41/86.60 tff(2623,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s8)), introduced(assumption)).
% 86.41/86.60 tff(2624,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s9)), introduced(assumption)).
% 86.41/86.60 tff(2625,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2626,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2627,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 86.41/86.60 tff(2628,plain,
% 86.41/86.60 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node22(c_e_h_2, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2627, 107])).
% 86.41/86.60 tff(2629,plain,
% 86.41/86.60 (~node22(c_e_h_2, c_r, s8, s9)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2628, 2624, 2623])).
% 86.41/86.60 tff(2630,plain,
% 86.41/86.60 (succ(s8, s9) <=> succ(s8, s9)),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2631,axiom,(succ(s8, s9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound9')).
% 86.41/86.60 tff(2632,plain,
% 86.41/86.60 (succ(s8, s9)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 86.41/86.60 tff(2633,plain,
% 86.41/86.60 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2634,plain,
% 86.41/86.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2635,plain,
% 86.41/86.60 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 86.41/86.60 tff(2636,plain,
% 86.41/86.60 (trans(s8, s9)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2635, 2632, 64])).
% 86.41/86.60 tff(2637,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_r, s8, s9) | node22(c_e_h_2, c_r, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_r, s8, s9) | node22(c_e_h_2, c_r, s8, s9))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2638,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_r, s8, s9) | node22(c_e_h_2, c_r, s8, s9))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2639,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_r, s8, s9) | node22(c_e_h_2, c_r, s8, s9)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 86.41/86.60 tff(2640,plain,
% 86.41/86.60 (node21(c_e_h_2, c_r, s8, s9)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2639, 81, 2636, 2629])).
% 86.41/86.60 tff(2641,assumption,(~node20(c_e_h_2, c_r, s8)), introduced(assumption)).
% 86.41/86.60 tff(2642,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node21(c_e_h_2, c_r, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node21(c_e_h_2, c_r, s8, s9)))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2643,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node21(c_e_h_2, c_r, s8, s9)))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2644,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | (~node21(c_e_h_2, c_r, s8, s9))),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2643, 2642])).
% 86.41/86.60 tff(2645,plain,
% 86.41/86.60 ($false),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2644, 51, 2641, 2624, 2640])).
% 86.41/86.60 tff(2646,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | node20(c_e_h_2, c_r, s8) | m_and_h_gate_v_out(c_e_h_2, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.60 tff(2647,plain,
% 86.41/86.60 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s9)) | m_and_h_gate_v_out(c_e_h_2, c_r, s8)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2646, 2622])).
% 86.41/86.60 tff(2648,plain,
% 86.41/86.60 (~m_and_h_gate_v_out(c_e_h_2, c_r, s9)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2647, 2163])).
% 86.41/86.60 tff(2649,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s10)), introduced(assumption)).
% 86.41/86.60 tff(2650,assumption,(node21(c_e_h_2, c_r, s9, s10)), introduced(assumption)).
% 86.41/86.60 tff(2651,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_r, s9)), introduced(assumption)).
% 86.41/86.60 tff(2652,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s3)), introduced(assumption)).
% 86.41/86.60 tff(2653,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s1)), introduced(assumption)).
% 86.41/86.60 tff(2654,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s2)), introduced(assumption)).
% 86.41/86.60 tff(2655,assumption,(node15(c_e_h_1, c_f, s1, s2)), introduced(assumption)).
% 86.41/86.60 tff(2656,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node15(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node15(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2657,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node15(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2658,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node15(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 86.41/86.60 tff(2659,plain,
% 86.41/86.60 ($false),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2658, 173, 2655, 2654, 2653])).
% 86.41/86.60 tff(2660,plain,((~node15(c_e_h_1, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.60 tff(2661,plain,
% 86.41/86.60 (~node15(c_e_h_1, c_f, s1, s2)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2660, 2653, 2654])).
% 86.41/86.60 tff(2662,assumption,(~node15(c_e_h_1, c_f, s1, s2)), introduced(assumption)).
% 86.41/86.60 tff(2663,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s1)), introduced(assumption)).
% 86.41/86.60 tff(2664,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s1)), introduced(assumption)).
% 86.41/86.60 tff(2665,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s0)), introduced(assumption)).
% 86.41/86.60 tff(2666,plain,
% 86.41/86.60 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2667,plain,
% 86.41/86.60 ($false),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2666, 13, 2665])).
% 86.41/86.60 tff(2668,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.60 tff(2669,plain,
% 86.41/86.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2670,plain,
% 86.41/86.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2671,plain,
% 86.41/86.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)) | m_c_h_element_v_out(c_e_h_1, c_h, s0)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2670, 2669])).
% 86.41/86.60 tff(2672,plain,
% 86.41/86.60 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2671, 23, 2668])).
% 86.41/86.60 tff(2673,plain,
% 86.41/86.60 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2674,plain,
% 86.41/86.60 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2675,plain,
% 86.41/86.60 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 86.41/86.60 tff(2676,plain,
% 86.41/86.60 (~node20(c_e_h_1, c_i, s0)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2675, 37, 2672])).
% 86.41/86.60 tff(2677,assumption,(node21(c_e_h_1, c_i, s0, s1)), introduced(assumption)).
% 86.41/86.60 tff(2678,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1)))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2679,plain,
% 86.41/86.60 ((node20(c_e_h_1, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1)))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2680,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1))))),
% 86.41/86.60 inference(monotonicity,[status(thm)],[2679])).
% 86.41/86.60 tff(2681,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1)))),
% 86.41/86.60 inference(transitivity,[status(thm)],[2680, 2678])).
% 86.41/86.60 tff(2682,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1)))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2683,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | node20(c_e_h_1, c_i, s0) | (~node21(c_e_h_1, c_i, s0, s1))),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 86.41/86.60 tff(2684,plain,
% 86.41/86.60 ($false),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2683, 51, 2664, 2677, 2676])).
% 86.41/86.60 tff(2685,plain,((~node21(c_e_h_1, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.60 tff(2686,plain,
% 86.41/86.60 (~node21(c_e_h_1, c_i, s0, s1)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2685, 2664])).
% 86.41/86.60 tff(2687,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2688,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2689,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 86.41/86.60 tff(2690,plain,
% 86.41/86.60 (node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2689, 81, 71])).
% 86.41/86.60 tff(2691,plain,
% 86.41/86.60 (node22(c_e_h_1, c_i, s0, s1)),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2690, 2686])).
% 86.41/86.60 tff(2692,plain,
% 86.41/86.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 86.41/86.60 inference(rewrite,[status(thm)],[])).
% 86.41/86.60 tff(2693,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 86.41/86.60 inference(quant_inst,[status(thm)],[])).
% 86.41/86.60 tff(2694,plain,
% 86.41/86.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0)),
% 86.41/86.60 inference(modus_ponens,[status(thm)],[2693, 2692])).
% 86.41/86.60 tff(2695,plain,
% 86.41/86.60 ($false),
% 86.41/86.60 inference(unit_resolution,[status(thm)],[2694, 107, 2664, 2691, 2211])).
% 86.41/86.61 tff(2696,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.61 tff(2697,plain,
% 86.41/86.61 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2698,plain,
% 86.41/86.61 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2699,plain,
% 86.41/86.61 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2698, 2697])).
% 86.41/86.61 tff(2700,plain,
% 86.41/86.61 (~m_c_h_element_v_in2(c_e_h_1, c_f, s1)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2699, 2218, 2696])).
% 86.41/86.61 tff(2701,plain,
% 86.41/86.61 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | m_c_h_element_v_in2(c_e_h_1, c_f, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | m_c_h_element_v_in2(c_e_h_1, c_f, s1))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2702,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | m_c_h_element_v_in2(c_e_h_1, c_f, s1))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2703,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | m_c_h_element_v_in2(c_e_h_1, c_f, s1)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 86.41/86.61 tff(2704,plain,
% 86.41/86.61 ((~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2703, 228, 2700])).
% 86.41/86.61 tff(2705,plain,
% 86.41/86.61 (~node16(c_e_h_1, c_f, s1)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2704, 2663])).
% 86.41/86.61 tff(2706,assumption,(node14(c_e_h_1, c_f, s1, s2)), introduced(assumption)).
% 86.41/86.61 tff(2707,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2708,plain,
% 86.41/86.61 (((~node14(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2709,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2))))),
% 86.41/86.61 inference(monotonicity,[status(thm)],[2708])).
% 86.41/86.61 tff(2710,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(transitivity,[status(thm)],[2709, 2707])).
% 86.41/86.61 tff(2711,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2712,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2))),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 86.41/86.61 tff(2713,plain,
% 86.41/86.61 ($false),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2712, 283, 2706, 2654, 2663])).
% 86.41/86.61 tff(2714,plain,((~node14(c_e_h_1, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.61 tff(2715,plain,
% 86.41/86.61 (~node14(c_e_h_1, c_f, s1, s2)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2714, 2663, 2654])).
% 86.41/86.61 tff(2716,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_f, s1, s2))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2717,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_f, s1, s2))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2718,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_f, s1, s2)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 86.41/86.61 tff(2719,plain,
% 86.41/86.61 (node19(c_e_h_1, c_f, s1, s2)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2718, 141, 344])).
% 86.41/86.61 tff(2720,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s1, s2) | node14(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)) | node16(c_e_h_1, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s1, s2) | node14(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)) | node16(c_e_h_1, c_f, s1))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2721,plain,
% 86.41/86.61 ((node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2) | node15(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2))) <=> (node15(c_e_h_1, c_f, s1, s2) | node14(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)) | node16(c_e_h_1, c_f, s1))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2722,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2) | node15(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s1, s2) | node14(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)) | node16(c_e_h_1, c_f, s1)))),
% 86.41/86.61 inference(monotonicity,[status(thm)],[2721])).
% 86.41/86.61 tff(2723,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2) | node15(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s1, s2) | node14(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)) | node16(c_e_h_1, c_f, s1))),
% 86.41/86.61 inference(transitivity,[status(thm)],[2722, 2720])).
% 86.41/86.61 tff(2724,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2) | node15(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2725,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s1, s2) | node14(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)) | node16(c_e_h_1, c_f, s1)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2724, 2723])).
% 86.41/86.61 tff(2726,plain,
% 86.41/86.61 (node15(c_e_h_1, c_f, s1, s2) | node14(c_e_h_1, c_f, s1, s2) | node16(c_e_h_1, c_f, s1)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2725, 189, 2719])).
% 86.41/86.61 tff(2727,plain,
% 86.41/86.61 ($false),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2726, 2715, 2705, 2662])).
% 86.41/86.61 tff(2728,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s1) | node15(c_e_h_1, c_f, s1, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.61 tff(2729,plain,
% 86.41/86.61 (m_c_h_element_v_in1(c_e_h_1, c_f, s1)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2728, 2661, 2654])).
% 86.41/86.61 tff(2730,plain,
% 86.41/86.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2731,plain,
% 86.41/86.61 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2732,plain,
% 86.41/86.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1))))),
% 86.41/86.61 inference(monotonicity,[status(thm)],[2731])).
% 86.41/86.61 tff(2733,plain,
% 86.41/86.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)))),
% 86.41/86.61 inference(transitivity,[status(thm)],[2732, 2730])).
% 86.41/86.61 tff(2734,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2735,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1))),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 86.41/86.61 tff(2736,plain,
% 86.41/86.61 ((~node17(c_e_h_1, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1))),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2735, 209, 2700])).
% 86.41/86.61 tff(2737,plain,
% 86.41/86.61 (~node17(c_e_h_1, c_f, s1)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2736, 2729])).
% 86.41/86.61 tff(2738,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2739,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2740,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2))),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 86.41/86.61 tff(2741,plain,
% 86.41/86.61 (node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2740, 156, 2719])).
% 86.41/86.61 tff(2742,plain,
% 86.41/86.61 (node18(c_e_h_1, c_f, s1, s2)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2741, 2737])).
% 86.41/86.61 tff(2743,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2744,plain,
% 86.41/86.61 (((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~node18(c_e_h_1, c_f, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2745,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~node18(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2))))),
% 86.41/86.61 inference(monotonicity,[status(thm)],[2744])).
% 86.41/86.61 tff(2746,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~node18(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(transitivity,[status(thm)],[2745, 2743])).
% 86.41/86.61 tff(2747,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~node18(c_e_h_1, c_f, s1, s2)))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2748,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2))),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2747, 2746])).
% 86.41/86.61 tff(2749,plain,
% 86.41/86.61 ($false),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2748, 124, 2742, 2654, 2653])).
% 86.41/86.61 tff(2750,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.61 tff(2751,plain,
% 86.41/86.61 (~m_c_h_element_v_out(c_e_h_1, c_f, s2)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2750, 2272])).
% 86.41/86.61 tff(2752,plain,
% 86.41/86.61 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2753,plain,
% 86.41/86.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2754,plain,
% 86.41/86.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s2)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 86.41/86.61 tff(2755,plain,
% 86.41/86.61 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2754, 1666, 2751])).
% 86.41/86.61 tff(2756,plain,
% 86.41/86.61 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s2))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2757,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s2))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2758,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s2)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2757, 2756])).
% 86.41/86.61 tff(2759,plain,
% 86.41/86.61 (~node20(c_e_h_1, c_q, s2)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2758, 37, 2755])).
% 86.41/86.61 tff(2760,assumption,(node21(c_e_h_1, c_q, s2, s3)), introduced(assumption)).
% 86.41/86.61 tff(2761,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2762,plain,
% 86.41/86.61 ((node20(c_e_h_1, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node21(c_e_h_1, c_q, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3)))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2763,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node21(c_e_h_1, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3))))),
% 86.41/86.61 inference(monotonicity,[status(thm)],[2762])).
% 86.41/86.61 tff(2764,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node21(c_e_h_1, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3)))),
% 86.41/86.61 inference(transitivity,[status(thm)],[2763, 2761])).
% 86.41/86.61 tff(2765,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node21(c_e_h_1, c_q, s2, s3)))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2766,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3))),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2765, 2764])).
% 86.41/86.61 tff(2767,plain,
% 86.41/86.61 ($false),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2766, 51, 2652, 2760, 2759])).
% 86.41/86.61 tff(2768,plain,((~node21(c_e_h_1, c_q, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.61 tff(2769,plain,
% 86.41/86.61 (~node21(c_e_h_1, c_q, s2, s3)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2768, 2652])).
% 86.41/86.61 tff(2770,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2771,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2772,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2771, 2770])).
% 86.41/86.61 tff(2773,plain,
% 86.41/86.61 (node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2772, 81, 582])).
% 86.41/86.61 tff(2774,plain,
% 86.41/86.61 (node22(c_e_h_1, c_q, s2, s3)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2773, 2769])).
% 86.41/86.61 tff(2775,plain,
% 86.41/86.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node22(c_e_h_1, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node22(c_e_h_1, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2776,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node22(c_e_h_1, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2777,plain,
% 86.41/86.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node22(c_e_h_1, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2776, 2775])).
% 86.41/86.61 tff(2778,plain,
% 86.41/86.61 ($false),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2777, 107, 2652, 2300, 2774])).
% 86.41/86.61 tff(2779,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.61 tff(2780,plain,
% 86.41/86.61 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s3))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2781,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s3))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2782,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s3)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2781, 2780])).
% 86.41/86.61 tff(2783,plain,
% 86.41/86.61 (node3(c_e_h_1, c_e_h_2, s3)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2782, 817, 814])).
% 86.41/86.61 tff(2784,plain,
% 86.41/86.61 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s3)) | (~node3(c_e_h_1, c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s3)) | (~node3(c_e_h_1, c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2785,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s3)) | (~node3(c_e_h_1, c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2786,plain,
% 86.41/86.61 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s3)) | (~node3(c_e_h_1, c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 86.41/86.61 tff(2787,plain,
% 86.41/86.61 ((~m_cell_v_ack(c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2786, 836, 2783])).
% 86.41/86.61 tff(2788,plain,
% 86.41/86.61 (~m_cell_v_ack(c_e_h_2, s3)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2787, 2779])).
% 86.41/86.61 tff(2789,plain,
% 86.41/86.61 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)) | m_cell_v_ack(c_e_h_2, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)) | m_cell_v_ack(c_e_h_2, s3))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2790,plain,
% 86.41/86.61 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)) | m_cell_v_ack(c_e_h_2, s3))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2791,plain,
% 86.41/86.61 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)) | m_cell_v_ack(c_e_h_2, s3)),
% 86.41/86.61 inference(modus_ponens,[status(thm)],[2790, 2789])).
% 86.41/86.61 tff(2792,plain,
% 86.41/86.61 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)),
% 86.41/86.61 inference(unit_resolution,[status(thm)],[2791, 848, 2788])).
% 86.41/86.61 tff(2793,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s3)), introduced(assumption)).
% 86.41/86.61 tff(2794,plain,
% 86.41/86.61 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 86.41/86.61 inference(rewrite,[status(thm)],[])).
% 86.41/86.61 tff(2795,plain,
% 86.41/86.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 86.41/86.61 inference(quant_inst,[status(thm)],[])).
% 86.41/86.61 tff(2796,plain,
% 86.41/86.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2795, 2794])).
% 86.41/86.62 tff(2797,plain,
% 86.41/86.62 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2796, 1638, 1249])).
% 86.41/86.62 tff(2798,plain,
% 86.41/86.62 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s2))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2799,plain,
% 86.41/86.62 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s2))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2800,plain,
% 86.41/86.62 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s2)),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 86.41/86.62 tff(2801,plain,
% 86.41/86.62 (~node20(c_e_h_2, c_l, s2)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2800, 1535, 2797])).
% 86.41/86.62 tff(2802,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2803,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3)))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2804,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3))),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2803, 2802])).
% 86.41/86.62 tff(2805,plain,
% 86.41/86.62 ((~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3))),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2804, 51, 2801])).
% 86.41/86.62 tff(2806,plain,
% 86.41/86.62 (~node21(c_e_h_2, c_l, s2, s3)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2805, 2793])).
% 86.41/86.62 tff(2807,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2808,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2809,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3)),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 86.41/86.62 tff(2810,plain,
% 86.41/86.62 (node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2809, 81, 582])).
% 86.41/86.62 tff(2811,plain,
% 86.41/86.62 (node22(c_e_h_2, c_l, s2, s3)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2810, 2806])).
% 86.41/86.62 tff(2812,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node22(c_e_h_2, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node22(c_e_h_2, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2813,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node22(c_e_h_2, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2814,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node22(c_e_h_2, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2)),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2813, 2812])).
% 86.41/86.62 tff(2815,plain,
% 86.41/86.62 ($false),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2814, 107, 2342, 2793, 2811])).
% 86.41/86.62 tff(2816,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.62 tff(2817,plain,
% 86.41/86.62 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2818,plain,
% 86.41/86.62 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2819,plain,
% 86.41/86.62 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3)),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 86.41/86.62 tff(2820,plain,
% 86.41/86.62 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2819, 801, 2816])).
% 86.41/86.62 tff(2821,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s4)), introduced(assumption)).
% 86.41/86.62 tff(2822,assumption,(node6(c_e_h_2, c_j, s3, s4)), introduced(assumption)).
% 86.41/86.62 tff(2823,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s3)), introduced(assumption)).
% 86.41/86.62 tff(2824,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2825,plain,
% 86.41/86.62 (((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2826,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4))))),
% 86.41/86.62 inference(monotonicity,[status(thm)],[2825])).
% 86.41/86.62 tff(2827,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4)))),
% 86.41/86.62 inference(transitivity,[status(thm)],[2826, 2824])).
% 86.41/86.62 tff(2828,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2829,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4))),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 86.41/86.62 tff(2830,plain,
% 86.41/86.62 ($false),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2829, 899, 2823, 2821, 2822])).
% 86.41/86.62 tff(2831,plain,((~node6(c_e_h_2, c_j, s3, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.62 tff(2832,plain,
% 86.41/86.62 ((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2831, 2373])).
% 86.41/86.62 tff(2833,plain,
% 86.41/86.62 (~node6(c_e_h_2, c_j, s3, s4)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2832, 2821])).
% 86.41/86.62 tff(2834,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2835,plain,
% 86.41/86.62 ((node6(c_e_h_2, c_j, s3, s4) | node5(c_e_h_2, c_j, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2836,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s3, s4) | node5(c_e_h_2, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4)))),
% 86.41/86.62 inference(monotonicity,[status(thm)],[2835])).
% 86.41/86.62 tff(2837,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s3, s4) | node5(c_e_h_2, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4))),
% 86.41/86.62 inference(transitivity,[status(thm)],[2836, 2834])).
% 86.41/86.62 tff(2838,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s3, s4) | node5(c_e_h_2, c_j, s3, s4) | (~trans(s3, s4)))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2839,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4)),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 86.41/86.62 tff(2840,plain,
% 86.41/86.62 (node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2839, 881, 679])).
% 86.41/86.62 tff(2841,plain,
% 86.41/86.62 (node5(c_e_h_2, c_j, s3, s4)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2840, 2833])).
% 86.41/86.62 tff(2842,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2843,plain,
% 86.41/86.62 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2844,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4))))),
% 86.41/86.62 inference(monotonicity,[status(thm)],[2843])).
% 86.41/86.62 tff(2845,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)))),
% 86.41/86.62 inference(transitivity,[status(thm)],[2844, 2842])).
% 86.41/86.62 tff(2846,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2847,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4))),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 86.41/86.62 tff(2848,plain,
% 86.41/86.62 ($false),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2847, 862, 2821, 2841, 2820, 2792])).
% 86.41/86.62 tff(2849,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.62 tff(2850,plain,
% 86.41/86.62 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2851,plain,
% 86.41/86.62 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2852,plain,
% 86.41/86.62 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 86.41/86.62 tff(2853,plain,
% 86.41/86.62 (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2852, 309, 2849])).
% 86.41/86.62 tff(2854,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s5)), introduced(assumption)).
% 86.41/86.62 tff(2855,assumption,(node18(c_e_h_2, c_h, s4, s5)), introduced(assumption)).
% 86.41/86.62 tff(2856,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node18(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node18(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2857,plain,
% 86.41/86.62 (((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~node18(c_e_h_2, c_h, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node18(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2858,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~node18(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node18(c_e_h_2, c_h, s4, s5))))),
% 86.41/86.62 inference(monotonicity,[status(thm)],[2857])).
% 86.41/86.62 tff(2859,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~node18(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node18(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.62 inference(transitivity,[status(thm)],[2858, 2856])).
% 86.41/86.62 tff(2860,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~node18(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2861,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node18(c_e_h_2, c_h, s4, s5))),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2860, 2859])).
% 86.41/86.62 tff(2862,plain,
% 86.41/86.62 ($false),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2861, 124, 2854, 2442, 2855])).
% 86.41/86.62 tff(2863,plain,((~node18(c_e_h_2, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.62 tff(2864,plain,
% 86.41/86.62 (~node18(c_e_h_2, c_h, s4, s5)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2863, 2854])).
% 86.41/86.62 tff(2865,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s4)), introduced(assumption)).
% 86.41/86.62 tff(2866,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node14(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node14(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2867,plain,
% 86.41/86.62 (((~node14(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node14(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2868,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node14(c_e_h_2, c_h, s4, s5))))),
% 86.41/86.62 inference(monotonicity,[status(thm)],[2867])).
% 86.41/86.62 tff(2869,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node14(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.62 inference(transitivity,[status(thm)],[2868, 2866])).
% 86.41/86.62 tff(2870,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2871,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node14(c_e_h_2, c_h, s4, s5))),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 86.41/86.62 tff(2872,plain,
% 86.41/86.62 ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node14(c_e_h_2, c_h, s4, s5))),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2871, 283])).
% 86.41/86.62 tff(2873,plain,
% 86.41/86.62 (~node14(c_e_h_2, c_h, s4, s5)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2872, 2854, 2865])).
% 86.41/86.62 tff(2874,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s4)), introduced(assumption)).
% 86.41/86.62 tff(2875,assumption,(node15(c_e_h_2, c_h, s4, s5)), introduced(assumption)).
% 86.41/86.62 tff(2876,plain,
% 86.41/86.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 86.41/86.62 inference(rewrite,[status(thm)],[])).
% 86.41/86.62 tff(2877,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 86.41/86.62 inference(quant_inst,[status(thm)],[])).
% 86.41/86.62 tff(2878,plain,
% 86.41/86.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4)),
% 86.41/86.62 inference(modus_ponens,[status(thm)],[2877, 2876])).
% 86.41/86.62 tff(2879,plain,
% 86.41/86.62 ($false),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2878, 173, 2854, 2874, 2875])).
% 86.41/86.62 tff(2880,plain,((~node15(c_e_h_2, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.62 tff(2881,plain,
% 86.41/86.62 (~node15(c_e_h_2, c_h, s4, s5)),
% 86.41/86.62 inference(unit_resolution,[status(thm)],[2880, 2854, 2874])).
% 86.41/86.62 tff(2882,assumption,(~node19(c_e_h_2, c_h, s4, s5)), introduced(assumption)).
% 86.41/86.63 tff(2883,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_h, s4, s5))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2884,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_h, s4, s5))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2885,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_h, s4, s5)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2884, 2883])).
% 86.41/86.63 tff(2886,plain,
% 86.41/86.63 ($false),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2885, 141, 1432, 2882])).
% 86.41/86.63 tff(2887,plain,(node19(c_e_h_2, c_h, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.63 tff(2888,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s4) | (~node19(c_e_h_2, c_h, s4, s5)) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s4) | (~node19(c_e_h_2, c_h, s4, s5)) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2889,plain,
% 86.41/86.63 ((node16(c_e_h_2, c_h, s4) | node14(c_e_h_2, c_h, s4, s5) | node15(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5))) <=> (node16(c_e_h_2, c_h, s4) | (~node19(c_e_h_2, c_h, s4, s5)) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2890,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s4) | node14(c_e_h_2, c_h, s4, s5) | node15(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s4) | (~node19(c_e_h_2, c_h, s4, s5)) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.63 inference(monotonicity,[status(thm)],[2889])).
% 86.41/86.63 tff(2891,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s4) | node14(c_e_h_2, c_h, s4, s5) | node15(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s4) | (~node19(c_e_h_2, c_h, s4, s5)) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5))),
% 86.41/86.63 inference(transitivity,[status(thm)],[2890, 2888])).
% 86.41/86.63 tff(2892,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s4) | node14(c_e_h_2, c_h, s4, s5) | node15(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2893,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s4) | (~node19(c_e_h_2, c_h, s4, s5)) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2892, 2891])).
% 86.41/86.63 tff(2894,plain,
% 86.41/86.63 (node16(c_e_h_2, c_h, s4) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2893, 189, 2887])).
% 86.41/86.63 tff(2895,plain,
% 86.41/86.63 (node16(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2894, 2881, 2873])).
% 86.41/86.63 tff(2896,plain,
% 86.41/86.63 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2897,plain,
% 86.41/86.63 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2898,plain,
% 86.41/86.63 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 86.41/86.63 tff(2899,plain,
% 86.41/86.63 ((~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2898, 228, 2865])).
% 86.41/86.63 tff(2900,plain,
% 86.41/86.63 (m_c_h_element_v_in2(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2899, 2895])).
% 86.41/86.63 tff(2901,plain,
% 86.41/86.63 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2902,plain,
% 86.41/86.63 ((m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | (~node17(c_e_h_2, c_h, s4))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2903,plain,
% 86.41/86.63 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | (~node17(c_e_h_2, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4))))),
% 86.41/86.63 inference(monotonicity,[status(thm)],[2902])).
% 86.41/86.63 tff(2904,plain,
% 86.41/86.63 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | (~node17(c_e_h_2, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)))),
% 86.41/86.63 inference(transitivity,[status(thm)],[2903, 2901])).
% 86.41/86.63 tff(2905,plain,
% 86.41/86.63 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | (~node17(c_e_h_2, c_h, s4)))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2906,plain,
% 86.41/86.63 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2905, 2904])).
% 86.41/86.63 tff(2907,plain,
% 86.41/86.63 ((~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2906, 245, 2865])).
% 86.41/86.63 tff(2908,plain,
% 86.41/86.63 (~node17(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2907, 2900])).
% 86.41/86.63 tff(2909,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s4, s5)) | node18(c_e_h_2, c_h, s4, s5) | node17(c_e_h_2, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s4, s5)) | node18(c_e_h_2, c_h, s4, s5) | node17(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2910,plain,
% 86.41/86.63 ((node17(c_e_h_2, c_h, s4) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5))) <=> ((~node19(c_e_h_2, c_h, s4, s5)) | node18(c_e_h_2, c_h, s4, s5) | node17(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2911,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s4) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s4, s5)) | node18(c_e_h_2, c_h, s4, s5) | node17(c_e_h_2, c_h, s4)))),
% 86.41/86.63 inference(monotonicity,[status(thm)],[2910])).
% 86.41/86.63 tff(2912,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s4) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s4, s5)) | node18(c_e_h_2, c_h, s4, s5) | node17(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(transitivity,[status(thm)],[2911, 2909])).
% 86.41/86.63 tff(2913,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s4) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2914,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s4, s5)) | node18(c_e_h_2, c_h, s4, s5) | node17(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2913, 2912])).
% 86.41/86.63 tff(2915,plain,
% 86.41/86.63 (node18(c_e_h_2, c_h, s4, s5) | node17(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2914, 156, 2887])).
% 86.41/86.63 tff(2916,plain,
% 86.41/86.63 (node18(c_e_h_2, c_h, s4, s5)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2915, 2908])).
% 86.41/86.63 tff(2917,plain,
% 86.41/86.63 ($false),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2861, 124, 2854, 2874, 2916])).
% 86.41/86.63 tff(2918,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | m_c_h_element_v_in1(c_e_h_2, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.63 tff(2919,plain,
% 86.41/86.63 ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2918, 2442])).
% 86.41/86.63 tff(2920,plain,
% 86.41/86.63 (m_c_h_element_v_in1(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2919, 2854])).
% 86.41/86.63 tff(2921,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s4)), introduced(assumption)).
% 86.41/86.63 tff(2922,plain,
% 86.41/86.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2923,plain,
% 86.41/86.63 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4))) <=> ((~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2924,plain,
% 86.41/86.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4)))),
% 86.41/86.63 inference(monotonicity,[status(thm)],[2923])).
% 86.41/86.63 tff(2925,plain,
% 86.41/86.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(transitivity,[status(thm)],[2924, 2922])).
% 86.41/86.63 tff(2926,plain,
% 86.41/86.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2927,plain,
% 86.41/86.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 86.41/86.63 tff(2928,plain,
% 86.41/86.63 ((~node17(c_e_h_2, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4))),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2927, 209, 2921])).
% 86.41/86.63 tff(2929,plain,
% 86.41/86.63 (~node17(c_e_h_2, c_h, s4)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2928, 2920])).
% 86.41/86.63 tff(2930,plain,
% 86.41/86.63 ($false),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2915, 2929, 2864])).
% 86.41/86.63 tff(2931,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.63 tff(2932,plain,
% 86.41/86.63 (~m_c_h_element_v_out(c_e_h_2, c_h, s5)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2931, 2853])).
% 86.41/86.63 tff(2933,plain,
% 86.41/86.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2934,plain,
% 86.41/86.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2935,plain,
% 86.41/86.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 86.41/86.63 tff(2936,plain,
% 86.41/86.63 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2935, 23, 2932])).
% 86.41/86.63 tff(2937,plain,
% 86.41/86.63 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2938,plain,
% 86.41/86.63 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2939,plain,
% 86.41/86.63 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2938, 2937])).
% 86.41/86.63 tff(2940,plain,
% 86.41/86.63 (~node20(c_e_h_2, c_i, s5)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2939, 37, 2936])).
% 86.41/86.63 tff(2941,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s5)), introduced(assumption)).
% 86.41/86.63 tff(2942,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s6)), introduced(assumption)).
% 86.41/86.63 tff(2943,assumption,(node22(c_e_h_2, c_i, s5, s6)), introduced(assumption)).
% 86.41/86.63 tff(2944,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2945,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2946,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2945, 2944])).
% 86.41/86.63 tff(2947,plain,
% 86.41/86.63 ($false),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2946, 107, 2941, 2942, 2943])).
% 86.41/86.63 tff(2948,plain,((~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.63 tff(2949,plain,
% 86.41/86.63 (~node22(c_e_h_2, c_i, s5, s6)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2948, 2942, 2941])).
% 86.41/86.63 tff(2950,assumption,(~node20(c_e_h_2, c_i, s5)), introduced(assumption)).
% 86.41/86.63 tff(2951,assumption,(node21(c_e_h_2, c_i, s5, s6)), introduced(assumption)).
% 86.41/86.63 tff(2952,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node21(c_e_h_2, c_i, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node21(c_e_h_2, c_i, s5, s6)))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2953,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node21(c_e_h_2, c_i, s5, s6)))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2954,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node21(c_e_h_2, c_i, s5, s6))),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2953, 2952])).
% 86.41/86.63 tff(2955,plain,
% 86.41/86.63 ($false),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2954, 51, 2942, 2951, 2950])).
% 86.41/86.63 tff(2956,plain,((~node21(c_e_h_2, c_i, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | node20(c_e_h_2, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.63 tff(2957,plain,
% 86.41/86.63 (~node21(c_e_h_2, c_i, s5, s6)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2956, 2942, 2950])).
% 86.41/86.63 tff(2958,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2959,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2960,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 86.41/86.63 tff(2961,plain,
% 86.41/86.63 (node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2960, 81, 1499])).
% 86.41/86.63 tff(2962,plain,
% 86.41/86.63 ($false),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2961, 2957, 2949])).
% 86.41/86.63 tff(2963,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | node20(c_e_h_2, c_i, s5) | m_and_h_gate_v_out(c_e_h_2, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.63 tff(2964,plain,
% 86.41/86.63 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | node20(c_e_h_2, c_i, s5)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2963, 2464])).
% 86.41/86.63 tff(2965,plain,
% 86.41/86.63 (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2964, 2940])).
% 86.41/86.63 tff(2966,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s6)), introduced(assumption)).
% 86.41/86.63 tff(2967,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s6)), introduced(assumption)).
% 86.41/86.63 tff(2968,plain,
% 86.41/86.63 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2969,plain,
% 86.41/86.63 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2970,plain,
% 86.41/86.63 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 86.41/86.63 tff(2971,plain,
% 86.41/86.63 ($false),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2970, 365, 2967, 2966])).
% 86.41/86.63 tff(2972,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.63 tff(2973,plain,
% 86.41/86.63 (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2972, 2965])).
% 86.41/86.63 tff(2974,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s6)), introduced(assumption)).
% 86.41/86.63 tff(2975,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s7)), introduced(assumption)).
% 86.41/86.63 tff(2976,assumption,(node18(c_e_h_2, c_e, s6, s7)), introduced(assumption)).
% 86.41/86.63 tff(2977,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2978,plain,
% 86.41/86.63 (((~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~node18(c_e_h_2, c_e, s6, s7))) <=> ((~node18(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2979,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~node18(c_e_h_2, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7))))),
% 86.41/86.63 inference(monotonicity,[status(thm)],[2978])).
% 86.41/86.63 tff(2980,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~node18(c_e_h_2, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)))),
% 86.41/86.63 inference(transitivity,[status(thm)],[2979, 2977])).
% 86.41/86.63 tff(2981,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~node18(c_e_h_2, c_e, s6, s7)))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2982,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7))),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2981, 2980])).
% 86.41/86.63 tff(2983,plain,
% 86.41/86.63 ($false),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2982, 124, 2976, 2541, 2975])).
% 86.41/86.63 tff(2984,plain,((~node18(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.63 tff(2985,plain,
% 86.41/86.63 (~node18(c_e_h_2, c_e, s6, s7)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2984, 2975, 2541])).
% 86.41/86.63 tff(2986,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_2, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_2, c_e, s6, s7))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2987,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_2, c_e, s6, s7))),
% 86.41/86.63 inference(quant_inst,[status(thm)],[])).
% 86.41/86.63 tff(2988,plain,
% 86.41/86.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_2, c_e, s6, s7)),
% 86.41/86.63 inference(modus_ponens,[status(thm)],[2987, 2986])).
% 86.41/86.63 tff(2989,plain,
% 86.41/86.63 (node19(c_e_h_2, c_e, s6, s7)),
% 86.41/86.63 inference(unit_resolution,[status(thm)],[2988, 141, 1552])).
% 86.41/86.63 tff(2990,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s6, s7)) | node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s6, s7)) | node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2991,plain,
% 86.41/86.63 ((node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7) | (~node19(c_e_h_2, c_e, s6, s7))) <=> ((~node19(c_e_h_2, c_e, s6, s7)) | node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7))),
% 86.41/86.63 inference(rewrite,[status(thm)],[])).
% 86.41/86.63 tff(2992,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7) | (~node19(c_e_h_2, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s6, s7)) | node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7)))),
% 86.41/86.63 inference(monotonicity,[status(thm)],[2991])).
% 86.41/86.63 tff(2993,plain,
% 86.41/86.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7) | (~node19(c_e_h_2, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s6, s7)) | node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7))),
% 86.41/86.64 inference(transitivity,[status(thm)],[2992, 2990])).
% 86.41/86.64 tff(2994,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7) | (~node19(c_e_h_2, c_e, s6, s7)))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(2995,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s6, s7)) | node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7)),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[2994, 2993])).
% 86.41/86.64 tff(2996,plain,
% 86.41/86.64 (node17(c_e_h_2, c_e, s6) | node18(c_e_h_2, c_e, s6, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2995, 156, 2989])).
% 86.41/86.64 tff(2997,plain,
% 86.41/86.64 (node17(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2996, 2985])).
% 86.41/86.64 tff(2998,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | m_c_h_element_v_in2(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | m_c_h_element_v_in2(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(2999,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | m_c_h_element_v_in2(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3000,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | m_c_h_element_v_in2(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 86.41/86.64 tff(3001,plain,
% 86.41/86.64 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~node17(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3000, 209, 2974])).
% 86.41/86.64 tff(3002,plain,
% 86.41/86.64 (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3001, 2997])).
% 86.41/86.64 tff(3003,assumption,(node15(c_e_h_2, c_e, s6, s7)), introduced(assumption)).
% 86.41/86.64 tff(3004,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | (~node15(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | (~node15(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3005,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | (~node15(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3006,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | (~node15(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3005, 3004])).
% 86.41/86.64 tff(3007,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3006, 173, 3003, 2541, 2975])).
% 86.41/86.64 tff(3008,plain,((~node15(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3009,plain,
% 86.41/86.64 (~node15(c_e_h_2, c_e, s6, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3008, 2975, 2541])).
% 86.41/86.64 tff(3010,assumption,(node16(c_e_h_2, c_e, s6)), introduced(assumption)).
% 86.41/86.64 tff(3011,assumption,(node17(c_e_h_2, c_e, s6)), introduced(assumption)).
% 86.41/86.64 tff(3012,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s6)), introduced(assumption)).
% 86.41/86.64 tff(3013,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | m_c_h_element_v_in2(c_e_h_2, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | m_c_h_element_v_in2(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3014,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | m_c_h_element_v_in2(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3015,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3014, 3013])).
% 86.41/86.64 tff(3016,plain,
% 86.41/86.64 (m_c_h_element_v_in1(c_e_h_2, c_e, s6) | m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3015, 228, 3010])).
% 86.41/86.64 tff(3017,plain,
% 86.41/86.64 (m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3016, 3012])).
% 86.41/86.64 tff(3018,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3019,plain,
% 86.41/86.64 ((m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | (~node17(c_e_h_2, c_e, s6))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3020,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | (~node17(c_e_h_2, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6))))),
% 86.41/86.64 inference(monotonicity,[status(thm)],[3019])).
% 86.41/86.64 tff(3021,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | (~node17(c_e_h_2, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(transitivity,[status(thm)],[3020, 3018])).
% 86.41/86.64 tff(3022,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | (~node17(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3023,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3022, 3021])).
% 86.41/86.64 tff(3024,plain,
% 86.41/86.64 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s6)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3023, 245, 3011])).
% 86.41/86.64 tff(3025,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3024, 3017, 3012])).
% 86.41/86.64 tff(3026,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~node17(c_e_h_2, c_e, s6)) | (~node16(c_e_h_2, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3027,plain,
% 86.41/86.64 (m_c_h_element_v_in1(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3026, 3011, 3010])).
% 86.41/86.64 tff(3028,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3029,plain,
% 86.41/86.64 (((~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3030,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6))))),
% 86.41/86.64 inference(monotonicity,[status(thm)],[3029])).
% 86.41/86.64 tff(3031,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(transitivity,[status(thm)],[3030, 3028])).
% 86.41/86.64 tff(3032,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3033,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~node16(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3032, 3031])).
% 86.41/86.64 tff(3034,plain,
% 86.41/86.64 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s6))),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3033, 263, 3010])).
% 86.41/86.64 tff(3035,plain,
% 86.41/86.64 (~m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3034, 3027])).
% 86.41/86.64 tff(3036,plain,
% 86.41/86.64 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s6)) | m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3000, 209, 3011])).
% 86.41/86.64 tff(3037,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3036, 3035, 3027])).
% 86.41/86.64 tff(3038,plain,((~node17(c_e_h_2, c_e, s6)) | (~node16(c_e_h_2, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3039,plain,
% 86.41/86.64 (~node16(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3038, 2997])).
% 86.41/86.64 tff(3040,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s6, s7)) | node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s6, s7)) | node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3041,plain,
% 86.41/86.64 ((node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7) | (~node19(c_e_h_2, c_e, s6, s7))) <=> ((~node19(c_e_h_2, c_e, s6, s7)) | node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3042,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7) | (~node19(c_e_h_2, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s6, s7)) | node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7)))),
% 86.41/86.64 inference(monotonicity,[status(thm)],[3041])).
% 86.41/86.64 tff(3043,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7) | (~node19(c_e_h_2, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s6, s7)) | node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7))),
% 86.41/86.64 inference(transitivity,[status(thm)],[3042, 3040])).
% 86.41/86.64 tff(3044,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7) | (~node19(c_e_h_2, c_e, s6, s7)))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3045,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s6, s7)) | node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7)),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3044, 3043])).
% 86.41/86.64 tff(3046,plain,
% 86.41/86.64 (node16(c_e_h_2, c_e, s6) | node14(c_e_h_2, c_e, s6, s7) | node15(c_e_h_2, c_e, s6, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3045, 189, 2989])).
% 86.41/86.64 tff(3047,plain,
% 86.41/86.64 (node14(c_e_h_2, c_e, s6, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3046, 3039, 3009])).
% 86.41/86.64 tff(3048,assumption,(node14(c_e_h_2, c_e, s6, s7)), introduced(assumption)).
% 86.41/86.64 tff(3049,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3050,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7)))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3051,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7))),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3050, 3049])).
% 86.41/86.64 tff(3052,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3051, 283, 3048, 3012, 2975])).
% 86.41/86.64 tff(3053,plain,((~node14(c_e_h_2, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s6) | (~m_c_h_element_v_out(c_e_h_2, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3054,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3053, 3047, 3002, 2975])).
% 86.41/86.64 tff(3055,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s6) | m_c_h_element_v_out(c_e_h_2, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3056,plain,
% 86.41/86.64 (~m_c_h_element_v_out(c_e_h_2, c_e, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3055, 2541, 2974])).
% 86.41/86.64 tff(3057,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)), introduced(assumption)).
% 86.41/86.64 tff(3058,plain,
% 86.41/86.64 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2546, 2541])).
% 86.41/86.64 tff(3059,plain,
% 86.41/86.64 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2099, 1048, 2096])).
% 86.41/86.64 tff(3060,plain,
% 86.41/86.64 (~node9(c_e_h_2, c_m, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2105, 1062, 3059])).
% 86.41/86.64 tff(3061,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)), introduced(assumption)).
% 86.41/86.64 tff(3062,plain,
% 86.41/86.64 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2550, 1142, 2108])).
% 86.41/86.64 tff(3063,plain,
% 86.41/86.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2577, 3062, 2553, 2096])).
% 86.41/86.64 tff(3064,assumption,(node11(c_e_h_2, c_n, s7, s8)), introduced(assumption)).
% 86.41/86.64 tff(3065,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)), introduced(assumption)).
% 86.41/86.64 tff(3066,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node11(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node11(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3067,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node11(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3068,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node11(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7))),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3067, 3066])).
% 86.41/86.64 tff(3069,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3068, 1161, 3057, 3065, 3064])).
% 86.41/86.64 tff(3070,plain,((~node11(c_e_h_2, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3071,plain,
% 86.41/86.64 (~node11(c_e_h_2, c_n, s7, s8)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3070, 3063, 3057])).
% 86.41/86.64 tff(3072,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_2, c_n, s7, s8) | node11(c_e_h_2, c_n, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_2, c_n, s7, s8) | node11(c_e_h_2, c_n, s7, s8))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3073,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_2, c_n, s7, s8) | node11(c_e_h_2, c_n, s7, s8))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3074,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_2, c_n, s7, s8) | node11(c_e_h_2, c_n, s7, s8)),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 86.41/86.64 tff(3075,plain,
% 86.41/86.64 (node10(c_e_h_2, c_n, s7, s8) | node11(c_e_h_2, c_n, s7, s8)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3074, 1092, 2152])).
% 86.41/86.64 tff(3076,plain,
% 86.41/86.64 (node10(c_e_h_2, c_n, s7, s8)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3075, 3071])).
% 86.41/86.64 tff(3077,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)), introduced(assumption)).
% 86.41/86.64 tff(3078,assumption,(node10(c_e_h_2, c_n, s7, s8)), introduced(assumption)).
% 86.41/86.64 tff(3079,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3080,plain,
% 86.41/86.64 (((~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3081,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))))),
% 86.41/86.64 inference(monotonicity,[status(thm)],[3080])).
% 86.41/86.64 tff(3082,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)))),
% 86.41/86.64 inference(transitivity,[status(thm)],[3081, 3079])).
% 86.41/86.64 tff(3083,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3084,plain,
% 86.41/86.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~node10(c_e_h_2, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 86.41/86.64 tff(3085,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3084, 1191, 3057, 3078, 3077, 3061])).
% 86.41/86.64 tff(3086,plain,((~node10(c_e_h_2, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3087,plain,
% 86.41/86.64 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3086, 3076, 3057, 3061])).
% 86.41/86.64 tff(3088,plain,
% 86.41/86.64 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3089,plain,
% 86.41/86.64 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3090,plain,
% 86.41/86.64 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3089, 3088])).
% 86.41/86.64 tff(3091,plain,
% 86.41/86.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3090, 1142, 3087])).
% 86.41/86.64 tff(3092,plain,
% 86.41/86.64 (~node11(c_e_h_2, c_m, s6, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2115, 3091, 2108])).
% 86.41/86.64 tff(3093,plain,
% 86.41/86.64 (node10(c_e_h_2, c_m, s6, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2120, 3092])).
% 86.41/86.64 tff(3094,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[2127, 1076, 3091, 3093, 3060])).
% 86.41/86.64 tff(3095,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3096,plain,
% 86.41/86.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3095, 1514])).
% 86.41/86.64 tff(3097,plain,
% 86.41/86.64 (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3096, 3058, 3057, 2096])).
% 86.41/86.64 tff(3098,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)), introduced(assumption)).
% 86.41/86.64 tff(3099,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s7)), introduced(assumption)).
% 86.41/86.64 tff(3100,plain,
% 86.41/86.64 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7) | m_c_h_element_v_out(c_e_h_2, c_e, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7) | m_c_h_element_v_out(c_e_h_2, c_e, s7))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3101,plain,
% 86.41/86.64 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7) | m_c_h_element_v_out(c_e_h_2, c_e, s7))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3102,plain,
% 86.41/86.64 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7) | m_c_h_element_v_out(c_e_h_2, c_e, s7)),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3101, 3100])).
% 86.41/86.64 tff(3103,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3102, 976, 3099, 3098])).
% 86.41/86.64 tff(3104,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s7) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3105,plain,
% 86.41/86.64 ($false),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3104, 3097, 3056])).
% 86.41/86.64 tff(3106,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) | m_c_h_element_v_in2(c_e_h_2, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.64 tff(3107,plain,
% 86.41/86.64 (m_c_h_element_v_out(c_e_h_2, c_e, s6) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3106, 2094])).
% 86.41/86.64 tff(3108,plain,
% 86.41/86.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3107, 2539])).
% 86.41/86.64 tff(3109,plain,
% 86.41/86.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3108, 2973])).
% 86.41/86.64 tff(3110,plain,
% 86.41/86.64 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3111,plain,
% 86.41/86.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3112,plain,
% 86.41/86.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3111, 3110])).
% 86.41/86.64 tff(3113,plain,
% 86.41/86.64 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3112, 1048, 3109])).
% 86.41/86.64 tff(3114,plain,
% 86.41/86.64 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8))),
% 86.41/86.64 inference(rewrite,[status(thm)],[])).
% 86.41/86.64 tff(3115,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8))),
% 86.41/86.64 inference(quant_inst,[status(thm)],[])).
% 86.41/86.64 tff(3116,plain,
% 86.41/86.64 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8)),
% 86.41/86.64 inference(modus_ponens,[status(thm)],[3115, 3114])).
% 86.41/86.64 tff(3117,plain,
% 86.41/86.64 (~node9(c_e_h_2, c_m, s8)),
% 86.41/86.64 inference(unit_resolution,[status(thm)],[3116, 1062, 3113])).
% 86.41/86.64 tff(3118,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)), introduced(assumption)).
% 86.41/86.64 tff(3119,assumption,(~node9(c_e_h_2, c_m, s8)), introduced(assumption)).
% 86.41/86.64 tff(3120,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)), introduced(assumption)).
% 86.41/86.64 tff(3121,assumption,(node11(c_e_h_2, c_m, s8, s9)), introduced(assumption)).
% 86.41/86.64 tff(3122,plain,
% 86.41/86.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | (~node11(c_e_h_2, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | (~node11(c_e_h_2, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3123,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | (~node11(c_e_h_2, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3124,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | (~node11(c_e_h_2, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3123, 3122])).
% 86.41/86.65 tff(3125,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3124, 1130, 3121, 3120, 3118])).
% 86.41/86.65 tff(3126,plain,((~node11(c_e_h_2, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3127,plain,
% 86.41/86.65 (~node11(c_e_h_2, c_m, s8, s9)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3126, 3118, 3120])).
% 86.41/86.65 tff(3128,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_2, c_m, s8, s9) | node11(c_e_h_2, c_m, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_2, c_m, s8, s9) | node11(c_e_h_2, c_m, s8, s9))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3129,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_2, c_m, s8, s9) | node11(c_e_h_2, c_m, s8, s9))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3130,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_2, c_m, s8, s9) | node11(c_e_h_2, c_m, s8, s9)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3129, 3128])).
% 86.41/86.65 tff(3131,plain,
% 86.41/86.65 (node10(c_e_h_2, c_m, s8, s9) | node11(c_e_h_2, c_m, s8, s9)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3130, 1092, 2636])).
% 86.41/86.65 tff(3132,plain,
% 86.41/86.65 (node10(c_e_h_2, c_m, s8, s9)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3131, 3127])).
% 86.41/86.65 tff(3133,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | node9(c_e_h_2, c_m, s8) | (~node10(c_e_h_2, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | node9(c_e_h_2, c_m, s8) | (~node10(c_e_h_2, c_m, s8, s9)))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3134,plain,
% 86.41/86.65 ((node9(c_e_h_2, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | (~node10(c_e_h_2, c_m, s8, s9))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | node9(c_e_h_2, c_m, s8) | (~node10(c_e_h_2, c_m, s8, s9)))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3135,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | (~node10(c_e_h_2, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | node9(c_e_h_2, c_m, s8) | (~node10(c_e_h_2, c_m, s8, s9))))),
% 86.41/86.65 inference(monotonicity,[status(thm)],[3134])).
% 86.41/86.65 tff(3136,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | (~node10(c_e_h_2, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | node9(c_e_h_2, c_m, s8) | (~node10(c_e_h_2, c_m, s8, s9)))),
% 86.41/86.65 inference(transitivity,[status(thm)],[3135, 3133])).
% 86.41/86.65 tff(3137,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | (~node10(c_e_h_2, c_m, s8, s9)))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3138,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | node9(c_e_h_2, c_m, s8) | (~node10(c_e_h_2, c_m, s8, s9))),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3137, 3136])).
% 86.41/86.65 tff(3139,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3138, 1076, 3132, 3119, 3118])).
% 86.41/86.65 tff(3140,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | node9(c_e_h_2, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3141,plain,
% 86.41/86.65 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)) | node9(c_e_h_2, c_m, s8)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3140, 2613])).
% 86.41/86.65 tff(3142,plain,
% 86.41/86.65 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3141, 3117])).
% 86.41/86.65 tff(3143,plain,
% 86.41/86.65 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3144,plain,
% 86.41/86.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3145,plain,
% 86.41/86.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3144, 3143])).
% 86.41/86.65 tff(3146,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3145, 1521, 3142, 2651])).
% 86.41/86.65 tff(3147,plain,(~m_and_h_gate_v_in2(c_e_h_2, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3148,plain,
% 86.41/86.65 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s9))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3149,plain,
% 86.41/86.65 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s9))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3150,plain,
% 86.41/86.65 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s9)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 86.41/86.65 tff(3151,plain,
% 86.41/86.65 (~node20(c_e_h_2, c_r, s9)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3150, 1535, 3147])).
% 86.41/86.65 tff(3152,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | node20(c_e_h_2, c_r, s9) | (~node21(c_e_h_2, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | node20(c_e_h_2, c_r, s9) | (~node21(c_e_h_2, c_r, s9, s10)))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3153,plain,
% 86.41/86.65 ((node20(c_e_h_2, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node21(c_e_h_2, c_r, s9, s10))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | node20(c_e_h_2, c_r, s9) | (~node21(c_e_h_2, c_r, s9, s10)))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3154,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node21(c_e_h_2, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | node20(c_e_h_2, c_r, s9) | (~node21(c_e_h_2, c_r, s9, s10))))),
% 86.41/86.65 inference(monotonicity,[status(thm)],[3153])).
% 86.41/86.65 tff(3155,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node21(c_e_h_2, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | node20(c_e_h_2, c_r, s9) | (~node21(c_e_h_2, c_r, s9, s10)))),
% 86.41/86.65 inference(transitivity,[status(thm)],[3154, 3152])).
% 86.41/86.65 tff(3156,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node21(c_e_h_2, c_r, s9, s10)))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3157,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | node20(c_e_h_2, c_r, s9) | (~node21(c_e_h_2, c_r, s9, s10))),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3156, 3155])).
% 86.41/86.65 tff(3158,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3157, 51, 3151, 2649, 2650])).
% 86.41/86.65 tff(3159,plain,((~node21(c_e_h_2, c_r, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3160,plain,
% 86.41/86.65 (~node21(c_e_h_2, c_r, s9, s10)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3159, 2649])).
% 86.41/86.65 tff(3161,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s9)), introduced(assumption)).
% 86.41/86.65 tff(3162,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node22(c_e_h_2, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node22(c_e_h_2, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3163,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node22(c_e_h_2, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3164,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node22(c_e_h_2, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3163, 3162])).
% 86.41/86.65 tff(3165,plain,
% 86.41/86.65 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | (~node22(c_e_h_2, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3164, 107])).
% 86.41/86.65 tff(3166,plain,
% 86.41/86.65 (~node22(c_e_h_2, c_r, s9, s10)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3165, 2649, 3161])).
% 86.41/86.65 tff(3167,assumption,(~node21(c_e_h_2, c_r, s9, s10)), introduced(assumption)).
% 86.41/86.65 tff(3168,assumption,(~node22(c_e_h_2, c_r, s9, s10)), introduced(assumption)).
% 86.41/86.65 tff(3169,plain,
% 86.41/86.65 (succ(s9, s10) <=> succ(s9, s10)),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3170,axiom,(succ(s9, s10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound10')).
% 86.41/86.65 tff(3171,plain,
% 86.41/86.65 (succ(s9, s10)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 86.41/86.65 tff(3172,plain,
% 86.41/86.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3173,plain,
% 86.41/86.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3174,plain,
% 86.41/86.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 86.41/86.65 tff(3175,plain,
% 86.41/86.65 (trans(s9, s10)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3174, 3171, 64])).
% 86.41/86.65 tff(3176,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_r, s9, s10) | node22(c_e_h_2, c_r, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_r, s9, s10) | node22(c_e_h_2, c_r, s9, s10))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3177,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_r, s9, s10) | node22(c_e_h_2, c_r, s9, s10))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3178,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_r, s9, s10) | node22(c_e_h_2, c_r, s9, s10)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3177, 3176])).
% 86.41/86.65 tff(3179,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3178, 81, 3175, 3168, 3167])).
% 86.41/86.65 tff(3180,plain,(node22(c_e_h_2, c_r, s9, s10) | node21(c_e_h_2, c_r, s9, s10)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3181,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3180, 3166, 3160])).
% 86.41/86.65 tff(3182,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s10)) | m_and_h_gate_v_out(c_e_h_2, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3183,plain,
% 86.41/86.65 (~m_and_h_gate_v_out(c_e_h_2, c_r, s10)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3182, 2648])).
% 86.41/86.65 tff(3184,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s4)), introduced(assumption)).
% 86.41/86.65 tff(3185,assumption,(node21(c_e_h_2, c_l, s3, s4)), introduced(assumption)).
% 86.41/86.65 tff(3186,plain,
% 86.41/86.65 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3187,plain,
% 86.41/86.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3188,plain,
% 86.41/86.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3187, 3186])).
% 86.41/86.65 tff(3189,plain,
% 86.41/86.65 ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3188, 1638])).
% 86.41/86.65 tff(3190,plain,
% 86.41/86.65 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3189, 1321])).
% 86.41/86.65 tff(3191,plain,
% 86.41/86.65 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s3))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3192,plain,
% 86.41/86.65 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s3))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3193,plain,
% 86.41/86.65 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s3)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3192, 3191])).
% 86.41/86.65 tff(3194,plain,
% 86.41/86.65 (~node20(c_e_h_2, c_l, s3)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3193, 1535, 3190])).
% 86.41/86.65 tff(3195,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | node20(c_e_h_2, c_l, s3) | (~node21(c_e_h_2, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | node20(c_e_h_2, c_l, s3) | (~node21(c_e_h_2, c_l, s3, s4)))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3196,plain,
% 86.41/86.65 ((node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node21(c_e_h_2, c_l, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | node20(c_e_h_2, c_l, s3) | (~node21(c_e_h_2, c_l, s3, s4)))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3197,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node21(c_e_h_2, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | node20(c_e_h_2, c_l, s3) | (~node21(c_e_h_2, c_l, s3, s4))))),
% 86.41/86.65 inference(monotonicity,[status(thm)],[3196])).
% 86.41/86.65 tff(3198,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node21(c_e_h_2, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | node20(c_e_h_2, c_l, s3) | (~node21(c_e_h_2, c_l, s3, s4)))),
% 86.41/86.65 inference(transitivity,[status(thm)],[3197, 3195])).
% 86.41/86.65 tff(3199,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node21(c_e_h_2, c_l, s3, s4)))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3200,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | node20(c_e_h_2, c_l, s3) | (~node21(c_e_h_2, c_l, s3, s4))),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 86.41/86.65 tff(3201,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3200, 51, 3184, 3194, 3185])).
% 86.41/86.65 tff(3202,plain,((~node21(c_e_h_2, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3203,plain,
% 86.41/86.65 (~node21(c_e_h_2, c_l, s3, s4)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3202, 3184])).
% 86.41/86.65 tff(3204,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3205,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3206,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3205, 3204])).
% 86.41/86.65 tff(3207,plain,
% 86.41/86.65 (node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3206, 81, 679])).
% 86.41/86.65 tff(3208,plain,
% 86.41/86.65 (node22(c_e_h_2, c_l, s3, s4)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3207, 3203])).
% 86.41/86.65 tff(3209,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node22(c_e_h_2, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node22(c_e_h_2, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3210,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node22(c_e_h_2, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3211,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node22(c_e_h_2, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 86.41/86.65 tff(3212,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3211, 107, 3184, 2816, 3208])).
% 86.41/86.65 tff(3213,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3214,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s4)), introduced(assumption)).
% 86.41/86.65 tff(3215,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s4)), introduced(assumption)).
% 86.41/86.65 tff(3216,plain,
% 86.41/86.65 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3217,plain,
% 86.41/86.65 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3218,plain,
% 86.41/86.65 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3217, 3216])).
% 86.41/86.65 tff(3219,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3218, 801, 3215, 3214])).
% 86.41/86.65 tff(3220,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3221,plain,
% 86.41/86.65 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3220, 3213])).
% 86.41/86.65 tff(3222,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)), introduced(assumption)).
% 86.41/86.65 tff(3223,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s5)), introduced(assumption)).
% 86.41/86.65 tff(3224,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s3)), introduced(assumption)).
% 86.41/86.65 tff(3225,assumption,(node18(c_e_h_1, c_f, s2, s3)), introduced(assumption)).
% 86.41/86.65 tff(3226,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s2)), introduced(assumption)).
% 86.41/86.65 tff(3227,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~node18(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~node18(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3228,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~node18(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3229,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~node18(c_e_h_1, c_f, s2, s3))),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 86.41/86.65 tff(3230,plain,
% 86.41/86.65 ($false),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3229, 124, 3226, 3224, 3225])).
% 86.41/86.65 tff(3231,plain,((~node18(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.65 tff(3232,plain,
% 86.41/86.65 ((~node18(c_e_h_1, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3231, 2751])).
% 86.41/86.65 tff(3233,plain,
% 86.41/86.65 (~node18(c_e_h_1, c_f, s2, s3)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3232, 3224])).
% 86.41/86.65 tff(3234,plain,
% 86.41/86.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))),
% 86.41/86.65 inference(rewrite,[status(thm)],[])).
% 86.41/86.65 tff(3235,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))),
% 86.41/86.65 inference(quant_inst,[status(thm)],[])).
% 86.41/86.65 tff(3236,plain,
% 86.41/86.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2)),
% 86.41/86.65 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 86.41/86.65 tff(3237,plain,
% 86.41/86.65 ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3236, 173])).
% 86.41/86.65 tff(3238,plain,
% 86.41/86.65 ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3))),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3237, 2751])).
% 86.41/86.65 tff(3239,plain,
% 86.41/86.65 (~node15(c_e_h_1, c_f, s2, s3)),
% 86.41/86.65 inference(unit_resolution,[status(thm)],[3238, 3224])).
% 86.41/86.65 tff(3240,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s2)), introduced(assumption)).
% 86.41/86.65 tff(3241,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s1)), introduced(assumption)).
% 86.41/86.65 tff(3242,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s0)), introduced(assumption)).
% 86.41/86.65 tff(3243,plain,
% 86.41/86.65 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3244,plain,
% 86.41/86.66 ($false),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3243, 299, 3242])).
% 86.41/86.66 tff(3245,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.66 tff(3246,plain,
% 86.41/86.66 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3247,plain,
% 86.41/86.66 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3248,plain,
% 86.41/86.66 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3247, 3246])).
% 86.41/86.66 tff(3249,plain,
% 86.41/86.66 (~m_c_h_element_v_in2(c_e_h_1, c_h, s0)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3248, 309, 3245])).
% 86.41/86.66 tff(3250,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s0)), introduced(assumption)).
% 86.41/86.66 tff(3251,assumption,(node18(c_e_h_1, c_h, s0, s1)), introduced(assumption)).
% 86.41/86.66 tff(3252,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0) | (~node18(c_e_h_1, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0) | (~node18(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3253,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0) | (~node18(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3254,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0) | (~node18(c_e_h_1, c_h, s0, s1))),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3253, 3252])).
% 86.41/86.66 tff(3255,plain,
% 86.41/86.66 ($false),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3254, 124, 3241, 2668, 3251])).
% 86.41/86.66 tff(3256,plain,((~node18(c_e_h_1, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.66 tff(3257,plain,
% 86.41/86.66 (~node18(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3256, 3241])).
% 86.41/86.66 tff(3258,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_h, s0, s1))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3259,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_h, s0, s1))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3260,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3259, 3258])).
% 86.41/86.66 tff(3261,plain,
% 86.41/86.66 (node19(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3260, 141, 71])).
% 86.41/86.66 tff(3262,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s0) | node18(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s0) | node18(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3263,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s0) | node18(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3264,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s0) | node18(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1))),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3263, 3262])).
% 86.41/86.66 tff(3265,plain,
% 86.41/86.66 (node17(c_e_h_1, c_h, s0) | node18(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3264, 156, 3261])).
% 86.41/86.66 tff(3266,plain,
% 86.41/86.66 (node17(c_e_h_1, c_h, s0)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3265, 3257])).
% 86.41/86.66 tff(3267,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | (~node17(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | (~node17(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3268,plain,
% 86.41/86.66 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0) | (~node17(c_e_h_1, c_h, s0))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | (~node17(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3269,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0) | (~node17(c_e_h_1, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | (~node17(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0)))),
% 86.41/86.66 inference(monotonicity,[status(thm)],[3268])).
% 86.41/86.66 tff(3270,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0) | (~node17(c_e_h_1, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | (~node17(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))),
% 86.41/86.66 inference(transitivity,[status(thm)],[3269, 3267])).
% 86.41/86.66 tff(3271,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0) | (~node17(c_e_h_1, c_h, s0)))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3272,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | (~node17(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3271, 3270])).
% 86.41/86.66 tff(3273,plain,
% 86.41/86.66 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_c_h_element_v_in2(c_e_h_1, c_h, s0)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3272, 209, 3266])).
% 86.41/86.66 tff(3274,plain,
% 86.41/86.66 (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3273, 3250])).
% 86.41/86.66 tff(3275,assumption,(~node15(c_e_h_1, c_h, s0, s1)), introduced(assumption)).
% 86.41/86.66 tff(3276,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3277,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3278,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | m_c_h_element_v_in2(c_e_h_1, c_h, s0)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3277, 3276])).
% 86.41/86.66 tff(3279,plain,
% 86.41/86.66 (~node16(c_e_h_1, c_h, s0)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3278, 228, 3274, 3250])).
% 86.41/86.66 tff(3280,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s0) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s0) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3281,plain,
% 86.41/86.66 ((node16(c_e_h_1, c_h, s0) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1))) <=> (node16(c_e_h_1, c_h, s0) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3282,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s0) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s0) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(monotonicity,[status(thm)],[3281])).
% 86.41/86.66 tff(3283,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s0) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s0) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1))),
% 86.41/86.66 inference(transitivity,[status(thm)],[3282, 3280])).
% 86.41/86.66 tff(3284,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s0) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3285,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s0) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)) | node14(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 86.41/86.66 tff(3286,plain,
% 86.41/86.66 (node16(c_e_h_1, c_h, s0) | node15(c_e_h_1, c_h, s0, s1) | node14(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3285, 189, 3261])).
% 86.41/86.66 tff(3287,plain,
% 86.41/86.66 (node14(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3286, 3279, 3275])).
% 86.41/86.66 tff(3288,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3289,plain,
% 86.41/86.66 (((~node14(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3290,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1))))),
% 86.41/86.66 inference(monotonicity,[status(thm)],[3289])).
% 86.41/86.66 tff(3291,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 86.41/86.66 inference(transitivity,[status(thm)],[3290, 3288])).
% 86.41/86.66 tff(3292,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3293,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node14(c_e_h_1, c_h, s0, s1))),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3292, 3291])).
% 86.41/86.66 tff(3294,plain,
% 86.41/86.66 ($false),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3293, 283, 3241, 3287, 3274])).
% 86.41/86.66 tff(3295,plain,(m_c_h_element_v_in2(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | node15(c_e_h_1, c_h, s0, s1)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.66 tff(3296,plain,
% 86.41/86.66 ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | node15(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3295, 3249])).
% 86.41/86.66 tff(3297,plain,
% 86.41/86.66 (node15(c_e_h_1, c_h, s0, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3296, 3241])).
% 86.41/86.66 tff(3298,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3299,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3300,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3299, 3298])).
% 86.41/86.66 tff(3301,plain,
% 86.41/86.66 ($false),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3300, 173, 3241, 2668, 3297])).
% 86.41/86.66 tff(3302,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.66 tff(3303,plain,
% 86.41/86.66 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3304,plain,
% 86.41/86.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3305,plain,
% 86.41/86.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3304, 3303])).
% 86.41/86.66 tff(3306,plain,
% 86.41/86.66 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3305, 23, 3302])).
% 86.41/86.66 tff(3307,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3308,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3309,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 86.41/86.66 tff(3310,plain,
% 86.41/86.66 (~node20(c_e_h_1, c_i, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3309, 37, 3306])).
% 86.41/86.66 tff(3311,assumption,(node21(c_e_h_1, c_i, s1, s2)), introduced(assumption)).
% 86.41/86.66 tff(3312,assumption,(~node20(c_e_h_1, c_i, s1)), introduced(assumption)).
% 86.41/86.66 tff(3313,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2)))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3314,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2)))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3315,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2))),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3314, 3313])).
% 86.41/86.66 tff(3316,plain,
% 86.41/86.66 ($false),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3315, 51, 3312, 3240, 3311])).
% 86.41/86.66 tff(3317,plain,((~node21(c_e_h_1, c_i, s1, s2)) | node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.66 tff(3318,plain,
% 86.41/86.66 ((~node21(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3317, 3310])).
% 86.41/86.66 tff(3319,plain,
% 86.41/86.66 (~node21(c_e_h_1, c_i, s1, s2)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3318, 3240])).
% 86.41/86.66 tff(3320,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3321,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3322,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3321, 3320])).
% 86.41/86.66 tff(3323,plain,
% 86.41/86.66 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3322, 107])).
% 86.41/86.66 tff(3324,plain,
% 86.41/86.66 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2))),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3323, 2696])).
% 86.41/86.66 tff(3325,plain,
% 86.41/86.66 (~node22(c_e_h_1, c_i, s1, s2)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3324, 3240])).
% 86.41/86.66 tff(3326,plain,
% 86.41/86.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3327,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3328,plain,
% 86.41/86.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 86.41/86.66 tff(3329,plain,
% 86.41/86.66 ($false),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3328, 81, 344, 3325, 3319])).
% 86.41/86.66 tff(3330,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.66 tff(3331,plain,
% 86.41/86.66 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3332,plain,
% 86.41/86.66 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3333,plain,
% 86.41/86.66 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3332, 3331])).
% 86.41/86.66 tff(3334,plain,
% 86.41/86.66 (~m_c_h_element_v_in2(c_e_h_1, c_f, s2)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3333, 2218, 3330])).
% 86.41/86.66 tff(3335,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s2)), introduced(assumption)).
% 86.41/86.66 tff(3336,assumption,(node17(c_e_h_1, c_f, s2)), introduced(assumption)).
% 86.41/86.66 tff(3337,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | (~node17(c_e_h_1, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | (~node17(c_e_h_1, c_f, s2)))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3338,plain,
% 86.41/86.66 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~node17(c_e_h_1, c_f, s2))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | (~node17(c_e_h_1, c_f, s2)))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3339,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~node17(c_e_h_1, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | (~node17(c_e_h_1, c_f, s2))))),
% 86.41/86.66 inference(monotonicity,[status(thm)],[3338])).
% 86.41/86.66 tff(3340,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~node17(c_e_h_1, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | (~node17(c_e_h_1, c_f, s2)))),
% 86.41/86.66 inference(transitivity,[status(thm)],[3339, 3337])).
% 86.41/86.66 tff(3341,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~node17(c_e_h_1, c_f, s2)))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.66 tff(3342,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | (~node17(c_e_h_1, c_f, s2))),
% 86.41/86.66 inference(modus_ponens,[status(thm)],[3341, 3340])).
% 86.41/86.66 tff(3343,plain,
% 86.41/86.66 (m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2))),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3342, 209, 3336])).
% 86.41/86.66 tff(3344,plain,
% 86.41/86.66 (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)),
% 86.41/86.66 inference(unit_resolution,[status(thm)],[3343, 3335])).
% 86.41/86.66 tff(3345,assumption,(~node15(c_e_h_1, c_f, s2, s3)), introduced(assumption)).
% 86.41/86.66 tff(3346,plain,
% 86.41/86.66 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))),
% 86.41/86.66 inference(rewrite,[status(thm)],[])).
% 86.41/86.66 tff(3347,plain,
% 86.41/86.66 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))),
% 86.41/86.66 inference(quant_inst,[status(thm)],[])).
% 86.41/86.67 tff(3348,plain,
% 86.41/86.67 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_in2(c_e_h_1, c_f, s2)),
% 86.41/86.67 inference(modus_ponens,[status(thm)],[3347, 3346])).
% 86.41/86.67 tff(3349,plain,
% 86.41/86.67 (~node16(c_e_h_1, c_f, s2)),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3348, 228, 3344, 3335])).
% 86.41/86.67 tff(3350,assumption,(~node19(c_e_h_1, c_f, s2, s3)), introduced(assumption)).
% 86.41/86.67 tff(3351,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_f, s2, s3))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3352,plain,
% 86.41/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_f, s2, s3))),
% 86.41/86.67 inference(quant_inst,[status(thm)],[])).
% 86.41/86.67 tff(3353,plain,
% 86.41/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_f, s2, s3)),
% 86.41/86.67 inference(modus_ponens,[status(thm)],[3352, 3351])).
% 86.41/86.67 tff(3354,plain,
% 86.41/86.67 ($false),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3353, 141, 582, 3350])).
% 86.41/86.67 tff(3355,plain,(node19(c_e_h_1, c_f, s2, s3)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.67 tff(3356,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s2, s3) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s2, s3) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3357,plain,
% 86.41/86.67 ((node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3))) <=> (node15(c_e_h_1, c_f, s2, s3) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3358,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s2, s3) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3))))),
% 86.41/86.67 inference(monotonicity,[status(thm)],[3357])).
% 86.41/86.67 tff(3359,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s2, s3) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.67 inference(transitivity,[status(thm)],[3358, 3356])).
% 86.41/86.67 tff(3360,plain,
% 86.41/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.67 inference(quant_inst,[status(thm)],[])).
% 86.41/86.67 tff(3361,plain,
% 86.41/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s2, s3) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3))),
% 86.41/86.67 inference(modus_ponens,[status(thm)],[3360, 3359])).
% 86.41/86.67 tff(3362,plain,
% 86.41/86.67 (node15(c_e_h_1, c_f, s2, s3) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3)),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3361, 189, 3355])).
% 86.41/86.67 tff(3363,plain,
% 86.41/86.67 (node14(c_e_h_1, c_f, s2, s3)),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3362, 3349, 3345])).
% 86.41/86.67 tff(3364,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3365,plain,
% 86.41/86.67 (((~node14(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3))) <=> ((~node14(c_e_h_1, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3366,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2)))),
% 86.41/86.67 inference(monotonicity,[status(thm)],[3365])).
% 86.41/86.67 tff(3367,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2))),
% 86.41/86.67 inference(transitivity,[status(thm)],[3366, 3364])).
% 86.41/86.67 tff(3368,plain,
% 86.41/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)))),
% 86.41/86.67 inference(quant_inst,[status(thm)],[])).
% 86.41/86.67 tff(3369,plain,
% 86.41/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2)),
% 86.41/86.67 inference(modus_ponens,[status(thm)],[3368, 3367])).
% 86.41/86.67 tff(3370,plain,
% 86.41/86.67 ($false),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3369, 283, 3224, 3363, 3344])).
% 86.41/86.67 tff(3371,plain,(m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | node15(c_e_h_1, c_f, s2, s3) | (~node17(c_e_h_1, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 86.41/86.67 tff(3372,plain,
% 86.41/86.67 ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | node15(c_e_h_1, c_f, s2, s3) | (~node17(c_e_h_1, c_f, s2))),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3371, 3334])).
% 86.41/86.67 tff(3373,plain,
% 86.41/86.67 (~node17(c_e_h_1, c_f, s2)),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3372, 3239, 3224])).
% 86.41/86.67 tff(3374,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s2, s3) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s2, s3) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3375,plain,
% 86.41/86.67 ((node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3))) <=> (node18(c_e_h_1, c_f, s2, s3) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3376,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s2, s3) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3))))),
% 86.41/86.67 inference(monotonicity,[status(thm)],[3375])).
% 86.41/86.67 tff(3377,plain,
% 86.41/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s2, s3) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.67 inference(transitivity,[status(thm)],[3376, 3374])).
% 86.41/86.67 tff(3378,plain,
% 86.41/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 86.41/86.67 inference(quant_inst,[status(thm)],[])).
% 86.41/86.67 tff(3379,plain,
% 86.41/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s2, s3) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3))),
% 86.41/86.67 inference(modus_ponens,[status(thm)],[3378, 3377])).
% 86.41/86.67 tff(3380,plain,
% 86.41/86.67 (node18(c_e_h_1, c_f, s2, s3) | node17(c_e_h_1, c_f, s2)),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3379, 156, 3355])).
% 86.41/86.67 tff(3381,plain,
% 86.41/86.67 ($false),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3380, 3373, 3233])).
% 86.41/86.67 tff(3382,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 86.41/86.67 tff(3383,plain,
% 86.41/86.67 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3384,plain,
% 86.41/86.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 86.41/86.67 inference(quant_inst,[status(thm)],[])).
% 86.41/86.67 tff(3385,plain,
% 86.41/86.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)),
% 86.41/86.67 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 86.41/86.67 tff(3386,plain,
% 86.41/86.67 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3385, 1666, 3382])).
% 86.41/86.67 tff(3387,plain,
% 86.41/86.67 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s3))),
% 86.41/86.67 inference(rewrite,[status(thm)],[])).
% 86.41/86.67 tff(3388,plain,
% 86.41/86.67 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s3))),
% 86.41/86.67 inference(quant_inst,[status(thm)],[])).
% 86.41/86.67 tff(3389,plain,
% 86.41/86.67 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s3)),
% 86.41/86.67 inference(modus_ponens,[status(thm)],[3388, 3387])).
% 86.41/86.67 tff(3390,plain,
% 86.41/86.67 (~node20(c_e_h_1, c_q, s3)),
% 86.41/86.67 inference(unit_resolution,[status(thm)],[3389, 37, 3386])).
% 86.48/86.67 tff(3391,assumption,(~node20(c_e_h_1, c_q, s3)), introduced(assumption)).
% 86.48/86.67 tff(3392,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s4)), introduced(assumption)).
% 86.48/86.67 tff(3393,assumption,(node21(c_e_h_1, c_q, s3, s4)), introduced(assumption)).
% 86.48/86.67 tff(3394,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3395,plain,
% 86.48/86.67 ((node20(c_e_h_1, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node21(c_e_h_1, c_q, s3, s4))) <=> (node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3396,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node21(c_e_h_1, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4))))),
% 86.48/86.67 inference(monotonicity,[status(thm)],[3395])).
% 86.48/86.67 tff(3397,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node21(c_e_h_1, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)))),
% 86.48/86.67 inference(transitivity,[status(thm)],[3396, 3394])).
% 86.48/86.67 tff(3398,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node21(c_e_h_1, c_q, s3, s4)))),
% 86.48/86.67 inference(quant_inst,[status(thm)],[])).
% 86.48/86.67 tff(3399,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 86.48/86.67 inference(modus_ponens,[status(thm)],[3398, 3397])).
% 86.48/86.67 tff(3400,plain,
% 86.48/86.67 ($false),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3399, 51, 3392, 3393, 3391])).
% 86.48/86.67 tff(3401,plain,((~node21(c_e_h_1, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | node20(c_e_h_1, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 86.48/86.67 tff(3402,plain,
% 86.48/86.67 (~node21(c_e_h_1, c_q, s3, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3401, 3392, 3391])).
% 86.48/86.67 tff(3403,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3404,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4))),
% 86.48/86.67 inference(quant_inst,[status(thm)],[])).
% 86.48/86.67 tff(3405,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4)),
% 86.48/86.67 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 86.48/86.67 tff(3406,plain,
% 86.48/86.67 (node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3405, 81, 679])).
% 86.48/86.67 tff(3407,plain,
% 86.48/86.67 (node22(c_e_h_1, c_q, s3, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3406, 3402])).
% 86.48/86.67 tff(3408,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s3)), introduced(assumption)).
% 86.48/86.67 tff(3409,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node22(c_e_h_1, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node22(c_e_h_1, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3410,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node22(c_e_h_1, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))),
% 86.48/86.67 inference(quant_inst,[status(thm)],[])).
% 86.48/86.67 tff(3411,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node22(c_e_h_1, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3)),
% 86.48/86.67 inference(modus_ponens,[status(thm)],[3410, 3409])).
% 86.48/86.67 tff(3412,plain,
% 86.48/86.67 ($false),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3411, 107, 3408, 3392, 3407])).
% 86.48/86.67 tff(3413,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3) | node20(c_e_h_1, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 86.48/86.67 tff(3414,plain,
% 86.48/86.67 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3413, 3390])).
% 86.48/86.67 tff(3415,plain,
% 86.48/86.67 (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3414, 2779])).
% 86.48/86.67 tff(3416,plain,
% 86.48/86.67 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s4))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3417,plain,
% 86.48/86.67 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s4))),
% 86.48/86.67 inference(quant_inst,[status(thm)],[])).
% 86.48/86.67 tff(3418,plain,
% 86.48/86.67 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s4)),
% 86.48/86.67 inference(modus_ponens,[status(thm)],[3417, 3416])).
% 86.48/86.67 tff(3419,plain,
% 86.48/86.67 (node3(c_e_h_1, c_e_h_2, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3418, 817, 814])).
% 86.48/86.67 tff(3420,plain,
% 86.48/86.67 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s4)) | (~node3(c_e_h_1, c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s4)) | (~node3(c_e_h_1, c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3421,plain,
% 86.48/86.67 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s4)) | (~node3(c_e_h_1, c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 86.48/86.67 inference(quant_inst,[status(thm)],[])).
% 86.48/86.67 tff(3422,plain,
% 86.48/86.67 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s4)) | (~node3(c_e_h_1, c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4)),
% 86.48/86.67 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 86.48/86.67 tff(3423,plain,
% 86.48/86.67 ((~m_cell_v_ack(c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3422, 836, 3419])).
% 86.48/86.67 tff(3424,plain,
% 86.48/86.67 (~m_cell_v_ack(c_e_h_2, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3423, 3415])).
% 86.48/86.67 tff(3425,plain,
% 86.48/86.67 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)) | m_cell_v_ack(c_e_h_2, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)) | m_cell_v_ack(c_e_h_2, s4))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3426,plain,
% 86.48/86.67 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)) | m_cell_v_ack(c_e_h_2, s4))),
% 86.48/86.67 inference(quant_inst,[status(thm)],[])).
% 86.48/86.67 tff(3427,plain,
% 86.48/86.67 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)) | m_cell_v_ack(c_e_h_2, s4)),
% 86.48/86.67 inference(modus_ponens,[status(thm)],[3426, 3425])).
% 86.48/86.67 tff(3428,plain,
% 86.48/86.67 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3427, 848, 3424])).
% 86.48/86.67 tff(3429,assumption,(node5(c_e_h_2, c_j, s4, s5)), introduced(assumption)).
% 86.48/86.67 tff(3430,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)), introduced(assumption)).
% 86.48/86.67 tff(3431,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3432,plain,
% 86.48/86.67 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3433,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5))))),
% 86.48/86.67 inference(monotonicity,[status(thm)],[3432])).
% 86.48/86.67 tff(3434,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)))),
% 86.48/86.67 inference(transitivity,[status(thm)],[3433, 3431])).
% 86.48/86.67 tff(3435,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))),
% 86.48/86.67 inference(quant_inst,[status(thm)],[])).
% 86.48/86.67 tff(3436,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5))),
% 86.48/86.67 inference(modus_ponens,[status(thm)],[3435, 3434])).
% 86.48/86.67 tff(3437,plain,
% 86.48/86.67 ($false),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3436, 862, 3430, 3223, 3222, 3429])).
% 86.48/86.67 tff(3438,plain,((~node5(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 86.48/86.67 tff(3439,plain,
% 86.48/86.67 ((~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3438, 3428])).
% 86.48/86.67 tff(3440,plain,
% 86.48/86.67 (~node5(c_e_h_2, c_j, s4, s5)),
% 86.48/86.67 inference(unit_resolution,[status(thm)],[3439, 3223, 3222])).
% 86.48/86.67 tff(3441,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3442,plain,
% 86.48/86.67 ((node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5))),
% 86.48/86.67 inference(rewrite,[status(thm)],[])).
% 86.48/86.67 tff(3443,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5)))),
% 86.48/86.67 inference(monotonicity,[status(thm)],[3442])).
% 86.48/86.67 tff(3444,plain,
% 86.48/86.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5))),
% 86.48/86.67 inference(transitivity,[status(thm)],[3443, 3441])).
% 86.48/86.67 tff(3445,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5) | (~trans(s4, s5)))),
% 86.48/86.67 inference(quant_inst,[status(thm)],[])).
% 86.48/86.67 tff(3446,plain,
% 86.48/86.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5)),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3445, 3444])).
% 86.48/86.68 tff(3447,plain,
% 86.48/86.68 (node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3446, 881, 1432])).
% 86.48/86.68 tff(3448,plain,
% 86.48/86.68 (node6(c_e_h_2, c_j, s4, s5)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3447, 3440])).
% 86.48/86.68 tff(3449,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s4)), introduced(assumption)).
% 86.48/86.68 tff(3450,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5)))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3451,plain,
% 86.48/86.68 (((~node6(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5)))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3452,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5))))),
% 86.48/86.68 inference(monotonicity,[status(thm)],[3451])).
% 86.48/86.68 tff(3453,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5)))),
% 86.48/86.68 inference(transitivity,[status(thm)],[3452, 3450])).
% 86.48/86.68 tff(3454,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3455,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5))),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 86.48/86.68 tff(3456,plain,
% 86.48/86.68 ($false),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3455, 899, 3223, 3449, 3448])).
% 86.48/86.68 tff(3457,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 86.48/86.68 tff(3458,plain,
% 86.48/86.68 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3457, 2849])).
% 86.48/86.68 tff(3459,plain,
% 86.48/86.68 (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3458, 3221])).
% 86.48/86.68 tff(3460,plain,
% 86.48/86.68 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3461,plain,
% 86.48/86.68 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3462,plain,
% 86.48/86.68 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5)),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 86.48/86.68 tff(3463,plain,
% 86.48/86.68 (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3462, 309, 3459])).
% 86.48/86.68 tff(3464,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s5)), introduced(assumption)).
% 86.48/86.68 tff(3465,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s6)), introduced(assumption)).
% 86.48/86.68 tff(3466,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s5)), introduced(assumption)).
% 86.48/86.68 tff(3467,assumption,(node18(c_e_h_2, c_h, s5, s6)), introduced(assumption)).
% 86.48/86.68 tff(3468,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3469,plain,
% 86.48/86.68 (((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~node18(c_e_h_2, c_h, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3470,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~node18(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6))))),
% 86.48/86.68 inference(monotonicity,[status(thm)],[3469])).
% 86.48/86.68 tff(3471,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~node18(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(transitivity,[status(thm)],[3470, 3468])).
% 86.48/86.68 tff(3472,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~node18(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3473,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3472, 3471])).
% 86.48/86.68 tff(3474,plain,
% 86.48/86.68 ($false),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3473, 124, 3465, 3464, 3467])).
% 86.48/86.68 tff(3475,plain,((~node18(c_e_h_2, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 86.48/86.68 tff(3476,plain,
% 86.48/86.68 (~node18(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3475, 3464, 3465])).
% 86.48/86.68 tff(3477,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_2, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3478,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3479,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3478, 3477])).
% 86.48/86.68 tff(3480,plain,
% 86.48/86.68 (node19(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3479, 141, 1499])).
% 86.48/86.68 tff(3481,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3482,plain,
% 86.48/86.68 ((node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6))) <=> (node17(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3483,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(monotonicity,[status(thm)],[3482])).
% 86.48/86.68 tff(3484,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(transitivity,[status(thm)],[3483, 3481])).
% 86.48/86.68 tff(3485,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3486,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3485, 3484])).
% 86.48/86.68 tff(3487,plain,
% 86.48/86.68 (node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3486, 156, 3480])).
% 86.48/86.68 tff(3488,plain,
% 86.48/86.68 (node17(c_e_h_2, c_h, s5)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3487, 3476])).
% 86.48/86.68 tff(3489,plain,
% 86.48/86.68 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3490,plain,
% 86.48/86.68 ((m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | (~node17(c_e_h_2, c_h, s5))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3491,plain,
% 86.48/86.68 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | (~node17(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5))))),
% 86.48/86.68 inference(monotonicity,[status(thm)],[3490])).
% 86.48/86.68 tff(3492,plain,
% 86.48/86.68 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | (~node17(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)))),
% 86.48/86.68 inference(transitivity,[status(thm)],[3491, 3489])).
% 86.48/86.68 tff(3493,plain,
% 86.48/86.68 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | (~node17(c_e_h_2, c_h, s5)))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3494,plain,
% 86.48/86.68 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 86.48/86.68 tff(3495,plain,
% 86.48/86.68 (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3494, 245, 3488])).
% 86.48/86.68 tff(3496,plain,
% 86.48/86.68 (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3495, 3466])).
% 86.48/86.68 tff(3497,assumption,(~node16(c_e_h_2, c_h, s5)), introduced(assumption)).
% 86.48/86.68 tff(3498,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3499,plain,
% 86.48/86.68 (((~node14(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3500,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6))))),
% 86.48/86.68 inference(monotonicity,[status(thm)],[3499])).
% 86.48/86.68 tff(3501,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(transitivity,[status(thm)],[3500, 3498])).
% 86.48/86.68 tff(3502,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3503,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3502, 3501])).
% 86.48/86.68 tff(3504,plain,
% 86.48/86.68 (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3503, 283])).
% 86.48/86.68 tff(3505,plain,
% 86.48/86.68 (~node14(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3504, 3465, 3466])).
% 86.48/86.68 tff(3506,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3507,plain,
% 86.48/86.68 ((node16(c_e_h_2, c_h, s5) | node14(c_e_h_2, c_h, s5, s6) | node15(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6))) <=> (node16(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3508,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s5) | node14(c_e_h_2, c_h, s5, s6) | node15(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(monotonicity,[status(thm)],[3507])).
% 86.48/86.68 tff(3509,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s5) | node14(c_e_h_2, c_h, s5, s6) | node15(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6))),
% 86.48/86.68 inference(transitivity,[status(thm)],[3508, 3506])).
% 86.48/86.68 tff(3510,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s5) | node14(c_e_h_2, c_h, s5, s6) | node15(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3511,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s5) | (~node19(c_e_h_2, c_h, s5, s6)) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 86.48/86.68 tff(3512,plain,
% 86.48/86.68 (node16(c_e_h_2, c_h, s5) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3511, 189, 3480])).
% 86.48/86.68 tff(3513,plain,
% 86.48/86.68 (node15(c_e_h_2, c_h, s5, s6)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3512, 3505, 3497])).
% 86.48/86.68 tff(3514,plain,
% 86.48/86.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node15(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node15(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.48/86.68 tff(3515,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node15(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 86.48/86.68 inference(quant_inst,[status(thm)],[])).
% 86.48/86.68 tff(3516,plain,
% 86.48/86.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node15(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)),
% 86.48/86.68 inference(modus_ponens,[status(thm)],[3515, 3514])).
% 86.48/86.68 tff(3517,plain,
% 86.48/86.68 ($false),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3516, 173, 3465, 3464, 3513])).
% 86.48/86.68 tff(3518,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | node16(c_e_h_2, c_h, s5) | m_c_h_element_v_in1(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 86.48/86.68 tff(3519,plain,
% 86.48/86.68 (node16(c_e_h_2, c_h, s5)),
% 86.48/86.68 inference(unit_resolution,[status(thm)],[3518, 3466, 3465, 3464])).
% 86.48/86.68 tff(3520,plain,
% 86.48/86.68 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 86.48/86.68 inference(rewrite,[status(thm)],[])).
% 86.50/86.68 tff(3521,plain,
% 86.50/86.68 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 86.50/86.68 inference(quant_inst,[status(thm)],[])).
% 86.50/86.68 tff(3522,plain,
% 86.50/86.68 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 86.50/86.68 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 86.50/86.68 tff(3523,plain,
% 86.50/86.68 ($false),
% 86.50/86.68 inference(unit_resolution,[status(thm)],[3522, 228, 3466, 3519, 3496])).
% 86.50/86.68 tff(3524,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.68 tff(3525,plain,
% 86.50/86.68 (m_c_h_element_v_in1(c_e_h_2, c_h, s5)),
% 86.50/86.68 inference(unit_resolution,[status(thm)],[3524, 3465, 3464])).
% 86.50/86.68 tff(3526,plain,
% 86.50/86.68 (~node18(c_e_h_2, c_h, s5, s6)),
% 86.50/86.68 inference(unit_resolution,[status(thm)],[3475, 3465, 3464])).
% 86.50/86.68 tff(3527,plain,
% 86.50/86.68 (node17(c_e_h_2, c_h, s5)),
% 86.50/86.68 inference(unit_resolution,[status(thm)],[3487, 3526])).
% 86.50/86.68 tff(3528,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s5)), introduced(assumption)).
% 86.50/86.68 tff(3529,plain,
% 86.50/86.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 86.50/86.68 inference(rewrite,[status(thm)],[])).
% 86.50/86.68 tff(3530,plain,
% 86.50/86.68 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5))) <=> ((~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 86.50/86.68 inference(rewrite,[status(thm)],[])).
% 86.50/86.68 tff(3531,plain,
% 86.50/86.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5)))),
% 86.50/86.68 inference(monotonicity,[status(thm)],[3530])).
% 86.50/86.68 tff(3532,plain,
% 86.50/86.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 86.50/86.69 inference(transitivity,[status(thm)],[3531, 3529])).
% 86.50/86.69 tff(3533,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3534,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 86.50/86.69 tff(3535,plain,
% 86.50/86.69 ((~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5))),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3534, 209, 3528])).
% 86.50/86.69 tff(3536,plain,
% 86.50/86.69 ($false),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3535, 3527, 3525])).
% 86.50/86.69 tff(3537,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | m_c_h_element_v_out(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.69 tff(3538,plain,
% 86.50/86.69 ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3537, 2932])).
% 86.50/86.69 tff(3539,plain,
% 86.50/86.69 (~m_c_h_element_v_out(c_e_h_2, c_h, s6)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3538, 3463])).
% 86.50/86.69 tff(3540,plain,
% 86.50/86.69 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3541,plain,
% 86.50/86.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3542,plain,
% 86.50/86.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s6)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3541, 3540])).
% 86.50/86.69 tff(3543,plain,
% 86.50/86.69 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3542, 23, 3539])).
% 86.50/86.69 tff(3544,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s6))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3545,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s6))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3546,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s6)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3545, 3544])).
% 86.50/86.69 tff(3547,plain,
% 86.50/86.69 (~node20(c_e_h_2, c_i, s6)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3546, 37, 3543])).
% 86.50/86.69 tff(3548,assumption,(~node20(c_e_h_2, c_i, s6)), introduced(assumption)).
% 86.50/86.69 tff(3549,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s7)), introduced(assumption)).
% 86.50/86.69 tff(3550,assumption,(node22(c_e_h_2, c_i, s6, s7)), introduced(assumption)).
% 86.50/86.69 tff(3551,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node22(c_e_h_2, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node22(c_e_h_2, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3552,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node22(c_e_h_2, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3553,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node22(c_e_h_2, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 86.50/86.69 tff(3554,plain,
% 86.50/86.69 ($false),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3553, 107, 3549, 2967, 3550])).
% 86.50/86.69 tff(3555,plain,((~node22(c_e_h_2, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.69 tff(3556,plain,
% 86.50/86.69 (~node22(c_e_h_2, c_i, s6, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3555, 3549, 2967])).
% 86.50/86.69 tff(3557,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3558,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3559,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3558, 3557])).
% 86.50/86.69 tff(3560,plain,
% 86.50/86.69 (node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3559, 81, 1552])).
% 86.50/86.69 tff(3561,plain,
% 86.50/86.69 (node21(c_e_h_2, c_i, s6, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3560, 3556])).
% 86.50/86.69 tff(3562,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node21(c_e_h_2, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node21(c_e_h_2, c_i, s6, s7)))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3563,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node21(c_e_h_2, c_i, s6, s7)))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3564,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node21(c_e_h_2, c_i, s6, s7))),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3563, 3562])).
% 86.50/86.69 tff(3565,plain,
% 86.50/86.69 ($false),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3564, 51, 3549, 3561, 3548])).
% 86.50/86.69 tff(3566,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.69 tff(3567,plain,
% 86.50/86.69 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3566, 2965])).
% 86.50/86.69 tff(3568,plain,
% 86.50/86.69 (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3567, 3547])).
% 86.50/86.69 tff(3569,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s7)), introduced(assumption)).
% 86.50/86.69 tff(3570,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s7)), introduced(assumption)).
% 86.50/86.69 tff(3571,plain,
% 86.50/86.69 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3572,plain,
% 86.50/86.69 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3573,plain,
% 86.50/86.69 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3572, 3571])).
% 86.50/86.69 tff(3574,plain,
% 86.50/86.69 ($false),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3573, 365, 3570, 3569])).
% 86.50/86.69 tff(3575,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.69 tff(3576,plain,
% 86.50/86.69 (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3575, 3568])).
% 86.50/86.69 tff(3577,plain,
% 86.50/86.69 ((~m_c_h_element_v_out(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s6)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3055, 2539])).
% 86.50/86.69 tff(3578,plain,
% 86.50/86.69 (~m_c_h_element_v_out(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3577, 2973])).
% 86.50/86.69 tff(3579,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s8)), introduced(assumption)).
% 86.50/86.69 tff(3580,assumption,(node18(c_e_h_2, c_e, s7, s8)), introduced(assumption)).
% 86.50/86.69 tff(3581,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node18(c_e_h_2, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node18(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3582,plain,
% 86.50/86.69 (((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~node18(c_e_h_2, c_e, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node18(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3583,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~node18(c_e_h_2, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node18(c_e_h_2, c_e, s7, s8))))),
% 86.50/86.69 inference(monotonicity,[status(thm)],[3582])).
% 86.50/86.69 tff(3584,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~node18(c_e_h_2, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node18(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.69 inference(transitivity,[status(thm)],[3583, 3581])).
% 86.50/86.69 tff(3585,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~node18(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3586,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node18(c_e_h_2, c_e, s7, s8))),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3585, 3584])).
% 86.50/86.69 tff(3587,plain,
% 86.50/86.69 ($false),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3586, 124, 3099, 3579, 3580])).
% 86.50/86.69 tff(3588,plain,((~node18(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 86.50/86.69 tff(3589,plain,
% 86.50/86.69 (~node18(c_e_h_2, c_e, s7, s8)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3588, 3579, 3099])).
% 86.50/86.69 tff(3590,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s7)), introduced(assumption)).
% 86.50/86.69 tff(3591,assumption,(node15(c_e_h_2, c_e, s7, s8)), introduced(assumption)).
% 86.50/86.69 tff(3592,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node15(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node15(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3593,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node15(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3594,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | (~node15(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3593, 3592])).
% 86.50/86.69 tff(3595,plain,
% 86.50/86.69 ($false),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3594, 173, 3099, 3579, 3591])).
% 86.50/86.69 tff(3596,plain,((~node15(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 86.50/86.69 tff(3597,plain,
% 86.50/86.69 (~node15(c_e_h_2, c_e, s7, s8)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3596, 3579, 3099])).
% 86.50/86.69 tff(3598,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_2, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_2, c_e, s7, s8))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3599,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_2, c_e, s7, s8))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3600,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_2, c_e, s7, s8)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3599, 3598])).
% 86.50/86.69 tff(3601,plain,
% 86.50/86.69 (node19(c_e_h_2, c_e, s7, s8)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3600, 141, 2152])).
% 86.50/86.69 tff(3602,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s7) | (~node19(c_e_h_2, c_e, s7, s8)) | node18(c_e_h_2, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s7) | (~node19(c_e_h_2, c_e, s7, s8)) | node18(c_e_h_2, c_e, s7, s8))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3603,plain,
% 86.50/86.69 ((node17(c_e_h_2, c_e, s7) | node18(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8))) <=> (node17(c_e_h_2, c_e, s7) | (~node19(c_e_h_2, c_e, s7, s8)) | node18(c_e_h_2, c_e, s7, s8))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3604,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s7) | node18(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s7) | (~node19(c_e_h_2, c_e, s7, s8)) | node18(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.69 inference(monotonicity,[status(thm)],[3603])).
% 86.50/86.69 tff(3605,plain,
% 86.50/86.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s7) | node18(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s7) | (~node19(c_e_h_2, c_e, s7, s8)) | node18(c_e_h_2, c_e, s7, s8))),
% 86.50/86.69 inference(transitivity,[status(thm)],[3604, 3602])).
% 86.50/86.69 tff(3606,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s7) | node18(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3607,plain,
% 86.50/86.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s7) | (~node19(c_e_h_2, c_e, s7, s8)) | node18(c_e_h_2, c_e, s7, s8)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3606, 3605])).
% 86.50/86.69 tff(3608,plain,
% 86.50/86.69 (node17(c_e_h_2, c_e, s7) | node18(c_e_h_2, c_e, s7, s8)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3607, 156, 3601])).
% 86.50/86.69 tff(3609,plain,
% 86.50/86.69 (node17(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3608, 3589])).
% 86.50/86.69 tff(3610,assumption,(node17(c_e_h_2, c_e, s7)), introduced(assumption)).
% 86.50/86.69 tff(3611,assumption,(node16(c_e_h_2, c_e, s7)), introduced(assumption)).
% 86.50/86.69 tff(3612,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s7)), introduced(assumption)).
% 86.50/86.69 tff(3613,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3614,plain,
% 86.50/86.69 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~node17(c_e_h_2, c_e, s7))) <=> ((~node17(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3615,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~node17(c_e_h_2, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7))))),
% 86.50/86.69 inference(monotonicity,[status(thm)],[3614])).
% 86.50/86.69 tff(3616,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~node17(c_e_h_2, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(transitivity,[status(thm)],[3615, 3613])).
% 86.50/86.69 tff(3617,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~node17(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3618,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3617, 3616])).
% 86.50/86.69 tff(3619,plain,
% 86.50/86.69 (m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3618, 209, 3610])).
% 86.50/86.69 tff(3620,plain,
% 86.50/86.69 (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3619, 3612])).
% 86.50/86.69 tff(3621,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | m_c_h_element_v_in2(c_e_h_2, c_e, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | m_c_h_element_v_in2(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3622,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | m_c_h_element_v_in2(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3623,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | m_c_h_element_v_in2(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3622, 3621])).
% 86.50/86.69 tff(3624,plain,
% 86.50/86.69 (m_c_h_element_v_in1(c_e_h_2, c_e, s7) | m_c_h_element_v_in2(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3623, 228, 3611])).
% 86.50/86.69 tff(3625,plain,
% 86.50/86.69 ($false),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3624, 3620, 3612])).
% 86.50/86.69 tff(3626,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s7) | (~node16(c_e_h_2, c_e, s7)) | (~node17(c_e_h_2, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 86.50/86.69 tff(3627,plain,
% 86.50/86.69 (m_c_h_element_v_in2(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3626, 3611, 3610])).
% 86.50/86.69 tff(3628,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3629,plain,
% 86.50/86.69 ((m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node17(c_e_h_2, c_e, s7))) <=> ((~node17(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3630,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node17(c_e_h_2, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(monotonicity,[status(thm)],[3629])).
% 86.50/86.69 tff(3631,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node17(c_e_h_2, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(transitivity,[status(thm)],[3630, 3628])).
% 86.50/86.69 tff(3632,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node17(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3633,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3632, 3631])).
% 86.50/86.69 tff(3634,plain,
% 86.50/86.69 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3633, 245, 3610])).
% 86.50/86.69 tff(3635,plain,
% 86.50/86.69 (m_c_h_element_v_in1(c_e_h_2, c_e, s7)),
% 86.50/86.69 inference(unit_resolution,[status(thm)],[3634, 3627])).
% 86.50/86.69 tff(3636,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3637,plain,
% 86.50/86.69 (((~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(rewrite,[status(thm)],[])).
% 86.50/86.69 tff(3638,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7))))),
% 86.50/86.69 inference(monotonicity,[status(thm)],[3637])).
% 86.50/86.69 tff(3639,plain,
% 86.50/86.69 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(transitivity,[status(thm)],[3638, 3636])).
% 86.50/86.69 tff(3640,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)))),
% 86.50/86.69 inference(quant_inst,[status(thm)],[])).
% 86.50/86.69 tff(3641,plain,
% 86.50/86.69 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~node16(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7))),
% 86.50/86.69 inference(modus_ponens,[status(thm)],[3640, 3639])).
% 86.50/86.69 tff(3642,plain,
% 86.50/86.70 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7))),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3641, 263, 3611])).
% 86.50/86.70 tff(3643,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3642, 3635, 3627])).
% 86.50/86.70 tff(3644,plain,((~node16(c_e_h_2, c_e, s7)) | (~node17(c_e_h_2, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3645,plain,
% 86.50/86.70 (~node16(c_e_h_2, c_e, s7)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3644, 3609])).
% 86.50/86.70 tff(3646,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s7) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)) | node14(c_e_h_2, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s7) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)) | node14(c_e_h_2, c_e, s7, s8))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3647,plain,
% 86.50/86.70 ((node16(c_e_h_2, c_e, s7) | node14(c_e_h_2, c_e, s7, s8) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8))) <=> (node16(c_e_h_2, c_e, s7) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)) | node14(c_e_h_2, c_e, s7, s8))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3648,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s7) | node14(c_e_h_2, c_e, s7, s8) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s7) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)) | node14(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.70 inference(monotonicity,[status(thm)],[3647])).
% 86.50/86.70 tff(3649,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s7) | node14(c_e_h_2, c_e, s7, s8) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s7) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)) | node14(c_e_h_2, c_e, s7, s8))),
% 86.50/86.70 inference(transitivity,[status(thm)],[3648, 3646])).
% 86.50/86.70 tff(3650,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s7) | node14(c_e_h_2, c_e, s7, s8) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3651,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s7) | node15(c_e_h_2, c_e, s7, s8) | (~node19(c_e_h_2, c_e, s7, s8)) | node14(c_e_h_2, c_e, s7, s8)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3650, 3649])).
% 86.50/86.70 tff(3652,plain,
% 86.50/86.70 (node16(c_e_h_2, c_e, s7) | node15(c_e_h_2, c_e, s7, s8) | node14(c_e_h_2, c_e, s7, s8)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3651, 189, 3601])).
% 86.50/86.70 tff(3653,plain,
% 86.50/86.70 (node14(c_e_h_2, c_e, s7, s8)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3652, 3645, 3597])).
% 86.50/86.70 tff(3654,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~node14(c_e_h_2, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~node14(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3655,plain,
% 86.50/86.70 (((~node14(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~node14(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3656,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~node14(c_e_h_2, c_e, s7, s8))))),
% 86.50/86.70 inference(monotonicity,[status(thm)],[3655])).
% 86.50/86.70 tff(3657,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~node14(c_e_h_2, c_e, s7, s8)))),
% 86.50/86.70 inference(transitivity,[status(thm)],[3656, 3654])).
% 86.50/86.70 tff(3658,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3659,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | (~node14(c_e_h_2, c_e, s7, s8))),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3658, 3657])).
% 86.50/86.70 tff(3660,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3659, 283, 3579, 3653, 3590])).
% 86.50/86.70 tff(3661,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s7) | m_c_h_element_v_out(c_e_h_2, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3662,plain,
% 86.50/86.70 (m_c_h_element_v_in1(c_e_h_2, c_e, s7)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3661, 3579, 3099])).
% 86.50/86.70 tff(3663,plain,
% 86.50/86.70 ((~node17(c_e_h_2, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s7))),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3618, 209, 3612])).
% 86.50/86.70 tff(3664,plain,
% 86.50/86.70 (~node17(c_e_h_2, c_e, s7)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3663, 3662])).
% 86.50/86.70 tff(3665,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3608, 3664, 3589])).
% 86.50/86.70 tff(3666,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7) | m_c_h_element_v_out(c_e_h_2, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3667,plain,
% 86.50/86.70 ((~m_c_h_element_v_out(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s7)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3666, 3578])).
% 86.50/86.70 tff(3668,plain,
% 86.50/86.70 (~m_c_h_element_v_out(c_e_h_2, c_e, s8)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3667, 3576])).
% 86.50/86.70 tff(3669,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)), introduced(assumption)).
% 86.50/86.70 tff(3670,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s8)), introduced(assumption)).
% 86.50/86.70 tff(3671,plain,
% 86.50/86.70 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8) | m_c_h_element_v_out(c_e_h_2, c_e, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8) | m_c_h_element_v_out(c_e_h_2, c_e, s8))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3672,plain,
% 86.50/86.70 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8) | m_c_h_element_v_out(c_e_h_2, c_e, s8))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3673,plain,
% 86.50/86.70 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8) | m_c_h_element_v_out(c_e_h_2, c_e, s8)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3672, 3671])).
% 86.50/86.70 tff(3674,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3673, 976, 3670, 3669])).
% 86.50/86.70 tff(3675,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8) | m_c_h_element_v_out(c_e_h_2, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3676,plain,
% 86.50/86.70 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3675, 3668])).
% 86.50/86.70 tff(3677,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)), introduced(assumption)).
% 86.50/86.70 tff(3678,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)), introduced(assumption)).
% 86.50/86.70 tff(3679,plain,
% 86.50/86.70 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s8)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3112, 1048, 3678])).
% 86.50/86.70 tff(3680,plain,
% 86.50/86.70 (~node9(c_e_h_2, c_m, s8)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3116, 1062, 3679])).
% 86.50/86.70 tff(3681,plain,
% 86.50/86.70 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3140, 3120, 3680])).
% 86.50/86.70 tff(3682,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)), introduced(assumption)).
% 86.50/86.70 tff(3683,assumption,(~node9(c_e_h_2, c_m, s9)), introduced(assumption)).
% 86.50/86.70 tff(3684,assumption,(node10(c_e_h_2, c_m, s9, s10)), introduced(assumption)).
% 86.50/86.70 tff(3685,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)) | node9(c_e_h_2, c_m, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)) | node9(c_e_h_2, c_m, s9))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3686,plain,
% 86.50/86.70 ((node9(c_e_h_2, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)) | node9(c_e_h_2, c_m, s9))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3687,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)) | node9(c_e_h_2, c_m, s9)))),
% 86.50/86.70 inference(monotonicity,[status(thm)],[3686])).
% 86.50/86.70 tff(3688,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)) | node9(c_e_h_2, c_m, s9))),
% 86.50/86.70 inference(transitivity,[status(thm)],[3687, 3685])).
% 86.50/86.70 tff(3689,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3690,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node10(c_e_h_2, c_m, s9, s10)) | node9(c_e_h_2, c_m, s9)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3689, 3688])).
% 86.50/86.70 tff(3691,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3690, 1076, 3677, 3684, 3683])).
% 86.50/86.70 tff(3692,plain,((~node10(c_e_h_2, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | node9(c_e_h_2, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3693,plain,
% 86.50/86.70 (~node10(c_e_h_2, c_m, s9, s10)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3692, 3677, 3683])).
% 86.50/86.70 tff(3694,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_2, c_m, s9, s10) | node11(c_e_h_2, c_m, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_2, c_m, s9, s10) | node11(c_e_h_2, c_m, s9, s10))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3695,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_2, c_m, s9, s10) | node11(c_e_h_2, c_m, s9, s10))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3696,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_2, c_m, s9, s10) | node11(c_e_h_2, c_m, s9, s10)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3695, 3694])).
% 86.50/86.70 tff(3697,plain,
% 86.50/86.70 (node10(c_e_h_2, c_m, s9, s10) | node11(c_e_h_2, c_m, s9, s10)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3696, 1092, 3175])).
% 86.50/86.70 tff(3698,plain,
% 86.50/86.70 (node11(c_e_h_2, c_m, s9, s10)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3697, 3693])).
% 86.50/86.70 tff(3699,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node11(c_e_h_2, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node11(c_e_h_2, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3700,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node11(c_e_h_2, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3701,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~node11(c_e_h_2, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3700, 3699])).
% 86.50/86.70 tff(3702,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3701, 1130, 3677, 3698, 3682])).
% 86.50/86.70 tff(3703,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9) | node9(c_e_h_2, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3704,plain,
% 86.50/86.70 (node9(c_e_h_2, c_m, s9)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3703, 3681, 3677])).
% 86.50/86.70 tff(3705,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)), introduced(assumption)).
% 86.50/86.70 tff(3706,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)), introduced(assumption)).
% 86.50/86.70 tff(3707,plain,
% 86.50/86.70 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3708,plain,
% 86.50/86.70 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3709,plain,
% 86.50/86.70 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3708, 3707])).
% 86.50/86.70 tff(3710,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3709, 1142, 3120, 3706])).
% 86.50/86.70 tff(3711,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3712,plain,
% 86.50/86.70 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3711, 3120])).
% 86.50/86.70 tff(3713,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)), introduced(assumption)).
% 86.50/86.70 tff(3714,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)), introduced(assumption)).
% 86.50/86.70 tff(3715,assumption,(node10(c_e_h_2, c_n, s8, s9)), introduced(assumption)).
% 86.50/86.70 tff(3716,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3717,plain,
% 86.50/86.70 (((~node10(c_e_h_2, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)) <=> ((~node10(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3718,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8))))),
% 86.50/86.70 inference(monotonicity,[status(thm)],[3717])).
% 86.50/86.70 tff(3719,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)))),
% 86.50/86.70 inference(transitivity,[status(thm)],[3718, 3716])).
% 86.50/86.70 tff(3720,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3721,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8))),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3720, 3719])).
% 86.50/86.70 tff(3722,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3721, 1191, 3714, 3715, 3705, 3713])).
% 86.50/86.70 tff(3723,plain,((~node10(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3724,plain,
% 86.50/86.70 (~node10(c_e_h_2, c_n, s8, s9)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3723, 3714, 3705, 3713])).
% 86.50/86.70 tff(3725,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_2, c_n, s8, s9) | node11(c_e_h_2, c_n, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_2, c_n, s8, s9) | node11(c_e_h_2, c_n, s8, s9))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3726,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_2, c_n, s8, s9) | node11(c_e_h_2, c_n, s8, s9))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3727,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_2, c_n, s8, s9) | node11(c_e_h_2, c_n, s8, s9)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3726, 3725])).
% 86.50/86.70 tff(3728,plain,
% 86.50/86.70 (node10(c_e_h_2, c_n, s8, s9) | node11(c_e_h_2, c_n, s8, s9)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3727, 1092, 2636])).
% 86.50/86.70 tff(3729,plain,
% 86.50/86.70 (node11(c_e_h_2, c_n, s8, s9)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3728, 3724])).
% 86.50/86.70 tff(3730,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~node11(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3731,plain,
% 86.50/86.70 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~node11(c_e_h_2, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))) <=> ((~node11(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3732,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~node11(c_e_h_2, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~node11(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))))),
% 86.50/86.70 inference(monotonicity,[status(thm)],[3731])).
% 86.50/86.70 tff(3733,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~node11(c_e_h_2, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))),
% 86.50/86.70 inference(transitivity,[status(thm)],[3732, 3730])).
% 86.50/86.70 tff(3734,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~node11(c_e_h_2, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3735,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_2, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3734, 3733])).
% 86.50/86.70 tff(3736,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3735, 1161, 3714, 3729, 3678])).
% 86.50/86.70 tff(3737,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3738,plain,
% 86.50/86.70 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3737, 3712, 3705, 3678])).
% 86.50/86.70 tff(3739,plain,
% 86.50/86.70 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3740,plain,
% 86.50/86.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3741,plain,
% 86.50/86.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9))),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 86.50/86.70 tff(3742,plain,
% 86.50/86.70 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3741, 1048, 3738])).
% 86.50/86.70 tff(3743,plain,
% 86.50/86.70 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3744,plain,
% 86.50/86.70 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3745,plain,
% 86.50/86.70 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s9)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3744, 3743])).
% 86.50/86.70 tff(3746,plain,
% 86.50/86.70 ($false),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3745, 1062, 3742, 3704])).
% 86.50/86.70 tff(3747,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 86.50/86.70 tff(3748,plain,
% 86.50/86.70 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3747, 2613])).
% 86.50/86.70 tff(3749,plain,
% 86.50/86.70 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8))),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3748, 3109])).
% 86.50/86.70 tff(3750,plain,
% 86.50/86.70 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3749, 3676])).
% 86.50/86.70 tff(3751,plain,
% 86.50/86.70 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3752,plain,
% 86.50/86.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3753,plain,
% 86.50/86.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3752, 3751])).
% 86.50/86.70 tff(3754,plain,
% 86.50/86.70 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s10)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3753, 1521, 3750])).
% 86.50/86.70 tff(3755,plain,
% 86.50/86.70 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s10))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3756,plain,
% 86.50/86.70 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s10))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3757,plain,
% 86.50/86.70 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s10)),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3756, 3755])).
% 86.50/86.70 tff(3758,plain,
% 86.50/86.70 (~node20(c_e_h_2, c_r, s10)),
% 86.50/86.70 inference(unit_resolution,[status(thm)],[3757, 1535, 3754])).
% 86.50/86.70 tff(3759,assumption,(~node20(c_e_h_2, c_r, s10)), introduced(assumption)).
% 86.50/86.70 tff(3760,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s11)), introduced(assumption)).
% 86.50/86.70 tff(3761,plain,
% 86.50/86.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node21(c_e_h_2, c_r, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node21(c_e_h_2, c_r, s10, s11)))),
% 86.50/86.70 inference(rewrite,[status(thm)],[])).
% 86.50/86.70 tff(3762,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node21(c_e_h_2, c_r, s10, s11)))),
% 86.50/86.70 inference(quant_inst,[status(thm)],[])).
% 86.50/86.70 tff(3763,plain,
% 86.50/86.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node21(c_e_h_2, c_r, s10, s11))),
% 86.50/86.70 inference(modus_ponens,[status(thm)],[3762, 3761])).
% 86.50/86.70 tff(3764,plain,
% 86.50/86.70 (node20(c_e_h_2, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node21(c_e_h_2, c_r, s10, s11))),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3763, 51])).
% 86.50/86.71 tff(3765,plain,
% 86.50/86.71 (~node21(c_e_h_2, c_r, s10, s11)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3764, 3760, 3759])).
% 86.50/86.71 tff(3766,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s10)), introduced(assumption)).
% 86.50/86.71 tff(3767,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node22(c_e_h_2, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_r, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node22(c_e_h_2, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_r, s10))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3768,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node22(c_e_h_2, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_r, s10))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3769,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node22(c_e_h_2, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_r, s10)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3768, 3767])).
% 86.50/86.71 tff(3770,plain,
% 86.50/86.71 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | (~node22(c_e_h_2, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_r, s10)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3769, 107])).
% 86.50/86.71 tff(3771,plain,
% 86.50/86.71 (~node22(c_e_h_2, c_r, s10, s11)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3770, 3760, 3766])).
% 86.50/86.71 tff(3772,plain,
% 86.50/86.71 (succ(s10, s11) <=> succ(s10, s11)),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3773,axiom,(succ(s10, s11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound11')).
% 86.50/86.71 tff(3774,plain,
% 86.50/86.71 (succ(s10, s11)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3773, 3772])).
% 86.50/86.71 tff(3775,plain,
% 86.50/86.71 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3776,plain,
% 86.50/86.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3777,plain,
% 86.50/86.71 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3776, 3775])).
% 86.50/86.71 tff(3778,plain,
% 86.50/86.71 (trans(s10, s11)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3777, 3774, 64])).
% 86.50/86.71 tff(3779,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_2, c_r, s10, s11) | node22(c_e_h_2, c_r, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_2, c_r, s10, s11) | node22(c_e_h_2, c_r, s10, s11))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3780,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_2, c_r, s10, s11) | node22(c_e_h_2, c_r, s10, s11))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3781,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_2, c_r, s10, s11) | node22(c_e_h_2, c_r, s10, s11)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3780, 3779])).
% 86.50/86.71 tff(3782,plain,
% 86.50/86.71 (node21(c_e_h_2, c_r, s10, s11) | node22(c_e_h_2, c_r, s10, s11)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3781, 81, 3778])).
% 86.50/86.71 tff(3783,plain,
% 86.50/86.71 ($false),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3782, 3771, 3765])).
% 86.50/86.71 tff(3784,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | m_and_h_gate_v_out(c_e_h_2, c_r, s10) | node20(c_e_h_2, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.71 tff(3785,plain,
% 86.50/86.71 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s11)) | m_and_h_gate_v_out(c_e_h_2, c_r, s10)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3784, 3758])).
% 86.50/86.71 tff(3786,plain,
% 86.50/86.71 (~m_and_h_gate_v_out(c_e_h_2, c_r, s11)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3785, 3183])).
% 86.50/86.71 tff(3787,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s5)), introduced(assumption)).
% 86.50/86.71 tff(3788,assumption,(node21(c_e_h_2, c_l, s4, s5)), introduced(assumption)).
% 86.50/86.71 tff(3789,plain,
% 86.50/86.71 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3790,plain,
% 86.50/86.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3791,plain,
% 86.50/86.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3790, 3789])).
% 86.50/86.71 tff(3792,plain,
% 86.50/86.71 ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3791, 1638])).
% 86.50/86.71 tff(3793,plain,
% 86.50/86.71 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3792, 1393])).
% 86.50/86.71 tff(3794,plain,
% 86.50/86.71 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s4))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3795,plain,
% 86.50/86.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s4))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3796,plain,
% 86.50/86.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s4)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3795, 3794])).
% 86.50/86.71 tff(3797,plain,
% 86.50/86.71 (~node20(c_e_h_2, c_l, s4)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3796, 1535, 3793])).
% 86.50/86.71 tff(3798,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node21(c_e_h_2, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node21(c_e_h_2, c_l, s4, s5)))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3799,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node21(c_e_h_2, c_l, s4, s5)))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3800,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node21(c_e_h_2, c_l, s4, s5))),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3799, 3798])).
% 86.50/86.71 tff(3801,plain,
% 86.50/86.71 ($false),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3800, 51, 3797, 3787, 3788])).
% 86.50/86.71 tff(3802,plain,((~node21(c_e_h_2, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5))), inference(lemma,lemma(discharge,[]))).
% 86.50/86.71 tff(3803,plain,
% 86.50/86.71 (~node21(c_e_h_2, c_l, s4, s5)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3802, 3787])).
% 86.50/86.71 tff(3804,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3805,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3806,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3805, 3804])).
% 86.50/86.71 tff(3807,plain,
% 86.50/86.71 ((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3806, 107])).
% 86.50/86.71 tff(3808,plain,
% 86.50/86.71 (~node22(c_e_h_2, c_l, s4, s5)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3807, 3787, 3214])).
% 86.50/86.71 tff(3809,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3810,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3811,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 86.50/86.71 tff(3812,plain,
% 86.50/86.71 ($false),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3811, 81, 1432, 3808, 3803])).
% 86.50/86.71 tff(3813,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 86.50/86.71 tff(3814,plain,
% 86.50/86.71 (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3813, 3213])).
% 86.50/86.71 tff(3815,plain,
% 86.50/86.71 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3816,plain,
% 86.50/86.71 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3817,plain,
% 86.50/86.71 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3816, 3815])).
% 86.50/86.71 tff(3818,plain,
% 86.50/86.71 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3817, 801, 3814])).
% 86.50/86.71 tff(3819,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s8)), introduced(assumption)).
% 86.50/86.71 tff(3820,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), introduced(assumption)).
% 86.50/86.71 tff(3821,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s5)), introduced(assumption)).
% 86.50/86.71 tff(3822,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s3)), introduced(assumption)).
% 86.50/86.71 tff(3823,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3824,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3825,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 86.50/86.71 tff(3826,plain,
% 86.50/86.71 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3))),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3825, 107, 3330])).
% 86.50/86.71 tff(3827,plain,
% 86.50/86.71 (~node22(c_e_h_1, c_i, s2, s3)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3826, 3822])).
% 86.50/86.71 tff(3828,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3829,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3))),
% 86.50/86.71 inference(quant_inst,[status(thm)],[])).
% 86.50/86.71 tff(3830,plain,
% 86.50/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3)),
% 86.50/86.71 inference(modus_ponens,[status(thm)],[3829, 3828])).
% 86.50/86.71 tff(3831,plain,
% 86.50/86.71 (node21(c_e_h_1, c_i, s2, s3)),
% 86.50/86.71 inference(unit_resolution,[status(thm)],[3830, 81, 582, 3827])).
% 86.50/86.71 tff(3832,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s2)), introduced(assumption)).
% 86.50/86.71 tff(3833,assumption,(node18(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 86.50/86.71 tff(3834,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3835,plain,
% 86.50/86.71 (((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2))) <=> ((~node18(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 86.50/86.71 inference(rewrite,[status(thm)],[])).
% 86.50/86.71 tff(3836,plain,
% 86.50/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)))),
% 86.53/86.71 inference(monotonicity,[status(thm)],[3835])).
% 86.53/86.71 tff(3837,plain,
% 86.53/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 86.53/86.71 inference(transitivity,[status(thm)],[3836, 3834])).
% 86.53/86.71 tff(3838,plain,
% 86.53/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3839,plain,
% 86.53/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)),
% 86.53/86.71 inference(modus_ponens,[status(thm)],[3838, 3837])).
% 86.53/86.71 tff(3840,plain,
% 86.53/86.71 ($false),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3839, 124, 3832, 3302, 3833])).
% 86.53/86.71 tff(3841,plain,((~node18(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 86.53/86.71 tff(3842,plain,
% 86.53/86.71 (~node18(c_e_h_1, c_h, s1, s2)),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3841, 3832])).
% 86.53/86.71 tff(3843,assumption,(~node19(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 86.53/86.71 tff(3844,plain,
% 86.53/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_h, s1, s2))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3845,plain,
% 86.53/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_h, s1, s2))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3846,plain,
% 86.53/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_h, s1, s2)),
% 86.53/86.71 inference(modus_ponens,[status(thm)],[3845, 3844])).
% 86.53/86.71 tff(3847,plain,
% 86.53/86.71 ($false),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3846, 141, 344, 3843])).
% 86.53/86.71 tff(3848,plain,(node19(c_e_h_1, c_h, s1, s2)), inference(lemma,lemma(discharge,[]))).
% 86.53/86.71 tff(3849,plain,
% 86.53/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node17(c_e_h_1, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node17(c_e_h_1, c_h, s1))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3850,plain,
% 86.53/86.71 ((node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2))) <=> (node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node17(c_e_h_1, c_h, s1))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3851,plain,
% 86.53/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node17(c_e_h_1, c_h, s1)))),
% 86.53/86.71 inference(monotonicity,[status(thm)],[3850])).
% 86.53/86.71 tff(3852,plain,
% 86.53/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node17(c_e_h_1, c_h, s1))),
% 86.53/86.71 inference(transitivity,[status(thm)],[3851, 3849])).
% 86.53/86.71 tff(3853,plain,
% 86.53/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3854,plain,
% 86.53/86.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)) | node17(c_e_h_1, c_h, s1)),
% 86.53/86.71 inference(modus_ponens,[status(thm)],[3853, 3852])).
% 86.53/86.71 tff(3855,plain,
% 86.53/86.71 (node18(c_e_h_1, c_h, s1, s2) | node17(c_e_h_1, c_h, s1)),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3854, 156, 3848])).
% 86.53/86.71 tff(3856,plain,
% 86.53/86.71 (node17(c_e_h_1, c_h, s1)),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3855, 3842])).
% 86.53/86.71 tff(3857,assumption,(~node3(c_e_h_3, c_e_h_1, s0)), introduced(assumption)).
% 86.53/86.71 tff(3858,plain,
% 86.53/86.71 (m_cell_v_left(c_e_h_3, c_e_h_1) <=> m_cell_v_left(c_e_h_3, c_e_h_1)),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3859,axiom,(m_cell_v_left(c_e_h_3, c_e_h_1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_7')).
% 86.53/86.71 tff(3860,plain,
% 86.53/86.71 (m_cell_v_left(c_e_h_3, c_e_h_1)),
% 86.53/86.71 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 86.53/86.71 tff(3861,plain,
% 86.53/86.71 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3862,plain,
% 86.53/86.71 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3863,plain,
% 86.53/86.71 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0)),
% 86.53/86.71 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 86.53/86.71 tff(3864,plain,
% 86.53/86.71 ($false),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3863, 3860, 814, 3857])).
% 86.53/86.71 tff(3865,plain,(node3(c_e_h_3, c_e_h_1, s0)), inference(lemma,lemma(discharge,[]))).
% 86.53/86.71 tff(3866,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s0)), introduced(assumption)).
% 86.53/86.71 tff(3867,plain,
% 86.53/86.71 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3868,plain,
% 86.53/86.71 ($false),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3867, 94, 3866])).
% 86.53/86.71 tff(3869,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 86.53/86.71 tff(3870,plain,
% 86.53/86.71 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3871,plain,
% 86.53/86.71 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3872,plain,
% 86.53/86.71 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 86.53/86.71 inference(modus_ponens,[status(thm)],[3871, 3870])).
% 86.53/86.71 tff(3873,plain,
% 86.53/86.71 ((~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3872, 836])).
% 86.53/86.71 tff(3874,plain,
% 86.53/86.71 (~m_cell_v_ack(c_e_h_1, s0)),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3873, 3869, 3865])).
% 86.53/86.71 tff(3875,plain,
% 86.53/86.71 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3876,plain,
% 86.53/86.71 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3877,plain,
% 86.53/86.71 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0)),
% 86.53/86.71 inference(modus_ponens,[status(thm)],[3876, 3875])).
% 86.53/86.71 tff(3878,plain,
% 86.53/86.71 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3877, 848, 3874])).
% 86.53/86.71 tff(3879,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s0)), introduced(assumption)).
% 86.53/86.71 tff(3880,plain,
% 86.53/86.71 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3881,plain,
% 86.53/86.71 ($false),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3880, 94, 3879])).
% 86.53/86.71 tff(3882,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 86.53/86.71 tff(3883,plain,
% 86.53/86.71 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3884,plain,
% 86.53/86.71 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 86.53/86.71 inference(quant_inst,[status(thm)],[])).
% 86.53/86.71 tff(3885,plain,
% 86.53/86.71 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0)),
% 86.53/86.71 inference(modus_ponens,[status(thm)],[3884, 3883])).
% 86.53/86.71 tff(3886,plain,
% 86.53/86.71 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)),
% 86.53/86.71 inference(unit_resolution,[status(thm)],[3885, 801, 3882])).
% 86.53/86.71 tff(3887,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s1)), introduced(assumption)).
% 86.53/86.71 tff(3888,assumption,(node6(c_e_h_1, c_j, s0, s1)), introduced(assumption)).
% 86.53/86.71 tff(3889,plain,
% 86.53/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3890,plain,
% 86.53/86.71 (((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 86.53/86.71 inference(rewrite,[status(thm)],[])).
% 86.53/86.71 tff(3891,plain,
% 86.53/86.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0)))),
% 86.53/86.72 inference(monotonicity,[status(thm)],[3890])).
% 86.53/86.72 tff(3892,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 86.53/86.72 inference(transitivity,[status(thm)],[3891, 3889])).
% 86.53/86.72 tff(3893,plain,
% 86.53/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3894,plain,
% 86.53/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0)),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3893, 3892])).
% 86.53/86.72 tff(3895,plain,
% 86.53/86.72 ($false),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3894, 899, 3888, 3887, 3245])).
% 86.53/86.72 tff(3896,plain,((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1))), inference(lemma,lemma(discharge,[]))).
% 86.53/86.72 tff(3897,plain,
% 86.53/86.72 (~node6(c_e_h_1, c_j, s0, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3896, 3887])).
% 86.53/86.72 tff(3898,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3899,plain,
% 86.53/86.72 ((node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3900,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1)))),
% 86.53/86.72 inference(monotonicity,[status(thm)],[3899])).
% 86.53/86.72 tff(3901,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1))),
% 86.53/86.72 inference(transitivity,[status(thm)],[3900, 3898])).
% 86.53/86.72 tff(3902,plain,
% 86.53/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1)))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3903,plain,
% 86.53/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1)),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3902, 3901])).
% 86.53/86.72 tff(3904,plain,
% 86.53/86.72 (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3903, 881, 71])).
% 86.53/86.72 tff(3905,plain,
% 86.53/86.72 (node5(c_e_h_1, c_j, s0, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3904, 3897])).
% 86.53/86.72 tff(3906,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3907,plain,
% 86.53/86.72 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3908,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1))))),
% 86.53/86.72 inference(monotonicity,[status(thm)],[3907])).
% 86.53/86.72 tff(3909,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)))),
% 86.53/86.72 inference(transitivity,[status(thm)],[3908, 3906])).
% 86.53/86.72 tff(3910,plain,
% 86.53/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3911,plain,
% 86.53/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1))),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3910, 3909])).
% 86.53/86.72 tff(3912,plain,
% 86.53/86.72 ($false),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3911, 862, 3905, 3887, 3886, 3878])).
% 86.53/86.72 tff(3913,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 86.53/86.72 tff(3914,plain,
% 86.53/86.72 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3915,plain,
% 86.53/86.72 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3916,plain,
% 86.53/86.72 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1)),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3915, 3914])).
% 86.53/86.72 tff(3917,plain,
% 86.53/86.72 (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3916, 309, 3913])).
% 86.53/86.72 tff(3918,plain,
% 86.53/86.72 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3919,plain,
% 86.53/86.72 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1))) <=> ((~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3920,plain,
% 86.53/86.72 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1)))),
% 86.53/86.72 inference(monotonicity,[status(thm)],[3919])).
% 86.53/86.72 tff(3921,plain,
% 86.53/86.72 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(transitivity,[status(thm)],[3920, 3918])).
% 86.53/86.72 tff(3922,plain,
% 86.53/86.72 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3923,plain,
% 86.53/86.72 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 86.53/86.72 tff(3924,plain,
% 86.53/86.72 ((~node17(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3923, 209, 3917])).
% 86.53/86.72 tff(3925,plain,
% 86.53/86.72 (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3924, 3856])).
% 86.53/86.72 tff(3926,assumption,(node15(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 86.53/86.72 tff(3927,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3928,plain,
% 86.53/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3929,plain,
% 86.53/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3928, 3927])).
% 86.53/86.72 tff(3930,plain,
% 86.53/86.72 ($false),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3929, 173, 3832, 3302, 3926])).
% 86.53/86.72 tff(3931,plain,((~node15(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 86.53/86.72 tff(3932,plain,
% 86.53/86.72 (~node15(c_e_h_1, c_h, s1, s2)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3931, 3832])).
% 86.53/86.72 tff(3933,assumption,(node17(c_e_h_1, c_h, s1)), introduced(assumption)).
% 86.53/86.72 tff(3934,assumption,(node16(c_e_h_1, c_h, s1)), introduced(assumption)).
% 86.53/86.72 tff(3935,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s1)), introduced(assumption)).
% 86.53/86.72 tff(3936,plain,
% 86.53/86.72 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3937,plain,
% 86.53/86.72 ((m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | (~node17(c_e_h_1, c_h, s1))) <=> ((~node17(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3938,plain,
% 86.53/86.72 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | (~node17(c_e_h_1, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1))))),
% 86.53/86.72 inference(monotonicity,[status(thm)],[3937])).
% 86.53/86.72 tff(3939,plain,
% 86.53/86.72 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | (~node17(c_e_h_1, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)))),
% 86.53/86.72 inference(transitivity,[status(thm)],[3938, 3936])).
% 86.53/86.72 tff(3940,plain,
% 86.53/86.72 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | (~node17(c_e_h_1, c_h, s1)))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3941,plain,
% 86.53/86.72 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3940, 3939])).
% 86.53/86.72 tff(3942,plain,
% 86.53/86.72 (m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3941, 245, 3933])).
% 86.53/86.72 tff(3943,plain,
% 86.53/86.72 (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3942, 3935])).
% 86.53/86.72 tff(3944,plain,
% 86.53/86.72 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3945,plain,
% 86.53/86.72 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3946,plain,
% 86.53/86.72 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3945, 3944])).
% 86.53/86.72 tff(3947,plain,
% 86.53/86.72 (m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3946, 228, 3934])).
% 86.53/86.72 tff(3948,plain,
% 86.53/86.72 ($false),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3947, 3943, 3935])).
% 86.53/86.72 tff(3949,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node16(c_e_h_1, c_h, s1)) | (~node17(c_e_h_1, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 86.53/86.72 tff(3950,plain,
% 86.53/86.72 (m_c_h_element_v_in1(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3949, 3934, 3933])).
% 86.53/86.72 tff(3951,plain,
% 86.53/86.72 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3923, 209, 3933])).
% 86.53/86.72 tff(3952,plain,
% 86.53/86.72 (m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3951, 3950])).
% 86.53/86.72 tff(3953,plain,
% 86.53/86.72 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3954,plain,
% 86.53/86.72 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)))),
% 86.53/86.72 inference(quant_inst,[status(thm)],[])).
% 86.53/86.72 tff(3955,plain,
% 86.53/86.72 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 86.53/86.72 tff(3956,plain,
% 86.53/86.72 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3955, 263, 3934])).
% 86.53/86.72 tff(3957,plain,
% 86.53/86.72 ($false),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3956, 3952, 3950])).
% 86.53/86.72 tff(3958,plain,((~node16(c_e_h_1, c_h, s1)) | (~node17(c_e_h_1, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 86.53/86.72 tff(3959,plain,
% 86.53/86.72 (~node16(c_e_h_1, c_h, s1)),
% 86.53/86.72 inference(unit_resolution,[status(thm)],[3958, 3856])).
% 86.53/86.72 tff(3960,plain,
% 86.53/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 86.53/86.72 inference(rewrite,[status(thm)],[])).
% 86.53/86.72 tff(3961,plain,
% 86.54/86.72 ((node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2))) <=> (node15(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 86.54/86.72 inference(rewrite,[status(thm)],[])).
% 86.54/86.72 tff(3962,plain,
% 86.54/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2))))),
% 86.54/86.72 inference(monotonicity,[status(thm)],[3961])).
% 86.54/86.72 tff(3963,plain,
% 86.54/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 86.54/86.72 inference(transitivity,[status(thm)],[3962, 3960])).
% 86.54/86.72 tff(3964,plain,
% 86.54/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 86.54/86.72 inference(quant_inst,[status(thm)],[])).
% 86.54/86.72 tff(3965,plain,
% 86.54/86.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2))),
% 86.54/86.72 inference(modus_ponens,[status(thm)],[3964, 3963])).
% 86.54/86.72 tff(3966,plain,
% 86.54/86.72 (node15(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2)),
% 86.54/86.72 inference(unit_resolution,[status(thm)],[3965, 189, 3848])).
% 86.54/86.72 tff(3967,plain,
% 86.54/86.72 (node14(c_e_h_1, c_h, s1, s2)),
% 86.54/86.72 inference(unit_resolution,[status(thm)],[3966, 3959, 3932])).
% 86.54/86.72 tff(3968,plain,
% 86.54/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 86.54/86.72 inference(rewrite,[status(thm)],[])).
% 86.54/86.72 tff(3969,plain,
% 86.54/86.72 (((~node14(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 86.54/86.72 inference(rewrite,[status(thm)],[])).
% 86.54/86.72 tff(3970,plain,
% 86.54/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2))))),
% 86.54/86.72 inference(monotonicity,[status(thm)],[3969])).
% 86.54/86.72 tff(3971,plain,
% 86.54/86.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 86.54/86.73 inference(transitivity,[status(thm)],[3970, 3968])).
% 86.54/86.73 tff(3972,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(3973,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2))),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[3972, 3971])).
% 86.54/86.73 tff(3974,plain,
% 86.54/86.73 ($false),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[3973, 283, 3832, 3967, 3925])).
% 86.54/86.73 tff(3975,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.73 tff(3976,plain,
% 86.54/86.73 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(3977,plain,
% 86.54/86.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(3978,plain,
% 86.54/86.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[3977, 3976])).
% 86.54/86.73 tff(3979,plain,
% 86.54/86.73 ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[3978, 23])).
% 86.54/86.73 tff(3980,plain,
% 86.54/86.73 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[3979, 3975])).
% 86.54/86.73 tff(3981,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(3982,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(3983,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2)),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[3982, 3981])).
% 86.54/86.73 tff(3984,plain,
% 86.54/86.73 (~node20(c_e_h_1, c_i, s2)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[3983, 37, 3980])).
% 86.54/86.73 tff(3985,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(3986,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(3987,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3))),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[3986, 3985])).
% 86.54/86.73 tff(3988,plain,
% 86.54/86.73 ($false),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[3987, 51, 3822, 3984, 3831])).
% 86.54/86.73 tff(3989,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.73 tff(3990,plain,
% 86.54/86.73 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(3991,plain,
% 86.54/86.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(3992,plain,
% 86.54/86.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[3991, 3990])).
% 86.54/86.73 tff(3993,plain,
% 86.54/86.73 (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[3992, 2218, 3989])).
% 86.54/86.73 tff(3994,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s3)), introduced(assumption)).
% 86.54/86.73 tff(3995,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s4)), introduced(assumption)).
% 86.54/86.73 tff(3996,assumption,(node18(c_e_h_1, c_f, s3, s4)), introduced(assumption)).
% 86.54/86.73 tff(3997,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~node18(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~node18(c_e_h_1, c_f, s3, s4)))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(3998,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~node18(c_e_h_1, c_f, s3, s4)))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(3999,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~node18(c_e_h_1, c_f, s3, s4))),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[3998, 3997])).
% 86.54/86.73 tff(4000,plain,
% 86.54/86.73 ($false),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[3999, 124, 3996, 3995, 3994])).
% 86.54/86.73 tff(4001,plain,((~node18(c_e_h_1, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.73 tff(4002,plain,
% 86.54/86.73 (~node18(c_e_h_1, c_f, s3, s4)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4001, 3995, 3994])).
% 86.54/86.73 tff(4003,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_f, s3, s4))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4004,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_f, s3, s4))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(4005,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_f, s3, s4)),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[4004, 4003])).
% 86.54/86.73 tff(4006,plain,
% 86.54/86.73 (node19(c_e_h_1, c_f, s3, s4)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4005, 141, 679])).
% 86.54/86.73 tff(4007,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s3, s4)) | node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s3, s4)) | node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4008,plain,
% 86.54/86.73 ((node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4))) <=> ((~node19(c_e_h_1, c_f, s3, s4)) | node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4009,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s3, s4)) | node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4)))),
% 86.54/86.73 inference(monotonicity,[status(thm)],[4008])).
% 86.54/86.73 tff(4010,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s3, s4)) | node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4))),
% 86.54/86.73 inference(transitivity,[status(thm)],[4009, 4007])).
% 86.54/86.73 tff(4011,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(4012,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s3, s4)) | node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4)),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[4011, 4010])).
% 86.54/86.73 tff(4013,plain,
% 86.54/86.73 (node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4012, 156, 4006])).
% 86.54/86.73 tff(4014,plain,
% 86.54/86.73 (node17(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4013, 4002])).
% 86.54/86.73 tff(4015,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s3)), introduced(assumption)).
% 86.54/86.73 tff(4016,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4017,plain,
% 86.54/86.73 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4018,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(monotonicity,[status(thm)],[4017])).
% 86.54/86.73 tff(4019,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(transitivity,[status(thm)],[4018, 4016])).
% 86.54/86.73 tff(4020,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(4021,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[4020, 4019])).
% 86.54/86.73 tff(4022,plain,
% 86.54/86.73 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4021, 209, 4015])).
% 86.54/86.73 tff(4023,plain,
% 86.54/86.73 (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4022, 4014])).
% 86.54/86.73 tff(4024,assumption,(node15(c_e_h_1, c_f, s3, s4)), introduced(assumption)).
% 86.54/86.73 tff(4025,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node15(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node15(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4026,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node15(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(4027,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node15(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[4026, 4025])).
% 86.54/86.73 tff(4028,plain,
% 86.54/86.73 ($false),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4027, 173, 4024, 3995, 3994])).
% 86.54/86.73 tff(4029,plain,((~node15(c_e_h_1, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.73 tff(4030,plain,
% 86.54/86.73 (~node15(c_e_h_1, c_f, s3, s4)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4029, 3995, 3994])).
% 86.54/86.73 tff(4031,assumption,(node17(c_e_h_1, c_f, s3)), introduced(assumption)).
% 86.54/86.73 tff(4032,assumption,(node16(c_e_h_1, c_f, s3)), introduced(assumption)).
% 86.54/86.73 tff(4033,plain,
% 86.54/86.73 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4021, 209, 4031])).
% 86.54/86.73 tff(4034,plain,
% 86.54/86.73 (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4033, 4015])).
% 86.54/86.73 tff(4035,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4036,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(4037,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 86.54/86.73 tff(4038,plain,
% 86.54/86.73 (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4037, 228, 4032])).
% 86.54/86.73 tff(4039,plain,
% 86.54/86.73 ($false),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4038, 4034, 4015])).
% 86.54/86.73 tff(4040,plain,(m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node16(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.73 tff(4041,plain,
% 86.54/86.73 (m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4040, 4032, 4031])).
% 86.54/86.73 tff(4042,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4043,plain,
% 86.54/86.73 ((m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4044,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3))))),
% 86.54/86.73 inference(monotonicity,[status(thm)],[4043])).
% 86.54/86.73 tff(4045,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(transitivity,[status(thm)],[4044, 4042])).
% 86.54/86.73 tff(4046,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(4047,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 86.54/86.73 tff(4048,plain,
% 86.54/86.73 (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4047, 245, 4031])).
% 86.54/86.73 tff(4049,plain,
% 86.54/86.73 (m_c_h_element_v_in1(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4048, 4041])).
% 86.54/86.73 tff(4050,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4051,plain,
% 86.54/86.73 (((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4052,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3))))),
% 86.54/86.73 inference(monotonicity,[status(thm)],[4051])).
% 86.54/86.73 tff(4053,plain,
% 86.54/86.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(transitivity,[status(thm)],[4052, 4050])).
% 86.54/86.73 tff(4054,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(4055,plain,
% 86.54/86.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[4054, 4053])).
% 86.54/86.73 tff(4056,plain,
% 86.54/86.73 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4055, 263, 4032])).
% 86.54/86.73 tff(4057,plain,
% 86.54/86.73 ($false),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4056, 4049, 4041])).
% 86.54/86.73 tff(4058,plain,((~node16(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.73 tff(4059,plain,
% 86.54/86.73 (~node16(c_e_h_1, c_f, s3)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4058, 4014])).
% 86.54/86.73 tff(4060,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4061,plain,
% 86.54/86.73 ((node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | node15(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4))) <=> (node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4062,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | node15(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4))))),
% 86.54/86.73 inference(monotonicity,[status(thm)],[4061])).
% 86.54/86.73 tff(4063,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | node15(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 86.54/86.73 inference(transitivity,[status(thm)],[4062, 4060])).
% 86.54/86.73 tff(4064,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | node15(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 86.54/86.73 inference(quant_inst,[status(thm)],[])).
% 86.54/86.73 tff(4065,plain,
% 86.54/86.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4))),
% 86.54/86.73 inference(modus_ponens,[status(thm)],[4064, 4063])).
% 86.54/86.73 tff(4066,plain,
% 86.54/86.73 (node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4065, 189, 4006])).
% 86.54/86.73 tff(4067,plain,
% 86.54/86.73 (node14(c_e_h_1, c_f, s3, s4)),
% 86.54/86.73 inference(unit_resolution,[status(thm)],[4066, 4059, 4030])).
% 86.54/86.73 tff(4068,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4069,plain,
% 86.54/86.73 (((~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 86.54/86.73 inference(rewrite,[status(thm)],[])).
% 86.54/86.73 tff(4070,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3)))),
% 86.54/86.73 inference(monotonicity,[status(thm)],[4069])).
% 86.54/86.73 tff(4071,plain,
% 86.54/86.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 86.54/86.74 inference(transitivity,[status(thm)],[4070, 4068])).
% 86.54/86.74 tff(4072,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4073,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4072, 4071])).
% 86.54/86.74 tff(4074,plain,
% 86.54/86.74 ($false),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4073, 283, 4067, 3995, 4023])).
% 86.54/86.74 tff(4075,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | m_c_h_element_v_out(c_e_h_1, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.74 tff(4076,plain,
% 86.54/86.74 ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4075, 3993])).
% 86.54/86.74 tff(4077,plain,
% 86.54/86.74 (~m_c_h_element_v_out(c_e_h_1, c_f, s4)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4076, 3382])).
% 86.54/86.74 tff(4078,plain,
% 86.54/86.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4079,plain,
% 86.54/86.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4080,plain,
% 86.54/86.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s4)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4079, 4078])).
% 86.54/86.74 tff(4081,plain,
% 86.54/86.74 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4080, 1666, 4077])).
% 86.54/86.74 tff(4082,plain,
% 86.54/86.74 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s4))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4083,plain,
% 86.54/86.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s4))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4084,plain,
% 86.54/86.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s4)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4083, 4082])).
% 86.54/86.74 tff(4085,plain,
% 86.54/86.74 (~node20(c_e_h_1, c_q, s4)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4084, 37, 4081])).
% 86.54/86.74 tff(4086,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s4)), introduced(assumption)).
% 86.54/86.74 tff(4087,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s5)), introduced(assumption)).
% 86.54/86.74 tff(4088,assumption,(node22(c_e_h_1, c_q, s4, s5)), introduced(assumption)).
% 86.54/86.74 tff(4089,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node22(c_e_h_1, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node22(c_e_h_1, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4090,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node22(c_e_h_1, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4091,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node22(c_e_h_1, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4090, 4089])).
% 86.54/86.74 tff(4092,plain,
% 86.54/86.74 ($false),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4091, 107, 4087, 4088, 4086])).
% 86.54/86.74 tff(4093,plain,((~node22(c_e_h_1, c_q, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.74 tff(4094,plain,
% 86.54/86.74 (~node22(c_e_h_1, c_q, s4, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4093, 4087, 4086])).
% 86.54/86.74 tff(4095,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4096,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4097,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4096, 4095])).
% 86.54/86.74 tff(4098,plain,
% 86.54/86.74 (node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4097, 81, 1432])).
% 86.54/86.74 tff(4099,plain,
% 86.54/86.74 (node21(c_e_h_1, c_q, s4, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4098, 4094])).
% 86.54/86.74 tff(4100,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5)))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4101,plain,
% 86.54/86.74 ((node20(c_e_h_1, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node21(c_e_h_1, c_q, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5)))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4102,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node21(c_e_h_1, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5))))),
% 86.54/86.74 inference(monotonicity,[status(thm)],[4101])).
% 86.54/86.74 tff(4103,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node21(c_e_h_1, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5)))),
% 86.54/86.74 inference(transitivity,[status(thm)],[4102, 4100])).
% 86.54/86.74 tff(4104,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node21(c_e_h_1, c_q, s4, s5)))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4105,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5))),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4104, 4103])).
% 86.54/86.74 tff(4106,plain,
% 86.54/86.74 ($false),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4105, 51, 4087, 4099, 4085])).
% 86.54/86.74 tff(4107,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.74 tff(4108,plain,
% 86.54/86.74 (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4107, 3415])).
% 86.54/86.74 tff(4109,plain,
% 86.54/86.74 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s5))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4110,plain,
% 86.54/86.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s5))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4111,plain,
% 86.54/86.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s5)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4110, 4109])).
% 86.54/86.74 tff(4112,plain,
% 86.54/86.74 (node3(c_e_h_1, c_e_h_2, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4111, 817, 814])).
% 86.54/86.74 tff(4113,plain,
% 86.54/86.74 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s5)) | (~node3(c_e_h_1, c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s5)) | (~node3(c_e_h_1, c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4114,plain,
% 86.54/86.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s5)) | (~node3(c_e_h_1, c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4115,plain,
% 86.54/86.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s5)) | (~node3(c_e_h_1, c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4114, 4113])).
% 86.54/86.74 tff(4116,plain,
% 86.54/86.74 ((~m_cell_v_ack(c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4115, 836, 4112])).
% 86.54/86.74 tff(4117,plain,
% 86.54/86.74 (~m_cell_v_ack(c_e_h_2, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4116, 4108])).
% 86.54/86.74 tff(4118,plain,
% 86.54/86.74 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)) | m_cell_v_ack(c_e_h_2, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)) | m_cell_v_ack(c_e_h_2, s5))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4119,plain,
% 86.54/86.74 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)) | m_cell_v_ack(c_e_h_2, s5))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4120,plain,
% 86.54/86.74 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)) | m_cell_v_ack(c_e_h_2, s5)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4119, 4118])).
% 86.54/86.74 tff(4121,plain,
% 86.54/86.74 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4120, 848, 4117])).
% 86.54/86.74 tff(4122,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)), introduced(assumption)).
% 86.54/86.74 tff(4123,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s6)), introduced(assumption)).
% 86.54/86.74 tff(4124,assumption,(node5(c_e_h_2, c_j, s5, s6)), introduced(assumption)).
% 86.54/86.74 tff(4125,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4126,plain,
% 86.54/86.74 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4127,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6))))),
% 86.54/86.74 inference(monotonicity,[status(thm)],[4126])).
% 86.54/86.74 tff(4128,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)))),
% 86.54/86.74 inference(transitivity,[status(thm)],[4127, 4125])).
% 86.54/86.74 tff(4129,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4130,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6))),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4129, 4128])).
% 86.54/86.74 tff(4131,plain,
% 86.54/86.74 ($false),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4130, 862, 4122, 4123, 4124, 3820])).
% 86.54/86.74 tff(4132,plain,((~node5(c_e_h_2, c_j, s5, s6)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.74 tff(4133,plain,
% 86.54/86.74 (~node5(c_e_h_2, c_j, s5, s6)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4132, 4123, 4122, 3820])).
% 86.54/86.74 tff(4134,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4135,plain,
% 86.54/86.74 ((node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6) | (~trans(s5, s6))) <=> ((~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4136,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6)))),
% 86.54/86.74 inference(monotonicity,[status(thm)],[4135])).
% 86.54/86.74 tff(4137,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6))),
% 86.54/86.74 inference(transitivity,[status(thm)],[4136, 4134])).
% 86.54/86.74 tff(4138,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6) | (~trans(s5, s6)))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4139,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4138, 4137])).
% 86.54/86.74 tff(4140,plain,
% 86.54/86.74 (node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4139, 881, 1499])).
% 86.54/86.74 tff(4141,plain,
% 86.54/86.74 (node6(c_e_h_2, c_j, s5, s6)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4140, 4133])).
% 86.54/86.74 tff(4142,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6)))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4143,plain,
% 86.54/86.74 (((~node6(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6)))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4144,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6))))),
% 86.54/86.74 inference(monotonicity,[status(thm)],[4143])).
% 86.54/86.74 tff(4145,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6)))),
% 86.54/86.74 inference(transitivity,[status(thm)],[4144, 4142])).
% 86.54/86.74 tff(4146,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4147,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6))),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4146, 4145])).
% 86.54/86.74 tff(4148,plain,
% 86.54/86.74 ($false),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4147, 899, 3821, 4123, 4141])).
% 86.54/86.74 tff(4149,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.74 tff(4150,plain,
% 86.54/86.74 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4149, 4121])).
% 86.54/86.74 tff(4151,plain,
% 86.54/86.74 (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4150, 3821, 3820])).
% 86.54/86.74 tff(4152,plain,
% 86.54/86.74 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4153,plain,
% 86.54/86.74 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4154,plain,
% 86.54/86.74 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4153, 4152])).
% 86.54/86.74 tff(4155,plain,
% 86.54/86.74 (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4154, 309, 4151])).
% 86.54/86.74 tff(4156,plain,
% 86.54/86.74 (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[3462, 309, 3821])).
% 86.54/86.74 tff(4157,plain,
% 86.54/86.74 (~m_c_h_element_v_out(c_e_h_2, c_h, s6)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[3538, 4156])).
% 86.54/86.74 tff(4158,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s6)), introduced(assumption)).
% 86.54/86.74 tff(4159,plain,
% 86.54/86.74 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[3542, 23, 4158])).
% 86.54/86.74 tff(4160,plain,
% 86.54/86.74 (~node20(c_e_h_2, c_i, s6)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[3546, 37, 4159])).
% 86.54/86.74 tff(4161,plain,
% 86.54/86.74 (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[3566, 4160, 2967])).
% 86.54/86.74 tff(4162,assumption,(node22(c_e_h_2, c_i, s7, s8)), introduced(assumption)).
% 86.54/86.74 tff(4163,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node22(c_e_h_2, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node22(c_e_h_2, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4164,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node22(c_e_h_2, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4165,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node22(c_e_h_2, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4164, 4163])).
% 86.54/86.74 tff(4166,plain,
% 86.54/86.74 ($false),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4165, 107, 3819, 3570, 4162])).
% 86.54/86.74 tff(4167,plain,((~node22(c_e_h_2, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.74 tff(4168,plain,
% 86.54/86.74 (~node22(c_e_h_2, c_i, s7, s8)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4167, 4161, 3819])).
% 86.54/86.74 tff(4169,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4170,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4171,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4170, 4169])).
% 86.54/86.74 tff(4172,plain,
% 86.54/86.74 (node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4171, 81, 2152])).
% 86.54/86.74 tff(4173,plain,
% 86.54/86.74 (node21(c_e_h_2, c_i, s7, s8)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4172, 4168])).
% 86.54/86.74 tff(4174,plain,
% 86.54/86.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node21(c_e_h_2, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node21(c_e_h_2, c_i, s7, s8)))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4175,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node21(c_e_h_2, c_i, s7, s8)))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4176,plain,
% 86.54/86.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node21(c_e_h_2, c_i, s7, s8))),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4175, 4174])).
% 86.54/86.74 tff(4177,plain,
% 86.54/86.74 (node20(c_e_h_2, c_i, s7)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4176, 51, 3819, 4173])).
% 86.54/86.74 tff(4178,plain,
% 86.54/86.74 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s7))),
% 86.54/86.74 inference(rewrite,[status(thm)],[])).
% 86.54/86.74 tff(4179,plain,
% 86.54/86.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s7))),
% 86.54/86.74 inference(quant_inst,[status(thm)],[])).
% 86.54/86.74 tff(4180,plain,
% 86.54/86.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s7)),
% 86.54/86.74 inference(modus_ponens,[status(thm)],[4179, 4178])).
% 86.54/86.74 tff(4181,plain,
% 86.54/86.74 (m_and_h_gate_v_in1(c_e_h_2, c_i, s7)),
% 86.54/86.74 inference(unit_resolution,[status(thm)],[4180, 37, 4177])).
% 86.54/86.75 tff(4182,plain,
% 86.54/86.75 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4183,plain,
% 86.54/86.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4184,plain,
% 86.54/86.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s7)),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4183, 4182])).
% 86.54/86.75 tff(4185,plain,
% 86.54/86.75 (m_c_h_element_v_out(c_e_h_2, c_h, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4184, 23, 4181])).
% 86.54/86.75 tff(4186,assumption,(node18(c_e_h_2, c_h, s6, s7)), introduced(assumption)).
% 86.54/86.75 tff(4187,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s7)), introduced(assumption)).
% 86.54/86.75 tff(4188,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4189,plain,
% 86.54/86.75 (((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~node18(c_e_h_2, c_h, s6, s7))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4190,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~node18(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7))))),
% 86.54/86.75 inference(monotonicity,[status(thm)],[4189])).
% 86.54/86.75 tff(4191,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~node18(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(transitivity,[status(thm)],[4190, 4188])).
% 86.54/86.75 tff(4192,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~node18(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4193,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7))),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4192, 4191])).
% 86.54/86.75 tff(4194,plain,
% 86.54/86.75 ($false),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4193, 124, 4158, 4187, 4186])).
% 86.54/86.75 tff(4195,plain,((~node18(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.75 tff(4196,plain,
% 86.54/86.75 (~node18(c_e_h_2, c_h, s6, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4195, 4185, 4158])).
% 86.54/86.75 tff(4197,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s6)), introduced(assumption)).
% 86.54/86.75 tff(4198,assumption,(node14(c_e_h_2, c_h, s6, s7)), introduced(assumption)).
% 86.54/86.75 tff(4199,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node14(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node14(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4200,plain,
% 86.54/86.75 (((~node14(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node14(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4201,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node14(c_e_h_2, c_h, s6, s7))))),
% 86.54/86.75 inference(monotonicity,[status(thm)],[4200])).
% 86.54/86.75 tff(4202,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node14(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(transitivity,[status(thm)],[4201, 4199])).
% 86.54/86.75 tff(4203,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4204,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node14(c_e_h_2, c_h, s6, s7))),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4203, 4202])).
% 86.54/86.75 tff(4205,plain,
% 86.54/86.75 ($false),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4204, 283, 4187, 4197, 4198])).
% 86.54/86.75 tff(4206,plain,((~node14(c_e_h_2, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.75 tff(4207,plain,
% 86.54/86.75 (~node14(c_e_h_2, c_h, s6, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4206, 4197, 4187])).
% 86.54/86.75 tff(4208,assumption,(node15(c_e_h_2, c_h, s6, s7)), introduced(assumption)).
% 86.54/86.75 tff(4209,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4210,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4211,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4210, 4209])).
% 86.54/86.75 tff(4212,plain,
% 86.54/86.75 ($false),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4211, 173, 4158, 4187, 4208])).
% 86.54/86.75 tff(4213,plain,((~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.75 tff(4214,plain,
% 86.54/86.75 (~node15(c_e_h_2, c_h, s6, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4213, 4158, 4187])).
% 86.54/86.75 tff(4215,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_2, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_2, c_h, s6, s7))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4216,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_2, c_h, s6, s7))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4217,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_2, c_h, s6, s7)),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4216, 4215])).
% 86.54/86.75 tff(4218,plain,
% 86.54/86.75 (node19(c_e_h_2, c_h, s6, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4217, 141, 1552])).
% 86.54/86.75 tff(4219,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node15(c_e_h_2, c_h, s6, s7) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s6) | node15(c_e_h_2, c_h, s6, s7) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4220,plain,
% 86.54/86.75 ((node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7))) <=> (node16(c_e_h_2, c_h, s6) | node15(c_e_h_2, c_h, s6, s7) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4221,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node15(c_e_h_2, c_h, s6, s7) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7))))),
% 86.54/86.75 inference(monotonicity,[status(thm)],[4220])).
% 86.54/86.75 tff(4222,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s6) | node15(c_e_h_2, c_h, s6, s7) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(transitivity,[status(thm)],[4221, 4219])).
% 86.54/86.75 tff(4223,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4224,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s6) | node15(c_e_h_2, c_h, s6, s7) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7))),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4223, 4222])).
% 86.54/86.75 tff(4225,plain,
% 86.54/86.75 (node16(c_e_h_2, c_h, s6) | node15(c_e_h_2, c_h, s6, s7) | node14(c_e_h_2, c_h, s6, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4224, 189, 4218])).
% 86.54/86.75 tff(4226,plain,
% 86.54/86.75 (node16(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4225, 4214, 4207])).
% 86.54/86.75 tff(4227,plain,
% 86.54/86.75 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4228,plain,
% 86.54/86.75 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4229,plain,
% 86.54/86.75 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4228, 4227])).
% 86.54/86.75 tff(4230,plain,
% 86.54/86.75 ((~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4229, 228, 4197])).
% 86.54/86.75 tff(4231,plain,
% 86.54/86.75 (m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4230, 4226])).
% 86.54/86.75 tff(4232,plain,
% 86.54/86.75 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4233,plain,
% 86.54/86.75 ((m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4234,plain,
% 86.54/86.75 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6))))),
% 86.54/86.75 inference(monotonicity,[status(thm)],[4233])).
% 86.54/86.75 tff(4235,plain,
% 86.54/86.75 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))),
% 86.54/86.75 inference(transitivity,[status(thm)],[4234, 4232])).
% 86.54/86.75 tff(4236,plain,
% 86.54/86.75 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6)))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4237,plain,
% 86.54/86.75 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4236, 4235])).
% 86.54/86.75 tff(4238,plain,
% 86.54/86.75 ((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4237, 245, 4197])).
% 86.54/86.75 tff(4239,plain,
% 86.54/86.75 (~node17(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4238, 4231])).
% 86.54/86.75 tff(4240,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4241,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4242,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7))),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4241, 4240])).
% 86.54/86.75 tff(4243,plain,
% 86.54/86.75 (node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4242, 156, 4218])).
% 86.54/86.75 tff(4244,plain,
% 86.54/86.75 (node18(c_e_h_2, c_h, s6, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4243, 4239])).
% 86.54/86.75 tff(4245,plain,
% 86.54/86.75 ($false),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4193, 124, 4158, 4187, 4244])).
% 86.54/86.75 tff(4246,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.75 tff(4247,plain,
% 86.54/86.75 (m_c_h_element_v_in1(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4246, 4185, 4158])).
% 86.54/86.75 tff(4248,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s6)), introduced(assumption)).
% 86.54/86.75 tff(4249,plain,
% 86.54/86.75 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4250,plain,
% 86.54/86.75 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6))) <=> ((~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4251,plain,
% 86.54/86.75 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)))),
% 86.54/86.75 inference(monotonicity,[status(thm)],[4250])).
% 86.54/86.75 tff(4252,plain,
% 86.54/86.75 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(transitivity,[status(thm)],[4251, 4249])).
% 86.54/86.75 tff(4253,plain,
% 86.54/86.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4254,plain,
% 86.54/86.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4253, 4252])).
% 86.54/86.75 tff(4255,plain,
% 86.54/86.75 ((~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6))),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4254, 209, 4248])).
% 86.54/86.75 tff(4256,plain,
% 86.54/86.75 (~node17(c_e_h_2, c_h, s6)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4255, 4247])).
% 86.54/86.75 tff(4257,plain,
% 86.54/86.75 ($false),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4243, 4256, 4196])).
% 86.54/86.75 tff(4258,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.75 tff(4259,plain,
% 86.54/86.75 (m_c_h_element_v_out(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4258, 2965])).
% 86.54/86.75 tff(4260,plain,
% 86.54/86.75 ($false),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4259, 4157, 4155, 3819])).
% 86.54/86.75 tff(4261,plain,(m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.75 tff(4262,plain,
% 86.54/86.75 (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4261, 3818, 3459])).
% 86.54/86.75 tff(4263,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s8)), introduced(assumption)).
% 86.54/86.75 tff(4264,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s8)), introduced(assumption)).
% 86.54/86.75 tff(4265,plain,
% 86.54/86.75 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4266,plain,
% 86.54/86.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4267,plain,
% 86.54/86.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8)),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 86.54/86.75 tff(4268,plain,
% 86.54/86.75 ($false),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4267, 365, 4264, 4263])).
% 86.54/86.75 tff(4269,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.75 tff(4270,plain,
% 86.54/86.75 (~m_c_h_element_v_in2(c_e_h_2, c_e, s8)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4269, 4262])).
% 86.54/86.75 tff(4271,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s8)), introduced(assumption)).
% 86.54/86.75 tff(4272,plain,
% 86.54/86.75 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[3104, 3578])).
% 86.54/86.75 tff(4273,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s9)), introduced(assumption)).
% 86.54/86.75 tff(4274,assumption,(node18(c_e_h_2, c_e, s8, s9)), introduced(assumption)).
% 86.54/86.75 tff(4275,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4276,plain,
% 86.54/86.75 (((~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4277,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9))))),
% 86.54/86.75 inference(monotonicity,[status(thm)],[4276])).
% 86.54/86.75 tff(4278,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)))),
% 86.54/86.75 inference(transitivity,[status(thm)],[4277, 4275])).
% 86.54/86.75 tff(4279,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.75 inference(quant_inst,[status(thm)],[])).
% 86.54/86.75 tff(4280,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~node18(c_e_h_2, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9))),
% 86.54/86.75 inference(modus_ponens,[status(thm)],[4279, 4278])).
% 86.54/86.75 tff(4281,plain,
% 86.54/86.75 ($false),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4280, 124, 3670, 4273, 4274])).
% 86.54/86.75 tff(4282,plain,((~node18(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.75 tff(4283,plain,
% 86.54/86.75 (~node18(c_e_h_2, c_e, s8, s9)),
% 86.54/86.75 inference(unit_resolution,[status(thm)],[4282, 3670, 4273])).
% 86.54/86.75 tff(4284,assumption,(node15(c_e_h_2, c_e, s8, s9)), introduced(assumption)).
% 86.54/86.75 tff(4285,plain,
% 86.54/86.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node15(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node15(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8))),
% 86.54/86.75 inference(rewrite,[status(thm)],[])).
% 86.54/86.75 tff(4286,plain,
% 86.54/86.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node15(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4287,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node15(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4286, 4285])).
% 86.54/86.76 tff(4288,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4287, 173, 3670, 4273, 4284])).
% 86.54/86.76 tff(4289,plain,((~node15(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4290,plain,
% 86.54/86.76 (~node15(c_e_h_2, c_e, s8, s9)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4289, 3670, 4273])).
% 86.54/86.76 tff(4291,assumption,(node17(c_e_h_2, c_e, s8)), introduced(assumption)).
% 86.54/86.76 tff(4292,plain,
% 86.54/86.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4293,plain,
% 86.54/86.76 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8) | (~node17(c_e_h_2, c_e, s8))) <=> ((~node17(c_e_h_2, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4294,plain,
% 86.54/86.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8) | (~node17(c_e_h_2, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)))),
% 86.54/86.76 inference(monotonicity,[status(thm)],[4293])).
% 86.54/86.76 tff(4295,plain,
% 86.54/86.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8) | (~node17(c_e_h_2, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8))),
% 86.54/86.76 inference(transitivity,[status(thm)],[4294, 4292])).
% 86.54/86.76 tff(4296,plain,
% 86.54/86.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8) | (~node17(c_e_h_2, c_e, s8)))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4297,plain,
% 86.54/86.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4296, 4295])).
% 86.54/86.76 tff(4298,plain,
% 86.54/86.76 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s8)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4297, 209, 4291])).
% 86.54/86.76 tff(4299,plain,
% 86.54/86.76 (~m_c_h_element_v_in1(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4298, 4271])).
% 86.54/86.76 tff(4300,assumption,(~node15(c_e_h_2, c_e, s8, s9)), introduced(assumption)).
% 86.54/86.76 tff(4301,plain,
% 86.54/86.76 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | m_c_h_element_v_in2(c_e_h_2, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | m_c_h_element_v_in2(c_e_h_2, c_e, s8))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4302,plain,
% 86.54/86.76 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | m_c_h_element_v_in2(c_e_h_2, c_e, s8))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4303,plain,
% 86.54/86.76 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s8)) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4302, 4301])).
% 86.54/86.76 tff(4304,plain,
% 86.54/86.76 (~node16(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4303, 228, 4271, 4299])).
% 86.54/86.76 tff(4305,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_2, c_e, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_2, c_e, s8, s9))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4306,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_2, c_e, s8, s9))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4307,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_2, c_e, s8, s9)),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4306, 4305])).
% 86.54/86.76 tff(4308,plain,
% 86.54/86.76 (node19(c_e_h_2, c_e, s8, s9)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4307, 141, 2636])).
% 86.54/86.76 tff(4309,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s8) | node15(c_e_h_2, c_e, s8, s9) | node14(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s8) | node15(c_e_h_2, c_e, s8, s9) | node14(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4310,plain,
% 86.54/86.76 ((node16(c_e_h_2, c_e, s8) | node14(c_e_h_2, c_e, s8, s9) | node15(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9))) <=> (node16(c_e_h_2, c_e, s8) | node15(c_e_h_2, c_e, s8, s9) | node14(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4311,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s8) | node14(c_e_h_2, c_e, s8, s9) | node15(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s8) | node15(c_e_h_2, c_e, s8, s9) | node14(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9))))),
% 86.54/86.76 inference(monotonicity,[status(thm)],[4310])).
% 86.54/86.76 tff(4312,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s8) | node14(c_e_h_2, c_e, s8, s9) | node15(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s8) | node15(c_e_h_2, c_e, s8, s9) | node14(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(transitivity,[status(thm)],[4311, 4309])).
% 86.54/86.76 tff(4313,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s8) | node14(c_e_h_2, c_e, s8, s9) | node15(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4314,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s8) | node15(c_e_h_2, c_e, s8, s9) | node14(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9))),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 86.54/86.76 tff(4315,plain,
% 86.54/86.76 (node16(c_e_h_2, c_e, s8) | node15(c_e_h_2, c_e, s8, s9) | node14(c_e_h_2, c_e, s8, s9)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4314, 189, 4308])).
% 86.54/86.76 tff(4316,plain,
% 86.54/86.76 (node14(c_e_h_2, c_e, s8, s9)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4315, 4304, 4300])).
% 86.54/86.76 tff(4317,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node14(c_e_h_2, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node14(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4318,plain,
% 86.54/86.76 (((~node14(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node14(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4319,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node14(c_e_h_2, c_e, s8, s9))))),
% 86.54/86.76 inference(monotonicity,[status(thm)],[4318])).
% 86.54/86.76 tff(4320,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node14(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(transitivity,[status(thm)],[4319, 4317])).
% 86.54/86.76 tff(4321,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4322,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | (~node14(c_e_h_2, c_e, s8, s9))),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4321, 4320])).
% 86.54/86.76 tff(4323,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4322, 283, 4273, 4316, 4299])).
% 86.54/86.76 tff(4324,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | node15(c_e_h_2, c_e, s8, s9) | (~node17(c_e_h_2, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4325,plain,
% 86.54/86.76 (~node17(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4324, 4290, 4273, 4271])).
% 86.54/86.76 tff(4326,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s8) | node18(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s8) | node18(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4327,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s8) | node18(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9)))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4328,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s8) | node18(c_e_h_2, c_e, s8, s9) | (~node19(c_e_h_2, c_e, s8, s9))),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4327, 4326])).
% 86.54/86.76 tff(4329,plain,
% 86.54/86.76 (node17(c_e_h_2, c_e, s8) | node18(c_e_h_2, c_e, s8, s9)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4328, 156, 4308])).
% 86.54/86.76 tff(4330,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4329, 4325, 4283])).
% 86.54/86.76 tff(4331,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~m_c_h_element_v_out(c_e_h_2, c_e, s9)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4332,plain,
% 86.54/86.76 (~m_c_h_element_v_out(c_e_h_2, c_e, s9)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4331, 3670, 4271])).
% 86.54/86.76 tff(4333,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)), introduced(assumption)).
% 86.54/86.76 tff(4334,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[3675, 3670])).
% 86.54/86.76 tff(4335,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)), introduced(assumption)).
% 86.54/86.76 tff(4336,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2056, 2050])).
% 86.54/86.76 tff(4337,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2093, 4336])).
% 86.54/86.76 tff(4338,plain,
% 86.54/86.76 (~m_c_h_element_v_out(c_e_h_2, c_e, s6)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2537, 2050, 2496])).
% 86.54/86.76 tff(4339,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2546, 4338])).
% 86.54/86.76 tff(4340,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[3096, 4339, 3061, 4337])).
% 86.54/86.76 tff(4341,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)), introduced(assumption)).
% 86.54/86.76 tff(4342,plain,
% 86.54/86.76 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4343,plain,
% 86.54/86.76 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4344,plain,
% 86.54/86.76 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 86.54/86.76 tff(4345,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4344, 1142, 3682, 4341])).
% 86.54/86.76 tff(4346,plain,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4347,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4346, 3681])).
% 86.54/86.76 tff(4348,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)), introduced(assumption)).
% 86.54/86.76 tff(4349,assumption,(node10(c_e_h_2, c_n, s9, s10)), introduced(assumption)).
% 86.54/86.76 tff(4350,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4351,plain,
% 86.54/86.76 (((~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4352,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9))))),
% 86.54/86.76 inference(monotonicity,[status(thm)],[4351])).
% 86.54/86.76 tff(4353,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)))),
% 86.54/86.76 inference(transitivity,[status(thm)],[4352, 4350])).
% 86.54/86.76 tff(4354,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4355,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node10(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9))),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4354, 4353])).
% 86.54/86.76 tff(4356,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4355, 1191, 4333, 4349, 4348, 4335])).
% 86.54/86.76 tff(4357,plain,((~node10(c_e_h_2, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4358,plain,
% 86.54/86.76 (~node10(c_e_h_2, c_n, s9, s10)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4357, 4333, 4348, 4335])).
% 86.54/86.76 tff(4359,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_2, c_n, s9, s10) | node11(c_e_h_2, c_n, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_2, c_n, s9, s10) | node11(c_e_h_2, c_n, s9, s10))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4360,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_2, c_n, s9, s10) | node11(c_e_h_2, c_n, s9, s10))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4361,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_2, c_n, s9, s10) | node11(c_e_h_2, c_n, s9, s10)),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4360, 4359])).
% 86.54/86.76 tff(4362,plain,
% 86.54/86.76 (node10(c_e_h_2, c_n, s9, s10) | node11(c_e_h_2, c_n, s9, s10)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4361, 1092, 3175])).
% 86.54/86.76 tff(4363,plain,
% 86.54/86.76 (node11(c_e_h_2, c_n, s9, s10)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4362, 4358])).
% 86.54/86.76 tff(4364,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)), introduced(assumption)).
% 86.54/86.76 tff(4365,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)) | (~node11(c_e_h_2, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)) | (~node11(c_e_h_2, c_n, s9, s10)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4366,plain,
% 86.54/86.76 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node11(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)) | (~node11(c_e_h_2, c_n, s9, s10)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4367,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node11(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)) | (~node11(c_e_h_2, c_n, s9, s10))))),
% 86.54/86.76 inference(monotonicity,[status(thm)],[4366])).
% 86.54/86.76 tff(4368,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node11(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)) | (~node11(c_e_h_2, c_n, s9, s10)))),
% 86.54/86.76 inference(transitivity,[status(thm)],[4367, 4365])).
% 86.54/86.76 tff(4369,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~node11(c_e_h_2, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4370,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)) | (~node11(c_e_h_2, c_n, s9, s10))),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4369, 4368])).
% 86.54/86.76 tff(4371,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4370, 1161, 4333, 4364, 4363])).
% 86.54/86.76 tff(4372,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4373,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4372, 4347, 3738, 4335, 4333])).
% 86.54/86.76 tff(4374,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4375,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4374, 4340, 4335, 3705, 4333])).
% 86.54/86.76 tff(4376,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2578, 4339, 4337])).
% 86.54/86.76 tff(4377,plain,
% 86.54/86.76 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2583, 1048, 4376])).
% 86.54/86.76 tff(4378,plain,
% 86.54/86.76 (~node9(c_e_h_2, c_m, s7)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2587, 1062, 4377])).
% 86.54/86.76 tff(4379,plain,
% 86.54/86.76 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2101, 4337])).
% 86.54/86.76 tff(4380,plain,
% 86.54/86.76 (~node9(c_e_h_2, c_m, s6)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2105, 1062, 4379])).
% 86.54/86.76 tff(4381,plain,
% 86.54/86.76 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2130, 4380])).
% 86.54/86.76 tff(4382,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[2611, 4381, 4378, 4375])).
% 86.54/86.76 tff(4383,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_c_h_element_v_in2(c_e_h_2, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4384,plain,
% 86.54/86.76 (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4383, 4334, 1877, 2496, 3061, 4333])).
% 86.54/86.76 tff(4385,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)), introduced(assumption)).
% 86.54/86.76 tff(4386,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s9)), introduced(assumption)).
% 86.54/86.76 tff(4387,plain,
% 86.54/86.76 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9) | m_c_h_element_v_out(c_e_h_2, c_e, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9) | m_c_h_element_v_out(c_e_h_2, c_e, s9))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4388,plain,
% 86.54/86.76 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9) | m_c_h_element_v_out(c_e_h_2, c_e, s9))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4389,plain,
% 86.54/86.76 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9) | m_c_h_element_v_out(c_e_h_2, c_e, s9)),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4388, 4387])).
% 86.54/86.76 tff(4390,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4389, 976, 4386, 4385])).
% 86.54/86.76 tff(4391,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9) | m_c_h_element_v_out(c_e_h_2, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4392,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4391, 4384, 4332])).
% 86.54/86.76 tff(4393,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s8) | m_c_h_element_v_in2(c_e_h_2, c_e, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4394,plain,
% 86.54/86.76 (m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4393, 2468])).
% 86.54/86.76 tff(4395,plain,
% 86.54/86.76 (m_c_h_element_v_out(c_e_h_2, c_e, s8) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4394, 4272])).
% 86.54/86.76 tff(4396,plain,
% 86.54/86.76 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4395, 3670, 4271])).
% 86.54/86.76 tff(4397,plain,
% 86.54/86.76 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4398,plain,
% 86.54/86.76 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4399,plain,
% 86.54/86.76 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10))),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4398, 4397])).
% 86.54/86.76 tff(4400,plain,
% 86.54/86.76 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4399, 1048, 4396])).
% 86.54/86.76 tff(4401,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)), introduced(assumption)).
% 86.54/86.76 tff(4402,plain,
% 86.54/86.76 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[3749, 4334])).
% 86.54/86.76 tff(4403,assumption,(~node9(c_e_h_2, c_m, s10)), introduced(assumption)).
% 86.54/86.76 tff(4404,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)), introduced(assumption)).
% 86.54/86.76 tff(4405,assumption,(node11(c_e_h_2, c_m, s10, s11)), introduced(assumption)).
% 86.54/86.76 tff(4406,plain,
% 86.54/86.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node11(c_e_h_2, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node11(c_e_h_2, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))),
% 86.54/86.76 inference(rewrite,[status(thm)],[])).
% 86.54/86.76 tff(4407,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node11(c_e_h_2, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))),
% 86.54/86.76 inference(quant_inst,[status(thm)],[])).
% 86.54/86.76 tff(4408,plain,
% 86.54/86.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node11(c_e_h_2, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 86.54/86.76 inference(modus_ponens,[status(thm)],[4407, 4406])).
% 86.54/86.76 tff(4409,plain,
% 86.54/86.76 ($false),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4408, 1130, 4404, 4401, 4405])).
% 86.54/86.76 tff(4410,plain,((~node11(c_e_h_2, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.76 tff(4411,plain,
% 86.54/86.76 (~node11(c_e_h_2, c_m, s10, s11)),
% 86.54/86.76 inference(unit_resolution,[status(thm)],[4410, 4401, 4404])).
% 86.54/86.77 tff(4412,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_2, c_m, s10, s11) | node11(c_e_h_2, c_m, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_2, c_m, s10, s11) | node11(c_e_h_2, c_m, s10, s11))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4413,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_2, c_m, s10, s11) | node11(c_e_h_2, c_m, s10, s11))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4414,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_2, c_m, s10, s11) | node11(c_e_h_2, c_m, s10, s11)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4413, 4412])).
% 86.54/86.77 tff(4415,plain,
% 86.54/86.77 (node10(c_e_h_2, c_m, s10, s11) | node11(c_e_h_2, c_m, s10, s11)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4414, 1092, 3778])).
% 86.54/86.77 tff(4416,plain,
% 86.54/86.77 (node10(c_e_h_2, c_m, s10, s11)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4415, 4411])).
% 86.54/86.77 tff(4417,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)) | node9(c_e_h_2, c_m, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)) | node9(c_e_h_2, c_m, s10))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4418,plain,
% 86.54/86.77 ((node9(c_e_h_2, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)) | node9(c_e_h_2, c_m, s10))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4419,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)) | node9(c_e_h_2, c_m, s10)))),
% 86.54/86.77 inference(monotonicity,[status(thm)],[4418])).
% 86.54/86.77 tff(4420,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)) | node9(c_e_h_2, c_m, s10))),
% 86.54/86.77 inference(transitivity,[status(thm)],[4419, 4417])).
% 86.54/86.77 tff(4421,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4422,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | (~node10(c_e_h_2, c_m, s10, s11)) | node9(c_e_h_2, c_m, s10)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4421, 4420])).
% 86.54/86.77 tff(4423,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4422, 1076, 4401, 4416, 4403])).
% 86.54/86.77 tff(4424,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | node9(c_e_h_2, c_m, s10) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4425,plain,
% 86.54/86.77 (node9(c_e_h_2, c_m, s10)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4424, 4402, 4401])).
% 86.54/86.77 tff(4426,plain,
% 86.54/86.77 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4427,plain,
% 86.54/86.77 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4428,plain,
% 86.54/86.77 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4427, 4426])).
% 86.54/86.77 tff(4429,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4428, 1062, 4425, 4400])).
% 86.54/86.77 tff(4430,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4431,plain,
% 86.54/86.77 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4430, 3668, 4270])).
% 86.54/86.77 tff(4432,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_r, s11)), introduced(assumption)).
% 86.54/86.77 tff(4433,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)), introduced(assumption)).
% 86.54/86.77 tff(4434,plain,
% 86.54/86.77 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4435,plain,
% 86.54/86.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4436,plain,
% 86.54/86.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 86.54/86.77 tff(4437,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4436, 1521, 4433, 4432])).
% 86.54/86.77 tff(4438,plain,((~m_and_h_gate_v_in2(c_e_h_2, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4439,plain,
% 86.54/86.77 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s11)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4438, 4431])).
% 86.54/86.77 tff(4440,assumption,(~m_and_h_gate_v_in2(c_e_h_2, c_r, s11)), introduced(assumption)).
% 86.54/86.77 tff(4441,assumption,(node20(c_e_h_2, c_r, s11)), introduced(assumption)).
% 86.54/86.77 tff(4442,plain,
% 86.54/86.77 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s11))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4443,plain,
% 86.54/86.77 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s11))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4444,plain,
% 86.54/86.77 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s11)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4443, 4442])).
% 86.54/86.77 tff(4445,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4444, 1535, 4441, 4440])).
% 86.54/86.77 tff(4446,plain,((~node20(c_e_h_2, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s11)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4447,plain,
% 86.54/86.77 (~node20(c_e_h_2, c_r, s11)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4446, 4439])).
% 86.54/86.77 tff(4448,assumption,(~node20(c_e_h_2, c_r, s11)), introduced(assumption)).
% 86.54/86.77 tff(4449,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s12)), introduced(assumption)).
% 86.54/86.77 tff(4450,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node21(c_e_h_2, c_r, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node21(c_e_h_2, c_r, s11, s12)))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4451,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node21(c_e_h_2, c_r, s11, s12)))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4452,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node21(c_e_h_2, c_r, s11, s12))),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4451, 4450])).
% 86.54/86.77 tff(4453,plain,
% 86.54/86.77 (node20(c_e_h_2, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node21(c_e_h_2, c_r, s11, s12))),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4452, 51])).
% 86.54/86.77 tff(4454,plain,
% 86.54/86.77 (~node21(c_e_h_2, c_r, s11, s12)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4453, 4449, 4448])).
% 86.54/86.77 tff(4455,plain,
% 86.54/86.77 (succ(s11, s12) <=> succ(s11, s12)),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4456,axiom,(succ(s11, s12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound12')).
% 86.54/86.77 tff(4457,plain,
% 86.54/86.77 (succ(s11, s12)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4456, 4455])).
% 86.54/86.77 tff(4458,plain,
% 86.54/86.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4459,plain,
% 86.54/86.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4460,plain,
% 86.54/86.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4459, 4458])).
% 86.54/86.77 tff(4461,plain,
% 86.54/86.77 (trans(s11, s12)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4460, 4457, 64])).
% 86.54/86.77 tff(4462,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_2, c_r, s11, s12) | node22(c_e_h_2, c_r, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_2, c_r, s11, s12) | node22(c_e_h_2, c_r, s11, s12))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4463,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_2, c_r, s11, s12) | node22(c_e_h_2, c_r, s11, s12))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4464,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_2, c_r, s11, s12) | node22(c_e_h_2, c_r, s11, s12)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4463, 4462])).
% 86.54/86.77 tff(4465,plain,
% 86.54/86.77 (node21(c_e_h_2, c_r, s11, s12) | node22(c_e_h_2, c_r, s11, s12)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4464, 81, 4461])).
% 86.54/86.77 tff(4466,plain,
% 86.54/86.77 (node22(c_e_h_2, c_r, s11, s12)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4465, 4454])).
% 86.54/86.77 tff(4467,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s11)), introduced(assumption)).
% 86.54/86.77 tff(4468,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node22(c_e_h_2, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node22(c_e_h_2, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s11))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4469,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node22(c_e_h_2, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s11))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4470,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | (~node22(c_e_h_2, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s11)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4469, 4468])).
% 86.54/86.77 tff(4471,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4470, 107, 4467, 4449, 4466])).
% 86.54/86.77 tff(4472,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s11) | node20(c_e_h_2, c_r, s11)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4473,plain,
% 86.54/86.77 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s11)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4472, 4447])).
% 86.54/86.77 tff(4474,plain,
% 86.54/86.77 (~m_and_h_gate_v_out(c_e_h_2, c_r, s12)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4473, 3786])).
% 86.54/86.77 tff(4475,plain,
% 86.54/86.77 (^[I0: $i, X: $i] : refl(((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X)) <=> ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X)))),
% 86.54/86.77 inference(bind,[status(th)],[])).
% 86.54/86.77 tff(4476,plain,
% 86.54/86.77 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X)) <=> ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 86.54/86.77 inference(quant_intro,[status(thm)],[4475])).
% 86.54/86.77 tff(4477,plain,
% 86.54/86.77 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X)) <=> ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4478,axiom,(![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_81')).
% 86.54/86.77 tff(4479,plain,
% 86.54/86.77 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4478, 4477])).
% 86.54/86.77 tff(4480,plain,(
% 86.54/86.77 ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 86.54/86.77 inference(skolemize,[status(sab)],[4479])).
% 86.54/86.77 tff(4481,plain,
% 86.54/86.77 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4480, 4476])).
% 86.54/86.77 tff(4482,plain,
% 86.54/86.77 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4483,plain,
% 86.54/86.77 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4484,plain,
% 86.54/86.77 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s12)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4483, 4482])).
% 86.54/86.77 tff(4485,plain,
% 86.54/86.77 (~m_user_v_ack(c_e_h_2, c_u, s12)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4484, 4481, 4474])).
% 86.54/86.77 tff(4486,plain,
% 86.54/86.77 (^[X: $i] : refl((m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X))) <=> (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X))))),
% 86.54/86.77 inference(bind,[status(th)],[])).
% 86.54/86.77 tff(4487,plain,
% 86.54/86.77 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 86.54/86.77 inference(quant_intro,[status(thm)],[4486])).
% 86.54/86.77 tff(4488,plain,
% 86.54/86.77 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4489,axiom,(![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty5')).
% 86.54/86.77 tff(4490,plain,
% 86.54/86.77 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4489, 4488])).
% 86.54/86.77 tff(4491,plain,(
% 86.54/86.77 ![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 86.54/86.77 inference(skolemize,[status(sab)],[4490])).
% 86.54/86.77 tff(4492,plain,
% 86.54/86.77 (![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4491, 4487])).
% 86.54/86.77 tff(4493,plain,
% 86.54/86.77 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s12)) | m_user_v_ack(c_e_h_2, c_u, s12))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s12)) | m_user_v_ack(c_e_h_2, c_u, s12))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4494,plain,
% 86.54/86.77 ((m_user_v_ack(c_e_h_2, c_u, s12) | (~node25(s12))) <=> ((~node25(s12)) | m_user_v_ack(c_e_h_2, c_u, s12))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4495,plain,
% 86.54/86.77 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s12) | (~node25(s12)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s12)) | m_user_v_ack(c_e_h_2, c_u, s12)))),
% 86.54/86.77 inference(monotonicity,[status(thm)],[4494])).
% 86.54/86.77 tff(4496,plain,
% 86.54/86.77 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s12) | (~node25(s12)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s12)) | m_user_v_ack(c_e_h_2, c_u, s12))),
% 86.54/86.77 inference(transitivity,[status(thm)],[4495, 4493])).
% 86.54/86.77 tff(4497,plain,
% 86.54/86.77 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s12) | (~node25(s12)))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4498,plain,
% 86.54/86.77 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s12)) | m_user_v_ack(c_e_h_2, c_u, s12)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4497, 4496])).
% 86.54/86.77 tff(4499,plain,
% 86.54/86.77 (~node25(s12)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4498, 4492, 4485])).
% 86.54/86.77 tff(4500,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s12)), introduced(assumption)).
% 86.54/86.77 tff(4501,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 86.54/86.77 tff(4502,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s2)), introduced(assumption)).
% 86.54/86.77 tff(4503,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s1)), introduced(assumption)).
% 86.54/86.77 tff(4504,assumption,(node22(c_e_h_1, c_r, s0, s1)), introduced(assumption)).
% 86.54/86.77 tff(4505,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s0)), introduced(assumption)).
% 86.54/86.77 tff(4506,plain,
% 86.54/86.77 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4507,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4506, 94, 4505])).
% 86.54/86.77 tff(4508,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4509,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4510,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4511,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4510, 4509])).
% 86.54/86.77 tff(4512,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4511, 107, 4508, 4504, 4503])).
% 86.54/86.77 tff(4513,plain,((~node22(c_e_h_1, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4514,plain,
% 86.54/86.77 (~node22(c_e_h_1, c_r, s0, s1)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4513, 4503])).
% 86.54/86.77 tff(4515,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4516,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4517,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4516, 4515])).
% 86.54/86.77 tff(4518,plain,
% 86.54/86.77 (node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4517, 81, 71])).
% 86.54/86.77 tff(4519,plain,
% 86.54/86.77 (node21(c_e_h_1, c_r, s0, s1)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4518, 4514])).
% 86.54/86.77 tff(4520,assumption,(m_cell_v_token(c_e_h_1, s0)), introduced(assumption)).
% 86.54/86.77 tff(4521,plain,
% 86.54/86.77 (^[X: $i] : refl((~m_cell_v_token(c_e_h_1, X)) <=> (~m_cell_v_token(c_e_h_1, X)))),
% 86.54/86.77 inference(bind,[status(th)],[])).
% 86.54/86.77 tff(4522,plain,
% 86.54/86.77 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 86.54/86.77 inference(quant_intro,[status(thm)],[4521])).
% 86.54/86.77 tff(4523,plain,
% 86.54/86.77 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4524,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_1, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_3')).
% 86.54/86.77 tff(4525,plain,
% 86.54/86.77 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4524, 4523])).
% 86.54/86.77 tff(4526,plain,(
% 86.54/86.77 ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 86.54/86.77 inference(skolemize,[status(sab)],[4525])).
% 86.54/86.77 tff(4527,plain,
% 86.54/86.77 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4526, 4522])).
% 86.54/86.77 tff(4528,plain,
% 86.54/86.77 ((~![X: $i] : (~m_cell_v_token(c_e_h_1, X))) | (~m_cell_v_token(c_e_h_1, s0))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4529,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4528, 4527, 4520])).
% 86.54/86.77 tff(4530,plain,(~m_cell_v_token(c_e_h_1, s0)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4531,plain,
% 86.54/86.77 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)) | m_cell_v_token(c_e_h_1, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)) | m_cell_v_token(c_e_h_1, s0))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4532,plain,
% 86.54/86.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)) | m_cell_v_token(c_e_h_1, s0))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4533,plain,
% 86.54/86.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)) | m_cell_v_token(c_e_h_1, s0)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4532, 4531])).
% 86.54/86.77 tff(4534,plain,
% 86.54/86.77 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4533, 1104, 4530])).
% 86.54/86.77 tff(4535,plain,
% 86.54/86.77 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4536,plain,
% 86.54/86.77 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4537,plain,
% 86.54/86.77 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4536, 4535])).
% 86.54/86.77 tff(4538,plain,
% 86.54/86.77 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4537, 1116, 4534])).
% 86.54/86.77 tff(4539,plain,
% 86.54/86.77 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4540,plain,
% 86.54/86.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4541,plain,
% 86.54/86.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4540, 4539])).
% 86.54/86.77 tff(4542,plain,
% 86.54/86.77 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4541, 1521, 4538])).
% 86.54/86.77 tff(4543,plain,
% 86.54/86.77 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4544,plain,
% 86.54/86.77 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4545,plain,
% 86.54/86.77 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4544, 4543])).
% 86.54/86.77 tff(4546,plain,
% 86.54/86.77 (~node20(c_e_h_1, c_r, s0)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4545, 1535, 4542])).
% 86.54/86.77 tff(4547,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4548,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4549,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1))),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4548, 4547])).
% 86.54/86.77 tff(4550,plain,
% 86.54/86.77 ($false),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4549, 51, 4546, 4519, 4503])).
% 86.54/86.77 tff(4551,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.77 tff(4552,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4553,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4554,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4553, 4552])).
% 86.54/86.77 tff(4555,plain,
% 86.54/86.77 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2))),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4554, 107, 4551])).
% 86.54/86.77 tff(4556,plain,
% 86.54/86.77 (~node22(c_e_h_1, c_r, s1, s2)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4555, 4502])).
% 86.54/86.77 tff(4557,plain,
% 86.54/86.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2))),
% 86.54/86.77 inference(rewrite,[status(thm)],[])).
% 86.54/86.77 tff(4558,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2))),
% 86.54/86.77 inference(quant_inst,[status(thm)],[])).
% 86.54/86.77 tff(4559,plain,
% 86.54/86.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2)),
% 86.54/86.77 inference(modus_ponens,[status(thm)],[4558, 4557])).
% 86.54/86.77 tff(4560,plain,
% 86.54/86.77 (node21(c_e_h_1, c_r, s1, s2)),
% 86.54/86.77 inference(unit_resolution,[status(thm)],[4559, 81, 344, 4556])).
% 86.54/86.77 tff(4561,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), introduced(assumption)).
% 86.54/86.77 tff(4562,plain,
% 86.54/86.77 (((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))) <=> ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4563,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4564,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4563, 4562])).
% 86.54/86.78 tff(4565,plain,
% 86.54/86.78 (m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4564, 1023])).
% 86.54/86.78 tff(4566,plain,
% 86.54/86.78 (m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4565, 4530])).
% 86.54/86.78 tff(4567,plain,
% 86.54/86.78 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4568,plain,
% 86.54/86.78 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4569,plain,
% 86.54/86.78 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4568, 4567])).
% 86.54/86.78 tff(4570,plain,
% 86.54/86.78 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4569, 1037, 4566])).
% 86.54/86.78 tff(4571,plain,
% 86.54/86.78 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4572,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4573,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4572, 4571])).
% 86.54/86.78 tff(4574,plain,
% 86.54/86.78 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4573, 1048, 4570])).
% 86.54/86.78 tff(4575,plain,
% 86.54/86.78 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4576,plain,
% 86.54/86.78 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4577,plain,
% 86.54/86.78 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4576, 4575])).
% 86.54/86.78 tff(4578,plain,
% 86.54/86.78 (~node9(c_e_h_1, c_m, s0)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4577, 1062, 4574])).
% 86.54/86.78 tff(4579,assumption,(node11(c_e_h_1, c_m, s0, s1)), introduced(assumption)).
% 86.54/86.78 tff(4580,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4581,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4582,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4581, 4580])).
% 86.54/86.78 tff(4583,plain,
% 86.54/86.78 ($false),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4582, 1130, 4579, 4538, 4561])).
% 86.54/86.78 tff(4584,plain,((~node11(c_e_h_1, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.78 tff(4585,plain,
% 86.54/86.78 (~node11(c_e_h_1, c_m, s0, s1)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4584, 4561])).
% 86.54/86.78 tff(4586,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4587,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4588,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4587, 4586])).
% 86.54/86.78 tff(4589,plain,
% 86.54/86.78 (node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4588, 1092, 71])).
% 86.54/86.78 tff(4590,plain,
% 86.54/86.78 (node10(c_e_h_1, c_m, s0, s1)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4589, 4585])).
% 86.54/86.78 tff(4591,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1)))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4592,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1)))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4593,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1))),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4592, 4591])).
% 86.54/86.78 tff(4594,plain,
% 86.54/86.78 ($false),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4593, 1076, 4590, 4578, 4561])).
% 86.54/86.78 tff(4595,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.78 tff(4596,plain,
% 86.54/86.78 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4597,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4598,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4597, 4596])).
% 86.54/86.78 tff(4599,plain,
% 86.54/86.78 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4598, 1521, 4595])).
% 86.54/86.78 tff(4600,plain,
% 86.54/86.78 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4601,plain,
% 86.54/86.78 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4602,plain,
% 86.54/86.78 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4601, 4600])).
% 86.54/86.78 tff(4603,plain,
% 86.54/86.78 (~node20(c_e_h_1, c_r, s1)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4602, 1535, 4599])).
% 86.54/86.78 tff(4604,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4605,plain,
% 86.54/86.78 ((node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2))) <=> ((~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4606,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1)))),
% 86.54/86.78 inference(monotonicity,[status(thm)],[4605])).
% 86.54/86.78 tff(4607,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1))),
% 86.54/86.78 inference(transitivity,[status(thm)],[4606, 4604])).
% 86.54/86.78 tff(4608,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4609,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | node20(c_e_h_1, c_r, s1)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4608, 4607])).
% 86.54/86.78 tff(4610,plain,
% 86.54/86.78 ($false),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4609, 51, 4603, 4502, 4560])).
% 86.54/86.78 tff(4611,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.78 tff(4612,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4613,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4614,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4613, 4612])).
% 86.54/86.78 tff(4615,plain,
% 86.54/86.78 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3))),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4614, 107, 4611])).
% 86.54/86.78 tff(4616,plain,
% 86.54/86.78 (~node22(c_e_h_1, c_r, s2, s3)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4615, 4501])).
% 86.54/86.78 tff(4617,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4618,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4619,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4618, 4617])).
% 86.54/86.78 tff(4620,plain,
% 86.54/86.78 (node21(c_e_h_1, c_r, s2, s3)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4619, 81, 582, 4616])).
% 86.54/86.78 tff(4621,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), introduced(assumption)).
% 86.54/86.78 tff(4622,assumption,(node11(c_e_h_1, c_m, s1, s2)), introduced(assumption)).
% 86.54/86.78 tff(4623,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4624,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4625,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4624, 4623])).
% 86.54/86.78 tff(4626,plain,
% 86.54/86.78 ($false),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4625, 1130, 4595, 4622, 4621])).
% 86.54/86.78 tff(4627,plain,((~node11(c_e_h_1, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.78 tff(4628,plain,
% 86.54/86.78 (~node11(c_e_h_1, c_m, s1, s2)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4627, 4621])).
% 86.54/86.78 tff(4629,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4630,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4631,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4630, 4629])).
% 86.54/86.78 tff(4632,plain,
% 86.54/86.78 (node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4631, 1092, 344])).
% 86.54/86.78 tff(4633,plain,
% 86.54/86.78 (node10(c_e_h_1, c_m, s1, s2)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4632, 4628])).
% 86.54/86.78 tff(4634,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), introduced(assumption)).
% 86.54/86.78 tff(4635,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s0)), introduced(assumption)).
% 86.54/86.78 tff(4636,plain,
% 86.54/86.78 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4637,plain,
% 86.54/86.78 ($false),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4636, 13, 4635])).
% 86.54/86.78 tff(4638,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.78 tff(4639,plain,
% 86.54/86.78 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4640,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4641,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4640, 4639])).
% 86.54/86.78 tff(4642,plain,
% 86.54/86.78 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4641, 976, 4638])).
% 86.54/86.78 tff(4643,plain,
% 86.54/86.78 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4644,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4645,plain,
% 86.54/86.78 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4644, 4643])).
% 86.54/86.78 tff(4646,plain,
% 86.54/86.78 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4645, 1142, 4538])).
% 86.54/86.78 tff(4647,assumption,(node10(c_e_h_1, c_n, s0, s1)), introduced(assumption)).
% 86.54/86.78 tff(4648,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4649,plain,
% 86.54/86.78 (((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4650,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0))))),
% 86.54/86.78 inference(monotonicity,[status(thm)],[4649])).
% 86.54/86.78 tff(4651,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)))),
% 86.54/86.78 inference(transitivity,[status(thm)],[4650, 4648])).
% 86.54/86.78 tff(4652,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4653,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0))),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4652, 4651])).
% 86.54/86.78 tff(4654,plain,
% 86.54/86.78 ($false),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4653, 1191, 4647, 4646, 4642, 4634])).
% 86.54/86.78 tff(4655,plain,((~node10(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.78 tff(4656,plain,
% 86.54/86.78 (~node10(c_e_h_1, c_n, s0, s1)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4655, 4634])).
% 86.54/86.78 tff(4657,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4658,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1))),
% 86.54/86.78 inference(quant_inst,[status(thm)],[])).
% 86.54/86.78 tff(4659,plain,
% 86.54/86.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1)),
% 86.54/86.78 inference(modus_ponens,[status(thm)],[4658, 4657])).
% 86.54/86.78 tff(4660,plain,
% 86.54/86.78 (node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4659, 1092, 71])).
% 86.54/86.78 tff(4661,plain,
% 86.54/86.78 (node11(c_e_h_1, c_n, s0, s1)),
% 86.54/86.78 inference(unit_resolution,[status(thm)],[4660, 4656])).
% 86.54/86.78 tff(4662,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4663,plain,
% 86.54/86.78 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)))),
% 86.54/86.78 inference(rewrite,[status(thm)],[])).
% 86.54/86.78 tff(4664,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1))))),
% 86.54/86.78 inference(monotonicity,[status(thm)],[4663])).
% 86.54/86.78 tff(4665,plain,
% 86.54/86.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)))),
% 86.54/86.79 inference(transitivity,[status(thm)],[4664, 4662])).
% 86.54/86.79 tff(4666,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4667,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4666, 4665])).
% 86.54/86.79 tff(4668,plain,
% 86.54/86.79 ($false),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4667, 1161, 4570, 4661, 4634])).
% 86.54/86.79 tff(4669,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.79 tff(4670,plain,
% 86.54/86.79 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4671,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4672,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4671, 4670])).
% 86.54/86.79 tff(4673,plain,
% 86.54/86.79 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4672, 1048, 4669])).
% 86.54/86.79 tff(4674,plain,
% 86.54/86.79 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4675,plain,
% 86.54/86.79 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4676,plain,
% 86.54/86.79 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4675, 4674])).
% 86.54/86.79 tff(4677,plain,
% 86.54/86.79 (~node9(c_e_h_1, c_m, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4676, 1062, 4673])).
% 86.54/86.79 tff(4678,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4679,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4680,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4679, 4678])).
% 86.54/86.79 tff(4681,plain,
% 86.54/86.79 ($false),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4680, 1076, 4677, 4633, 4621])).
% 86.54/86.79 tff(4682,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.79 tff(4683,plain,
% 86.54/86.79 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4684,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4685,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4684, 4683])).
% 86.54/86.79 tff(4686,plain,
% 86.54/86.79 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4685, 1521, 4682])).
% 86.54/86.79 tff(4687,plain,
% 86.54/86.79 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4688,plain,
% 86.54/86.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4689,plain,
% 86.54/86.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4688, 4687])).
% 86.54/86.79 tff(4690,plain,
% 86.54/86.79 (~node20(c_e_h_1, c_r, s2)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4689, 1535, 4686])).
% 86.54/86.79 tff(4691,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4692,plain,
% 86.54/86.79 ((node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4693,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3))))),
% 86.54/86.79 inference(monotonicity,[status(thm)],[4692])).
% 86.54/86.79 tff(4694,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 86.54/86.79 inference(transitivity,[status(thm)],[4693, 4691])).
% 86.54/86.79 tff(4695,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4696,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4695, 4694])).
% 86.54/86.79 tff(4697,plain,
% 86.54/86.79 ($false),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4696, 51, 4690, 4501, 4620])).
% 86.54/86.79 tff(4698,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.79 tff(4699,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 86.54/86.79 tff(4700,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 86.54/86.79 tff(4701,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 86.54/86.79 tff(4702,assumption,(node10(c_e_h_1, c_m, s2, s3)), introduced(assumption)).
% 86.54/86.79 tff(4703,plain,
% 86.54/86.79 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4704,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4705,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4704, 4703])).
% 86.54/86.79 tff(4706,plain,
% 86.54/86.79 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4705, 1142, 4595])).
% 86.54/86.79 tff(4707,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s1)), introduced(assumption)).
% 86.54/86.79 tff(4708,assumption,(node15(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 86.54/86.79 tff(4709,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4710,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4711,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 86.54/86.79 tff(4712,plain,
% 86.54/86.79 ($false),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4711, 173, 4638, 4707, 4708])).
% 86.54/86.79 tff(4713,plain,((~node15(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.79 tff(4714,plain,
% 86.54/86.79 (~node15(c_e_h_1, c_e, s0, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4713, 4707])).
% 86.54/86.79 tff(4715,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s0)), introduced(assumption)).
% 86.54/86.79 tff(4716,plain,
% 86.54/86.79 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4717,plain,
% 86.54/86.79 ($false),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4716, 94, 4715])).
% 86.54/86.79 tff(4718,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.79 tff(4719,plain,
% 86.54/86.79 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4720,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4721,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4720, 4719])).
% 86.54/86.79 tff(4722,plain,
% 86.54/86.79 (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4721, 385, 4718])).
% 86.54/86.79 tff(4723,assumption,(node14(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 86.54/86.79 tff(4724,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node14(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4725,plain,
% 86.54/86.79 (((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4726,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node14(c_e_h_1, c_e, s0, s1))))),
% 86.54/86.79 inference(monotonicity,[status(thm)],[4725])).
% 86.54/86.79 tff(4727,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(transitivity,[status(thm)],[4726, 4724])).
% 86.54/86.79 tff(4728,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4729,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node14(c_e_h_1, c_e, s0, s1))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4728, 4727])).
% 86.54/86.79 tff(4730,plain,
% 86.54/86.79 ($false),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4729, 283, 4707, 4723, 4722])).
% 86.54/86.79 tff(4731,plain,((~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.79 tff(4732,plain,
% 86.54/86.79 (~node14(c_e_h_1, c_e, s0, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4731, 4707])).
% 86.54/86.79 tff(4733,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_e, s0, s1))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4734,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_e, s0, s1))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4735,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_e, s0, s1)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4734, 4733])).
% 86.54/86.79 tff(4736,plain,
% 86.54/86.79 (node19(c_e_h_1, c_e, s0, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4735, 141, 71])).
% 86.54/86.79 tff(4737,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4738,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4739,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4738, 4737])).
% 86.54/86.79 tff(4740,plain,
% 86.54/86.79 (node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4739, 189, 4736])).
% 86.54/86.79 tff(4741,plain,
% 86.54/86.79 (node16(c_e_h_1, c_e, s0)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4740, 4732, 4714])).
% 86.54/86.79 tff(4742,plain,
% 86.54/86.79 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4743,plain,
% 86.54/86.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4744,plain,
% 86.54/86.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4743, 4742])).
% 86.54/86.79 tff(4745,plain,
% 86.54/86.79 ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4744, 228, 4722])).
% 86.54/86.79 tff(4746,plain,
% 86.54/86.79 (m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4745, 4741])).
% 86.54/86.79 tff(4747,plain,
% 86.54/86.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4748,plain,
% 86.54/86.79 ((m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4749,plain,
% 86.54/86.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0))))),
% 86.54/86.79 inference(monotonicity,[status(thm)],[4748])).
% 86.54/86.79 tff(4750,plain,
% 86.54/86.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 86.54/86.79 inference(transitivity,[status(thm)],[4749, 4747])).
% 86.54/86.79 tff(4751,plain,
% 86.54/86.79 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4752,plain,
% 86.54/86.79 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4751, 4750])).
% 86.54/86.79 tff(4753,plain,
% 86.54/86.79 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0))),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4752, 245, 4722])).
% 86.54/86.79 tff(4754,plain,
% 86.54/86.79 (~node17(c_e_h_1, c_e, s0)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4753, 4746])).
% 86.54/86.79 tff(4755,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4756,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4757,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4756, 4755])).
% 86.54/86.79 tff(4758,plain,
% 86.54/86.79 (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4757, 156, 4736])).
% 86.54/86.79 tff(4759,plain,
% 86.54/86.79 (node18(c_e_h_1, c_e, s0, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4758, 4754])).
% 86.54/86.79 tff(4760,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4761,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4762,plain,
% 86.54/86.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1))),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4761, 4760])).
% 86.54/86.79 tff(4763,plain,
% 86.54/86.79 ($false),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4762, 124, 4638, 4707, 4759])).
% 86.54/86.79 tff(4764,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.79 tff(4765,plain,
% 86.54/86.79 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.79 tff(4766,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 86.54/86.79 inference(quant_inst,[status(thm)],[])).
% 86.54/86.79 tff(4767,plain,
% 86.54/86.79 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 86.54/86.79 inference(modus_ponens,[status(thm)],[4766, 4765])).
% 86.54/86.79 tff(4768,plain,
% 86.54/86.79 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)),
% 86.54/86.79 inference(unit_resolution,[status(thm)],[4767, 976, 4764])).
% 86.54/86.79 tff(4769,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 86.54/86.79 tff(4770,plain,
% 86.54/86.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 86.54/86.79 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4771,plain,
% 86.54/86.80 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))) <=> ((~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4772,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 86.54/86.80 inference(monotonicity,[status(thm)],[4771])).
% 86.54/86.80 tff(4773,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 86.54/86.80 inference(transitivity,[status(thm)],[4772, 4770])).
% 86.54/86.80 tff(4774,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4775,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4774, 4773])).
% 86.54/86.80 tff(4776,plain,
% 86.54/86.80 ((~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4775, 1161])).
% 86.54/86.80 tff(4777,plain,
% 86.54/86.80 ((~node11(c_e_h_1, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4776, 4669])).
% 86.54/86.80 tff(4778,plain,
% 86.54/86.80 (~node11(c_e_h_1, c_n, s1, s2)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4777, 4769])).
% 86.54/86.80 tff(4779,assumption,(~node10(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 86.54/86.80 tff(4780,assumption,(~node11(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 86.54/86.80 tff(4781,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4782,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4783,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4782, 4781])).
% 86.54/86.80 tff(4784,plain,
% 86.54/86.80 ($false),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4783, 1092, 344, 4780, 4779])).
% 86.54/86.80 tff(4785,plain,(node11(c_e_h_1, c_n, s1, s2) | node10(c_e_h_1, c_n, s1, s2)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.80 tff(4786,plain,
% 86.54/86.80 (node10(c_e_h_1, c_n, s1, s2)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4785, 4778])).
% 86.54/86.80 tff(4787,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4788,plain,
% 86.54/86.80 (((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4789,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1))))),
% 86.54/86.80 inference(monotonicity,[status(thm)],[4788])).
% 86.54/86.80 tff(4790,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)))),
% 86.54/86.80 inference(transitivity,[status(thm)],[4789, 4787])).
% 86.54/86.80 tff(4791,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4792,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1))),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4791, 4790])).
% 86.54/86.80 tff(4793,plain,
% 86.54/86.80 ($false),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4792, 1191, 4769, 4786, 4768, 4706])).
% 86.54/86.80 tff(4794,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.80 tff(4795,plain,
% 86.54/86.80 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4796,plain,
% 86.54/86.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4797,plain,
% 86.54/86.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4796, 4795])).
% 86.54/86.80 tff(4798,plain,
% 86.54/86.80 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4797, 1048, 4794])).
% 86.54/86.80 tff(4799,plain,
% 86.54/86.80 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4800,plain,
% 86.54/86.80 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4801,plain,
% 86.54/86.80 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4800, 4799])).
% 86.54/86.80 tff(4802,plain,
% 86.54/86.80 (~node9(c_e_h_1, c_m, s2)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4801, 1062, 4798])).
% 86.54/86.80 tff(4803,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4804,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4805,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3))),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4804, 4803])).
% 86.54/86.80 tff(4806,plain,
% 86.54/86.80 ($false),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4805, 1076, 4701, 4802, 4702])).
% 86.54/86.80 tff(4807,plain,((~node10(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.80 tff(4808,plain,
% 86.54/86.80 (~node10(c_e_h_1, c_m, s2, s3)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4807, 4701])).
% 86.54/86.80 tff(4809,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4810,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4811,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4810, 4809])).
% 86.54/86.80 tff(4812,plain,
% 86.54/86.80 (node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4811, 1092, 582])).
% 86.54/86.80 tff(4813,plain,
% 86.54/86.80 (node11(c_e_h_1, c_m, s2, s3)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4812, 4808])).
% 86.54/86.80 tff(4814,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4815,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4816,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4815, 4814])).
% 86.54/86.80 tff(4817,plain,
% 86.54/86.80 ($false),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4816, 1130, 4701, 4682, 4813])).
% 86.54/86.80 tff(4818,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.80 tff(4819,plain,
% 86.54/86.80 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4820,plain,
% 86.54/86.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4821,plain,
% 86.54/86.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4820, 4819])).
% 86.54/86.80 tff(4822,plain,
% 86.54/86.80 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4821, 1521])).
% 86.54/86.80 tff(4823,plain,
% 86.54/86.80 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4822, 4818])).
% 86.54/86.80 tff(4824,plain,
% 86.54/86.80 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4825,plain,
% 86.54/86.80 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4826,plain,
% 86.54/86.80 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 86.54/86.80 tff(4827,plain,
% 86.54/86.80 (~node20(c_e_h_1, c_r, s3)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4826, 1535, 4823])).
% 86.54/86.80 tff(4828,assumption,(node21(c_e_h_1, c_r, s3, s4)), introduced(assumption)).
% 86.54/86.80 tff(4829,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4830,plain,
% 86.54/86.80 ((node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4831,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4))))),
% 86.54/86.80 inference(monotonicity,[status(thm)],[4830])).
% 86.54/86.80 tff(4832,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 86.54/86.80 inference(transitivity,[status(thm)],[4831, 4829])).
% 86.54/86.80 tff(4833,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4834,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | node20(c_e_h_1, c_r, s3) | (~node21(c_e_h_1, c_r, s3, s4))),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4833, 4832])).
% 86.54/86.80 tff(4835,plain,
% 86.54/86.80 ($false),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4834, 51, 4828, 4827, 4700])).
% 86.54/86.80 tff(4836,plain,((~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.80 tff(4837,plain,
% 86.54/86.80 (~node21(c_e_h_1, c_r, s3, s4)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4836, 4700])).
% 86.54/86.80 tff(4838,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4839,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4840,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4839, 4838])).
% 86.54/86.80 tff(4841,plain,
% 86.54/86.80 (node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4840, 81, 679])).
% 86.54/86.80 tff(4842,plain,
% 86.54/86.80 (node22(c_e_h_1, c_r, s3, s4)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4841, 4837])).
% 86.54/86.80 tff(4843,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4844,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4845,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4844, 4843])).
% 86.54/86.80 tff(4846,plain,
% 86.54/86.80 ($false),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4845, 107, 4842, 4700, 4699])).
% 86.54/86.80 tff(4847,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 86.54/86.80 tff(4848,plain,
% 86.54/86.80 (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4847, 4698])).
% 86.54/86.80 tff(4849,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 86.54/86.80 tff(4850,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s5)), introduced(assumption)).
% 86.54/86.80 tff(4851,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), introduced(assumption)).
% 86.54/86.80 tff(4852,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4853,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4854,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4853, 4852])).
% 86.54/86.80 tff(4855,plain,
% 86.54/86.80 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4854, 1130])).
% 86.54/86.80 tff(4856,plain,
% 86.54/86.80 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4))),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4855, 4818])).
% 86.54/86.80 tff(4857,plain,
% 86.54/86.80 (~node11(c_e_h_1, c_m, s3, s4)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4856, 4851])).
% 86.54/86.80 tff(4858,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s2)), introduced(assumption)).
% 86.54/86.80 tff(4859,assumption,(node18(c_e_h_1, c_e, s1, s2)), introduced(assumption)).
% 86.54/86.80 tff(4860,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4861,plain,
% 86.54/86.80 (((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4862,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2))))),
% 86.54/86.80 inference(monotonicity,[status(thm)],[4861])).
% 86.54/86.80 tff(4863,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))),
% 86.54/86.80 inference(transitivity,[status(thm)],[4862, 4860])).
% 86.54/86.80 tff(4864,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4865,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4864, 4863])).
% 86.54/86.80 tff(4866,plain,
% 86.54/86.80 ($false),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4865, 124, 4764, 4859, 4858])).
% 86.54/86.80 tff(4867,plain,((~node18(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.80 tff(4868,plain,
% 86.54/86.80 (~node18(c_e_h_1, c_e, s1, s2)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4867, 4858])).
% 86.54/86.80 tff(4869,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_e, s1, s2))),
% 86.54/86.80 inference(rewrite,[status(thm)],[])).
% 86.54/86.80 tff(4870,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_e, s1, s2))),
% 86.54/86.80 inference(quant_inst,[status(thm)],[])).
% 86.54/86.80 tff(4871,plain,
% 86.54/86.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_e, s1, s2)),
% 86.54/86.80 inference(modus_ponens,[status(thm)],[4870, 4869])).
% 86.54/86.80 tff(4872,plain,
% 86.54/86.80 (node19(c_e_h_1, c_e, s1, s2)),
% 86.54/86.80 inference(unit_resolution,[status(thm)],[4871, 141, 344])).
% 86.54/86.80 tff(4873,plain,
% 86.54/86.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2) | node17(c_e_h_1, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2) | node17(c_e_h_1, c_e, s1))),
% 86.54/86.81 inference(rewrite,[status(thm)],[])).
% 86.54/86.81 tff(4874,plain,
% 86.54/86.81 ((node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2))) <=> ((~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2) | node17(c_e_h_1, c_e, s1))),
% 86.54/86.81 inference(rewrite,[status(thm)],[])).
% 86.54/86.81 tff(4875,plain,
% 86.54/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2) | node17(c_e_h_1, c_e, s1)))),
% 86.54/86.81 inference(monotonicity,[status(thm)],[4874])).
% 86.54/86.81 tff(4876,plain,
% 86.54/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2) | node17(c_e_h_1, c_e, s1))),
% 86.54/86.81 inference(transitivity,[status(thm)],[4875, 4873])).
% 86.54/86.81 tff(4877,plain,
% 86.54/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 86.54/86.81 inference(quant_inst,[status(thm)],[])).
% 86.54/86.81 tff(4878,plain,
% 86.54/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2) | node17(c_e_h_1, c_e, s1)),
% 86.54/86.81 inference(modus_ponens,[status(thm)],[4877, 4876])).
% 86.54/86.81 tff(4879,plain,
% 86.54/86.81 (node18(c_e_h_1, c_e, s1, s2) | node17(c_e_h_1, c_e, s1)),
% 86.54/86.81 inference(unit_resolution,[status(thm)],[4878, 156, 4872])).
% 86.54/86.81 tff(4880,plain,
% 86.54/86.81 (node17(c_e_h_1, c_e, s1)),
% 86.54/86.81 inference(unit_resolution,[status(thm)],[4879, 4868])).
% 86.54/86.81 tff(4881,plain,
% 86.54/86.81 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 86.54/86.81 inference(rewrite,[status(thm)],[])).
% 86.54/86.81 tff(4882,plain,
% 86.54/86.81 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 86.54/86.81 inference(quant_inst,[status(thm)],[])).
% 86.54/86.81 tff(4883,plain,
% 86.54/86.81 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 86.54/86.81 inference(modus_ponens,[status(thm)],[4882, 4881])).
% 86.54/86.81 tff(4884,plain,
% 86.54/86.81 (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 86.54/86.81 inference(unit_resolution,[status(thm)],[4883, 365, 2696])).
% 86.54/86.81 tff(4885,plain,
% 86.54/86.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)))),
% 86.54/86.81 inference(rewrite,[status(thm)],[])).
% 86.54/86.81 tff(4886,plain,
% 86.54/86.81 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)))),
% 86.54/86.81 inference(rewrite,[status(thm)],[])).
% 86.54/86.81 tff(4887,plain,
% 86.54/86.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1))))),
% 86.54/86.81 inference(monotonicity,[status(thm)],[4886])).
% 86.54/86.81 tff(4888,plain,
% 86.54/86.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)))),
% 86.54/86.81 inference(transitivity,[status(thm)],[4887, 4885])).
% 86.54/86.81 tff(4889,plain,
% 86.54/86.81 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)))),
% 86.54/86.81 inference(quant_inst,[status(thm)],[])).
% 86.54/86.81 tff(4890,plain,
% 86.54/86.81 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1))),
% 86.54/86.81 inference(modus_ponens,[status(thm)],[4889, 4888])).
% 86.54/86.81 tff(4891,plain,
% 86.54/86.81 ((~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1))),
% 86.54/86.81 inference(unit_resolution,[status(thm)],[4890, 209, 4884])).
% 86.54/86.81 tff(4892,plain,
% 86.54/86.81 (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 86.54/86.81 inference(unit_resolution,[status(thm)],[4891, 4880])).
% 86.54/86.81 tff(4893,assumption,(node15(c_e_h_1, c_e, s1, s2)), introduced(assumption)).
% 86.54/86.81 tff(4894,plain,
% 86.54/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 86.54/86.81 inference(rewrite,[status(thm)],[])).
% 86.54/86.81 tff(4895,plain,
% 86.54/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 86.54/86.81 inference(quant_inst,[status(thm)],[])).
% 86.54/86.81 tff(4896,plain,
% 86.54/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 86.54/86.81 inference(modus_ponens,[status(thm)],[4895, 4894])).
% 86.54/86.81 tff(4897,plain,
% 86.54/86.81 ($false),
% 86.54/86.81 inference(unit_resolution,[status(thm)],[4896, 173, 4764, 4893, 4858])).
% 86.54/86.81 tff(4898,plain,((~node15(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 86.54/86.81 tff(4899,plain,
% 86.54/86.81 (~node15(c_e_h_1, c_e, s1, s2)),
% 86.54/86.81 inference(unit_resolution,[status(thm)],[4898, 4858])).
% 86.54/86.81 tff(4900,assumption,(node17(c_e_h_1, c_e, s1)), introduced(assumption)).
% 86.54/86.81 tff(4901,assumption,(node16(c_e_h_1, c_e, s1)), introduced(assumption)).
% 86.54/86.81 tff(4902,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s1)), introduced(assumption)).
% 86.62/86.81 tff(4903,plain,
% 86.62/86.81 (m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1))),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4890, 209, 4900])).
% 86.62/86.81 tff(4904,plain,
% 86.62/86.81 (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4903, 4902])).
% 86.62/86.81 tff(4905,plain,
% 86.62/86.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4906,plain,
% 86.62/86.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1))),
% 86.62/86.81 inference(quant_inst,[status(thm)],[])).
% 86.62/86.81 tff(4907,plain,
% 86.62/86.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 86.62/86.81 inference(modus_ponens,[status(thm)],[4906, 4905])).
% 86.62/86.81 tff(4908,plain,
% 86.62/86.81 (m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4907, 228, 4901])).
% 86.62/86.81 tff(4909,plain,
% 86.62/86.81 ($false),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4908, 4904, 4902])).
% 86.62/86.81 tff(4910,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node16(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.81 tff(4911,plain,
% 86.62/86.81 (m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4910, 4901, 4900])).
% 86.62/86.81 tff(4912,plain,
% 86.62/86.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4913,plain,
% 86.62/86.81 ((m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1))) <=> ((~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4914,plain,
% 86.62/86.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1)))),
% 86.62/86.81 inference(monotonicity,[status(thm)],[4913])).
% 86.62/86.81 tff(4915,plain,
% 86.62/86.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1))),
% 86.62/86.81 inference(transitivity,[status(thm)],[4914, 4912])).
% 86.62/86.81 tff(4916,plain,
% 86.62/86.81 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1)))),
% 86.62/86.81 inference(quant_inst,[status(thm)],[])).
% 86.62/86.81 tff(4917,plain,
% 86.62/86.81 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 86.62/86.81 inference(modus_ponens,[status(thm)],[4916, 4915])).
% 86.62/86.81 tff(4918,plain,
% 86.62/86.81 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4917, 245, 4900])).
% 86.62/86.81 tff(4919,plain,
% 86.62/86.81 (m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4918, 4911])).
% 86.62/86.81 tff(4920,plain,
% 86.62/86.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4921,plain,
% 86.62/86.81 (((~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1))) <=> ((~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4922,plain,
% 86.62/86.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1))))),
% 86.62/86.81 inference(monotonicity,[status(thm)],[4921])).
% 86.62/86.81 tff(4923,plain,
% 86.62/86.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)))),
% 86.62/86.81 inference(transitivity,[status(thm)],[4922, 4920])).
% 86.62/86.81 tff(4924,plain,
% 86.62/86.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)))),
% 86.62/86.81 inference(quant_inst,[status(thm)],[])).
% 86.62/86.81 tff(4925,plain,
% 86.62/86.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1))),
% 86.62/86.81 inference(modus_ponens,[status(thm)],[4924, 4923])).
% 86.62/86.81 tff(4926,plain,
% 86.62/86.81 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1))),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4925, 263, 4901])).
% 86.62/86.81 tff(4927,plain,
% 86.62/86.81 ($false),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4926, 4919, 4911])).
% 86.62/86.81 tff(4928,plain,((~node16(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.81 tff(4929,plain,
% 86.62/86.81 (~node16(c_e_h_1, c_e, s1)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4928, 4880])).
% 86.62/86.81 tff(4930,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4931,plain,
% 86.62/86.81 ((node16(c_e_h_1, c_e, s1) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2))) <=> (node14(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4932,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s1) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2))))),
% 86.62/86.81 inference(monotonicity,[status(thm)],[4931])).
% 86.62/86.81 tff(4933,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s1) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 86.62/86.81 inference(transitivity,[status(thm)],[4932, 4930])).
% 86.62/86.81 tff(4934,plain,
% 86.62/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s1) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 86.62/86.81 inference(quant_inst,[status(thm)],[])).
% 86.62/86.81 tff(4935,plain,
% 86.62/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2))),
% 86.62/86.81 inference(modus_ponens,[status(thm)],[4934, 4933])).
% 86.62/86.81 tff(4936,plain,
% 86.62/86.81 (node14(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | node15(c_e_h_1, c_e, s1, s2)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4935, 189, 4872])).
% 86.62/86.81 tff(4937,plain,
% 86.62/86.81 (node14(c_e_h_1, c_e, s1, s2)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4936, 4929, 4899])).
% 86.62/86.81 tff(4938,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node14(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node14(c_e_h_1, c_e, s1, s2)))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4939,plain,
% 86.62/86.81 (((~node14(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node14(c_e_h_1, c_e, s1, s2)))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4940,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node14(c_e_h_1, c_e, s1, s2))))),
% 86.62/86.81 inference(monotonicity,[status(thm)],[4939])).
% 86.62/86.81 tff(4941,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node14(c_e_h_1, c_e, s1, s2)))),
% 86.62/86.81 inference(transitivity,[status(thm)],[4940, 4938])).
% 86.62/86.81 tff(4942,plain,
% 86.62/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))),
% 86.62/86.81 inference(quant_inst,[status(thm)],[])).
% 86.62/86.81 tff(4943,plain,
% 86.62/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node14(c_e_h_1, c_e, s1, s2))),
% 86.62/86.81 inference(modus_ponens,[status(thm)],[4942, 4941])).
% 86.62/86.81 tff(4944,plain,
% 86.62/86.81 ($false),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4943, 283, 4937, 4858, 4892])).
% 86.62/86.81 tff(4945,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.81 tff(4946,plain,
% 86.62/86.81 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4947,plain,
% 86.62/86.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 86.62/86.81 inference(quant_inst,[status(thm)],[])).
% 86.62/86.81 tff(4948,plain,
% 86.62/86.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 86.62/86.81 inference(modus_ponens,[status(thm)],[4947, 4946])).
% 86.62/86.81 tff(4949,plain,
% 86.62/86.81 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4948, 976, 4945])).
% 86.62/86.81 tff(4950,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)), introduced(assumption)).
% 86.62/86.81 tff(4951,plain,
% 86.62/86.81 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4952,plain,
% 86.62/86.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 86.62/86.81 inference(quant_inst,[status(thm)],[])).
% 86.62/86.81 tff(4953,plain,
% 86.62/86.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 86.62/86.81 inference(modus_ponens,[status(thm)],[4952, 4951])).
% 86.62/86.81 tff(4954,plain,
% 86.62/86.81 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4953, 1142, 4682])).
% 86.62/86.81 tff(4955,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), introduced(assumption)).
% 86.62/86.81 tff(4956,assumption,(node11(c_e_h_1, c_n, s2, s3)), introduced(assumption)).
% 86.62/86.81 tff(4957,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 86.62/86.81 tff(4958,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4959,plain,
% 86.62/86.81 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4960,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3))))),
% 86.62/86.81 inference(monotonicity,[status(thm)],[4959])).
% 86.62/86.81 tff(4961,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 86.62/86.81 inference(transitivity,[status(thm)],[4960, 4958])).
% 86.62/86.81 tff(4962,plain,
% 86.62/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 86.62/86.81 inference(quant_inst,[status(thm)],[])).
% 86.62/86.81 tff(4963,plain,
% 86.62/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3))),
% 86.62/86.81 inference(modus_ponens,[status(thm)],[4962, 4961])).
% 86.62/86.81 tff(4964,plain,
% 86.62/86.81 ($false),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4963, 1161, 4957, 4955, 4956])).
% 86.62/86.81 tff(4965,plain,((~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.81 tff(4966,plain,
% 86.62/86.81 ((~node11(c_e_h_1, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4965, 4794])).
% 86.62/86.81 tff(4967,plain,
% 86.62/86.81 (~node11(c_e_h_1, c_n, s2, s3)),
% 86.62/86.81 inference(unit_resolution,[status(thm)],[4966, 4955])).
% 86.62/86.81 tff(4968,plain,
% 86.62/86.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3))),
% 86.62/86.81 inference(rewrite,[status(thm)],[])).
% 86.62/86.81 tff(4969,plain,
% 86.62/86.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(4970,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[4969, 4968])).
% 86.62/86.82 tff(4971,plain,
% 86.62/86.82 (node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4970, 1092, 582])).
% 86.62/86.82 tff(4972,plain,
% 86.62/86.82 (node10(c_e_h_1, c_n, s2, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4971, 4967])).
% 86.62/86.82 tff(4973,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(4974,plain,
% 86.62/86.82 (((~node10(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(4975,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3))))),
% 86.62/86.82 inference(monotonicity,[status(thm)],[4974])).
% 86.62/86.82 tff(4976,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 86.62/86.82 inference(transitivity,[status(thm)],[4975, 4973])).
% 86.62/86.82 tff(4977,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(4978,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3))),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[4977, 4976])).
% 86.62/86.82 tff(4979,plain,
% 86.62/86.82 ($false),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4978, 1191, 4955, 4972, 4954, 4950])).
% 86.62/86.82 tff(4980,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.82 tff(4981,plain,
% 86.62/86.82 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4980, 4949])).
% 86.62/86.82 tff(4982,plain,
% 86.62/86.82 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(4983,plain,
% 86.62/86.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(4984,plain,
% 86.62/86.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[4983, 4982])).
% 86.62/86.82 tff(4985,plain,
% 86.62/86.82 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4984, 1048, 4981])).
% 86.62/86.82 tff(4986,plain,
% 86.62/86.82 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(4987,plain,
% 86.62/86.82 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(4988,plain,
% 86.62/86.82 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[4987, 4986])).
% 86.62/86.82 tff(4989,plain,
% 86.62/86.82 (~node9(c_e_h_1, c_m, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4988, 1062, 4985])).
% 86.62/86.82 tff(4990,assumption,(node10(c_e_h_1, c_m, s3, s4)), introduced(assumption)).
% 86.62/86.82 tff(4991,assumption,(~node9(c_e_h_1, c_m, s3)), introduced(assumption)).
% 86.62/86.82 tff(4992,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(4993,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(4994,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4))),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[4993, 4992])).
% 86.62/86.82 tff(4995,plain,
% 86.62/86.82 ($false),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4994, 1076, 4851, 4991, 4990])).
% 86.62/86.82 tff(4996,plain,((~node10(c_e_h_1, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | node9(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.82 tff(4997,plain,
% 86.62/86.82 ((~node10(c_e_h_1, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4996, 4989])).
% 86.62/86.82 tff(4998,plain,
% 86.62/86.82 (~node10(c_e_h_1, c_m, s3, s4)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[4997, 4851])).
% 86.62/86.82 tff(4999,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5000,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5001,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5000, 4999])).
% 86.62/86.82 tff(5002,plain,
% 86.62/86.82 (node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5001, 1092, 679])).
% 86.62/86.82 tff(5003,plain,
% 86.62/86.82 ($false),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5002, 4998, 4857])).
% 86.62/86.82 tff(5004,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.82 tff(5005,plain,
% 86.62/86.82 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5006,plain,
% 86.62/86.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5007,plain,
% 86.62/86.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5006, 5005])).
% 86.62/86.82 tff(5008,plain,
% 86.62/86.82 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s4)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5007, 1521, 5004])).
% 86.62/86.82 tff(5009,plain,
% 86.62/86.82 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s4))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5010,plain,
% 86.62/86.82 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s4))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5011,plain,
% 86.62/86.82 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s4)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5010, 5009])).
% 86.62/86.82 tff(5012,plain,
% 86.62/86.82 (~node20(c_e_h_1, c_r, s4)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5011, 1535, 5008])).
% 86.62/86.82 tff(5013,assumption,(~node20(c_e_h_1, c_r, s4)), introduced(assumption)).
% 86.62/86.82 tff(5014,assumption,(node21(c_e_h_1, c_r, s4, s5)), introduced(assumption)).
% 86.62/86.82 tff(5015,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | node20(c_e_h_1, c_r, s4) | (~node21(c_e_h_1, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | node20(c_e_h_1, c_r, s4) | (~node21(c_e_h_1, c_r, s4, s5)))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5016,plain,
% 86.62/86.82 ((node20(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | node20(c_e_h_1, c_r, s4) | (~node21(c_e_h_1, c_r, s4, s5)))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5017,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | node20(c_e_h_1, c_r, s4) | (~node21(c_e_h_1, c_r, s4, s5))))),
% 86.62/86.82 inference(monotonicity,[status(thm)],[5016])).
% 86.62/86.82 tff(5018,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | node20(c_e_h_1, c_r, s4) | (~node21(c_e_h_1, c_r, s4, s5)))),
% 86.62/86.82 inference(transitivity,[status(thm)],[5017, 5015])).
% 86.62/86.82 tff(5019,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5)))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5020,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | node20(c_e_h_1, c_r, s4) | (~node21(c_e_h_1, c_r, s4, s5))),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5019, 5018])).
% 86.62/86.82 tff(5021,plain,
% 86.62/86.82 ($false),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5020, 51, 4850, 5014, 5013])).
% 86.62/86.82 tff(5022,plain,((~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | node20(c_e_h_1, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.82 tff(5023,plain,
% 86.62/86.82 ((~node21(c_e_h_1, c_r, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5022, 5012])).
% 86.62/86.82 tff(5024,plain,
% 86.62/86.82 (~node21(c_e_h_1, c_r, s4, s5)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5023, 4850])).
% 86.62/86.82 tff(5025,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5026,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5027,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5026, 5025])).
% 86.62/86.82 tff(5028,plain,
% 86.62/86.82 (node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5027, 81, 1432])).
% 86.62/86.82 tff(5029,plain,
% 86.62/86.82 (node22(c_e_h_1, c_r, s4, s5)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5028, 5024])).
% 86.62/86.82 tff(5030,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5031,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5032,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5031, 5030])).
% 86.62/86.82 tff(5033,plain,
% 86.62/86.82 ($false),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5032, 107, 4850, 5029, 4849])).
% 86.62/86.82 tff(5034,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.82 tff(5035,plain,
% 86.62/86.82 (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5034, 4848])).
% 86.62/86.82 tff(5036,plain,
% 86.62/86.82 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5037,plain,
% 86.62/86.82 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5038,plain,
% 86.62/86.82 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5037, 5036])).
% 86.62/86.82 tff(5039,plain,
% 86.62/86.82 (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5038, 365, 3330])).
% 86.62/86.82 tff(5040,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s2)), introduced(assumption)).
% 86.62/86.82 tff(5041,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s3)), introduced(assumption)).
% 86.62/86.82 tff(5042,assumption,(node18(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 86.62/86.82 tff(5043,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5044,plain,
% 86.62/86.82 (((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5045,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3))))),
% 86.62/86.82 inference(monotonicity,[status(thm)],[5044])).
% 86.62/86.82 tff(5046,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.82 inference(transitivity,[status(thm)],[5045, 5043])).
% 86.62/86.82 tff(5047,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5048,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node18(c_e_h_1, c_e, s2, s3))),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5047, 5046])).
% 86.62/86.82 tff(5049,plain,
% 86.62/86.82 ($false),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5048, 124, 5040, 5041, 5042])).
% 86.62/86.82 tff(5050,plain,((~node18(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.82 tff(5051,plain,
% 86.62/86.82 (~node18(c_e_h_1, c_e, s2, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5050, 5041, 5040])).
% 86.62/86.82 tff(5052,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5053,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5054,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5053, 5052])).
% 86.62/86.82 tff(5055,plain,
% 86.62/86.82 (node19(c_e_h_1, c_e, s2, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5054, 141, 582])).
% 86.62/86.82 tff(5056,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node18(c_e_h_1, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node18(c_e_h_1, c_e, s2, s3))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5057,plain,
% 86.62/86.82 ((node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3))) <=> (node17(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node18(c_e_h_1, c_e, s2, s3))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5058,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node18(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.82 inference(monotonicity,[status(thm)],[5057])).
% 86.62/86.82 tff(5059,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node18(c_e_h_1, c_e, s2, s3))),
% 86.62/86.82 inference(transitivity,[status(thm)],[5058, 5056])).
% 86.62/86.82 tff(5060,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5061,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s2) | (~node19(c_e_h_1, c_e, s2, s3)) | node18(c_e_h_1, c_e, s2, s3)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5060, 5059])).
% 86.62/86.82 tff(5062,plain,
% 86.62/86.82 (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5061, 156, 5055])).
% 86.62/86.82 tff(5063,plain,
% 86.62/86.82 (node17(c_e_h_1, c_e, s2)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5062, 5051])).
% 86.62/86.82 tff(5064,assumption,(node15(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 86.62/86.82 tff(5065,plain,
% 86.62/86.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5066,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 86.62/86.82 inference(quant_inst,[status(thm)],[])).
% 86.62/86.82 tff(5067,plain,
% 86.62/86.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 86.62/86.82 inference(modus_ponens,[status(thm)],[5066, 5065])).
% 86.62/86.82 tff(5068,plain,
% 86.62/86.82 ($false),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5067, 173, 5040, 5041, 5064])).
% 86.62/86.82 tff(5069,plain,((~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.82 tff(5070,plain,
% 86.62/86.82 (~node15(c_e_h_1, c_e, s2, s3)),
% 86.62/86.82 inference(unit_resolution,[status(thm)],[5069, 5041, 5040])).
% 86.62/86.82 tff(5071,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s2)), introduced(assumption)).
% 86.62/86.82 tff(5072,assumption,(node17(c_e_h_1, c_e, s2)), introduced(assumption)).
% 86.62/86.82 tff(5073,plain,
% 86.62/86.82 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5074,plain,
% 86.62/86.82 ((m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 86.62/86.82 inference(rewrite,[status(thm)],[])).
% 86.62/86.82 tff(5075,plain,
% 86.62/86.82 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2)))),
% 86.62/86.83 inference(monotonicity,[status(thm)],[5074])).
% 86.62/86.83 tff(5076,plain,
% 86.62/86.83 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 86.62/86.83 inference(transitivity,[status(thm)],[5075, 5073])).
% 86.62/86.83 tff(5077,plain,
% 86.62/86.83 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5078,plain,
% 86.62/86.83 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5077, 5076])).
% 86.62/86.83 tff(5079,plain,
% 86.62/86.83 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5078, 245, 5072])).
% 86.62/86.83 tff(5080,plain,
% 86.62/86.83 (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5079, 5071])).
% 86.62/86.83 tff(5081,assumption,(~node15(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 86.62/86.83 tff(5082,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5083,plain,
% 86.62/86.83 (((~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5084,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3))))),
% 86.62/86.83 inference(monotonicity,[status(thm)],[5083])).
% 86.62/86.83 tff(5085,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.83 inference(transitivity,[status(thm)],[5084, 5082])).
% 86.62/86.83 tff(5086,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5087,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3))),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 86.62/86.83 tff(5088,plain,
% 86.62/86.83 ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3))),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5087, 283])).
% 86.62/86.83 tff(5089,plain,
% 86.62/86.83 (~node14(c_e_h_1, c_e, s2, s3)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5088, 5071, 5041])).
% 86.62/86.83 tff(5090,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5091,plain,
% 86.62/86.83 ((node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3))) <=> (node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5092,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2)))),
% 86.62/86.83 inference(monotonicity,[status(thm)],[5091])).
% 86.62/86.83 tff(5093,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2))),
% 86.62/86.83 inference(transitivity,[status(thm)],[5092, 5090])).
% 86.62/86.83 tff(5094,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5095,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5094, 5093])).
% 86.62/86.83 tff(5096,plain,
% 86.62/86.83 (node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | node16(c_e_h_1, c_e, s2)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5095, 189, 5055])).
% 86.62/86.83 tff(5097,plain,
% 86.62/86.83 (node16(c_e_h_1, c_e, s2)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5096, 5089, 5081])).
% 86.62/86.83 tff(5098,plain,
% 86.62/86.83 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5099,plain,
% 86.62/86.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5100,plain,
% 86.62/86.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5099, 5098])).
% 86.62/86.83 tff(5101,plain,
% 86.62/86.83 ($false),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5100, 228, 5071, 5097, 5080])).
% 86.62/86.83 tff(5102,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s2) | node15(c_e_h_1, c_e, s2, s3) | (~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.83 tff(5103,plain,
% 86.62/86.83 (m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5102, 5063, 5070, 5041])).
% 86.62/86.83 tff(5104,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s2)), introduced(assumption)).
% 86.62/86.83 tff(5105,plain,
% 86.62/86.83 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5106,plain,
% 86.62/86.83 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2))) <=> ((~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5107,plain,
% 86.62/86.83 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2))))),
% 86.62/86.83 inference(monotonicity,[status(thm)],[5106])).
% 86.62/86.83 tff(5108,plain,
% 86.62/86.83 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)))),
% 86.62/86.83 inference(transitivity,[status(thm)],[5107, 5105])).
% 86.62/86.83 tff(5109,plain,
% 86.62/86.83 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5110,plain,
% 86.62/86.83 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5109, 5108])).
% 86.62/86.83 tff(5111,plain,
% 86.62/86.83 ((~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5110, 209, 5104])).
% 86.62/86.83 tff(5112,plain,
% 86.62/86.83 ($false),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5111, 5103, 5063])).
% 86.62/86.83 tff(5113,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.83 tff(5114,plain,
% 86.62/86.83 (~m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5113, 5039, 4945])).
% 86.62/86.83 tff(5115,plain,
% 86.62/86.83 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5116,plain,
% 86.62/86.83 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5117,plain,
% 86.62/86.83 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5116, 5115])).
% 86.62/86.83 tff(5118,plain,
% 86.62/86.83 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5117, 976, 5114])).
% 86.62/86.83 tff(5119,plain,
% 86.62/86.83 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5120,plain,
% 86.62/86.83 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5121,plain,
% 86.62/86.83 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5120, 5119])).
% 86.62/86.83 tff(5122,plain,
% 86.62/86.83 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5121, 1142, 4818])).
% 86.62/86.83 tff(5123,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), introduced(assumption)).
% 86.62/86.83 tff(5124,assumption,(node11(c_e_h_1, c_n, s3, s4)), introduced(assumption)).
% 86.62/86.83 tff(5125,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), introduced(assumption)).
% 86.62/86.83 tff(5126,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | (~node11(c_e_h_1, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | (~node11(c_e_h_1, c_n, s3, s4)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5127,plain,
% 86.62/86.83 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | (~node11(c_e_h_1, c_n, s3, s4)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5128,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | (~node11(c_e_h_1, c_n, s3, s4))))),
% 86.62/86.83 inference(monotonicity,[status(thm)],[5127])).
% 86.62/86.83 tff(5129,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | (~node11(c_e_h_1, c_n, s3, s4)))),
% 86.62/86.83 inference(transitivity,[status(thm)],[5128, 5126])).
% 86.62/86.83 tff(5130,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5131,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | (~node11(c_e_h_1, c_n, s3, s4))),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5130, 5129])).
% 86.62/86.83 tff(5132,plain,
% 86.62/86.83 ($false),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5131, 1161, 5125, 5123, 5124])).
% 86.62/86.83 tff(5133,plain,((~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.83 tff(5134,plain,
% 86.62/86.83 (~node11(c_e_h_1, c_n, s3, s4)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5133, 5123, 4981])).
% 86.62/86.83 tff(5135,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5136,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5137,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5136, 5135])).
% 86.62/86.83 tff(5138,plain,
% 86.62/86.83 (node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5137, 1092, 679])).
% 86.62/86.83 tff(5139,plain,
% 86.62/86.83 (node10(c_e_h_1, c_n, s3, s4)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5138, 5134])).
% 86.62/86.83 tff(5140,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5141,plain,
% 86.62/86.83 (((~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5142,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3))))),
% 86.62/86.83 inference(monotonicity,[status(thm)],[5141])).
% 86.62/86.83 tff(5143,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)))),
% 86.62/86.83 inference(transitivity,[status(thm)],[5142, 5140])).
% 86.62/86.83 tff(5144,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5145,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3))),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5144, 5143])).
% 86.62/86.83 tff(5146,plain,
% 86.62/86.83 ($false),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5145, 1191, 5123, 5139, 5122, 5118])).
% 86.62/86.83 tff(5147,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.83 tff(5148,plain,
% 86.62/86.83 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5149,plain,
% 86.62/86.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5150,plain,
% 86.62/86.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5149, 5148])).
% 86.62/86.83 tff(5151,plain,
% 86.62/86.83 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5150, 1048, 5147])).
% 86.62/86.83 tff(5152,plain,
% 86.62/86.83 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5153,plain,
% 86.62/86.83 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5154,plain,
% 86.62/86.83 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5153, 5152])).
% 86.62/86.83 tff(5155,plain,
% 86.62/86.83 (~node9(c_e_h_1, c_m, s4)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5154, 1062, 5151])).
% 86.62/86.83 tff(5156,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), introduced(assumption)).
% 86.62/86.83 tff(5157,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), introduced(assumption)).
% 86.62/86.83 tff(5158,assumption,(node11(c_e_h_1, c_m, s4, s5)), introduced(assumption)).
% 86.62/86.83 tff(5159,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5160,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5161,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5160, 5159])).
% 86.62/86.83 tff(5162,plain,
% 86.62/86.83 ($false),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5161, 1130, 5157, 5156, 5158])).
% 86.62/86.83 tff(5163,plain,((~node11(c_e_h_1, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.83 tff(5164,plain,
% 86.62/86.83 (~node11(c_e_h_1, c_m, s4, s5)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5163, 5157, 5156])).
% 86.62/86.83 tff(5165,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5166,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5167,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5166, 5165])).
% 86.62/86.83 tff(5168,plain,
% 86.62/86.83 (node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5167, 1092, 1432])).
% 86.62/86.83 tff(5169,plain,
% 86.62/86.83 (node10(c_e_h_1, c_m, s4, s5)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5168, 5164])).
% 86.62/86.83 tff(5170,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)) | node9(c_e_h_1, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)) | node9(c_e_h_1, c_m, s4))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5171,plain,
% 86.62/86.83 ((node9(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)) | node9(c_e_h_1, c_m, s4))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5172,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)) | node9(c_e_h_1, c_m, s4)))),
% 86.62/86.83 inference(monotonicity,[status(thm)],[5171])).
% 86.62/86.83 tff(5173,plain,
% 86.62/86.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)) | node9(c_e_h_1, c_m, s4))),
% 86.62/86.83 inference(transitivity,[status(thm)],[5172, 5170])).
% 86.62/86.83 tff(5174,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)))),
% 86.62/86.83 inference(quant_inst,[status(thm)],[])).
% 86.62/86.83 tff(5175,plain,
% 86.62/86.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)) | node9(c_e_h_1, c_m, s4)),
% 86.62/86.83 inference(modus_ponens,[status(thm)],[5174, 5173])).
% 86.62/86.83 tff(5176,plain,
% 86.62/86.83 ($false),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5175, 1076, 5157, 5169, 5155])).
% 86.62/86.83 tff(5177,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.83 tff(5178,plain,
% 86.62/86.83 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 86.62/86.83 inference(unit_resolution,[status(thm)],[5177, 5004])).
% 86.62/86.83 tff(5179,plain,
% 86.62/86.83 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 86.62/86.83 inference(rewrite,[status(thm)],[])).
% 86.62/86.83 tff(5180,plain,
% 86.62/86.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5181,plain,
% 86.62/86.84 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5180, 5179])).
% 86.62/86.84 tff(5182,plain,
% 86.62/86.84 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5181, 1521])).
% 86.62/86.84 tff(5183,plain,
% 86.62/86.84 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s5)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5182, 5178])).
% 86.62/86.84 tff(5184,plain,
% 86.62/86.84 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s5))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5185,plain,
% 86.62/86.84 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s5))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5186,plain,
% 86.62/86.84 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s5)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5185, 5184])).
% 86.62/86.84 tff(5187,plain,
% 86.62/86.84 (~node20(c_e_h_1, c_r, s5)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5186, 1535, 5183])).
% 86.62/86.84 tff(5188,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s5)), introduced(assumption)).
% 86.62/86.84 tff(5189,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s6)), introduced(assumption)).
% 86.62/86.84 tff(5190,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5191,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5192,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5191, 5190])).
% 86.62/86.84 tff(5193,plain,
% 86.62/86.84 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5192, 107])).
% 86.62/86.84 tff(5194,plain,
% 86.62/86.84 (~node22(c_e_h_1, c_r, s5, s6)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5193, 5189, 5188])).
% 86.62/86.84 tff(5195,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5196,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5197,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5196, 5195])).
% 86.62/86.84 tff(5198,plain,
% 86.62/86.84 (node21(c_e_h_1, c_r, s5, s6)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5197, 81, 1499, 5194])).
% 86.62/86.84 tff(5199,assumption,(~node20(c_e_h_1, c_r, s5)), introduced(assumption)).
% 86.62/86.84 tff(5200,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)) | node20(c_e_h_1, c_r, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)) | node20(c_e_h_1, c_r, s5))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5201,plain,
% 86.62/86.84 ((node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)) | node20(c_e_h_1, c_r, s5))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5202,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)) | node20(c_e_h_1, c_r, s5)))),
% 86.62/86.84 inference(monotonicity,[status(thm)],[5201])).
% 86.62/86.84 tff(5203,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)) | node20(c_e_h_1, c_r, s5))),
% 86.62/86.84 inference(transitivity,[status(thm)],[5202, 5200])).
% 86.62/86.84 tff(5204,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5205,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)) | node20(c_e_h_1, c_r, s5)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5204, 5203])).
% 86.62/86.84 tff(5206,plain,
% 86.62/86.84 ($false),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5205, 51, 5189, 5199, 5198])).
% 86.62/86.84 tff(5207,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | node20(c_e_h_1, c_r, s5) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.84 tff(5208,plain,
% 86.62/86.84 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5207, 5187])).
% 86.62/86.84 tff(5209,plain,
% 86.62/86.84 (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5208, 5035])).
% 86.62/86.84 tff(5210,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s7)), introduced(assumption)).
% 86.62/86.84 tff(5211,plain,
% 86.62/86.84 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5212,plain,
% 86.62/86.84 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5213,plain,
% 86.62/86.84 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5212, 5211])).
% 86.62/86.84 tff(5214,plain,
% 86.62/86.84 (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5213, 365, 3989])).
% 86.62/86.84 tff(5215,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s4)), introduced(assumption)).
% 86.62/86.84 tff(5216,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s3)), introduced(assumption)).
% 86.62/86.84 tff(5217,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5218,plain,
% 86.62/86.84 (((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5219,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))))),
% 86.62/86.84 inference(monotonicity,[status(thm)],[5218])).
% 86.62/86.84 tff(5220,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 86.62/86.84 inference(transitivity,[status(thm)],[5219, 5217])).
% 86.62/86.84 tff(5221,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5222,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5221, 5220])).
% 86.62/86.84 tff(5223,plain,
% 86.62/86.84 (m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5222, 124])).
% 86.62/86.84 tff(5224,plain,
% 86.62/86.84 (~node18(c_e_h_1, c_e, s3, s4)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5223, 5216, 5215])).
% 86.62/86.84 tff(5225,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5226,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5227,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5226, 5225])).
% 86.62/86.84 tff(5228,plain,
% 86.62/86.84 (node19(c_e_h_1, c_e, s3, s4)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5227, 141, 679])).
% 86.62/86.84 tff(5229,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5230,plain,
% 86.62/86.84 ((node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4))) <=> ((~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5231,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4)))),
% 86.62/86.84 inference(monotonicity,[status(thm)],[5230])).
% 86.62/86.84 tff(5232,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4))),
% 86.62/86.84 inference(transitivity,[status(thm)],[5231, 5229])).
% 86.62/86.84 tff(5233,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5234,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s3, s4)) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5233, 5232])).
% 86.62/86.84 tff(5235,plain,
% 86.62/86.84 (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5234, 156, 5228])).
% 86.62/86.84 tff(5236,plain,
% 86.62/86.84 (node17(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5235, 5224])).
% 86.62/86.84 tff(5237,assumption,(~node14(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 86.62/86.84 tff(5238,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5239,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5240,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5239, 5238])).
% 86.62/86.84 tff(5241,plain,
% 86.62/86.84 ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5240, 173])).
% 86.62/86.84 tff(5242,plain,
% 86.62/86.84 (~node15(c_e_h_1, c_e, s3, s4)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5241, 5216, 5215])).
% 86.62/86.84 tff(5243,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s3, s4)) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | node16(c_e_h_1, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s3, s4)) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | node16(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5244,plain,
% 86.62/86.84 ((node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4))) <=> ((~node19(c_e_h_1, c_e, s3, s4)) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | node16(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5245,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s3, s4)) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | node16(c_e_h_1, c_e, s3)))),
% 86.62/86.84 inference(monotonicity,[status(thm)],[5244])).
% 86.62/86.84 tff(5246,plain,
% 86.62/86.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s3, s4)) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | node16(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(transitivity,[status(thm)],[5245, 5243])).
% 86.62/86.84 tff(5247,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5248,plain,
% 86.62/86.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s3, s4)) | node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | node16(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5247, 5246])).
% 86.62/86.84 tff(5249,plain,
% 86.62/86.84 (node15(c_e_h_1, c_e, s3, s4) | node14(c_e_h_1, c_e, s3, s4) | node16(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5248, 189, 5228])).
% 86.62/86.84 tff(5250,plain,
% 86.62/86.84 (node16(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5249, 5242, 5237])).
% 86.62/86.84 tff(5251,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s3)), introduced(assumption)).
% 86.62/86.84 tff(5252,assumption,(node16(c_e_h_1, c_e, s3)), introduced(assumption)).
% 86.62/86.84 tff(5253,plain,
% 86.62/86.84 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5254,plain,
% 86.62/86.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5255,plain,
% 86.62/86.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5254, 5253])).
% 86.62/86.84 tff(5256,plain,
% 86.62/86.84 (m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5255, 228, 5252])).
% 86.62/86.84 tff(5257,plain,
% 86.62/86.84 (m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5256, 5251])).
% 86.62/86.84 tff(5258,assumption,(node17(c_e_h_1, c_e, s3)), introduced(assumption)).
% 86.62/86.84 tff(5259,plain,
% 86.62/86.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5260,plain,
% 86.62/86.84 ((m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(rewrite,[status(thm)],[])).
% 86.62/86.84 tff(5261,plain,
% 86.62/86.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 86.62/86.84 inference(monotonicity,[status(thm)],[5260])).
% 86.62/86.84 tff(5262,plain,
% 86.62/86.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 86.62/86.84 inference(transitivity,[status(thm)],[5261, 5259])).
% 86.62/86.84 tff(5263,plain,
% 86.62/86.84 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)))),
% 86.62/86.84 inference(quant_inst,[status(thm)],[])).
% 86.62/86.84 tff(5264,plain,
% 86.62/86.84 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(modus_ponens,[status(thm)],[5263, 5262])).
% 86.62/86.84 tff(5265,plain,
% 86.62/86.84 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5264, 245, 5258])).
% 86.62/86.84 tff(5266,plain,
% 86.62/86.84 ($false),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5265, 5257, 5251])).
% 86.62/86.84 tff(5267,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.84 tff(5268,plain,
% 86.62/86.84 (m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 86.62/86.84 inference(unit_resolution,[status(thm)],[5267, 5236, 5250])).
% 86.62/86.84 tff(5269,plain,
% 86.62/86.84 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5270,plain,
% 86.62/86.85 (((~node16(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5271,plain,
% 86.62/86.85 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3))))),
% 86.62/86.85 inference(monotonicity,[status(thm)],[5270])).
% 86.62/86.85 tff(5272,plain,
% 86.62/86.85 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(transitivity,[status(thm)],[5271, 5269])).
% 86.62/86.85 tff(5273,plain,
% 86.62/86.85 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5274,plain,
% 86.62/86.85 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node16(c_e_h_1, c_e, s3))),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5273, 5272])).
% 86.62/86.85 tff(5275,plain,
% 86.62/86.85 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5274, 263, 5250])).
% 86.62/86.85 tff(5276,plain,
% 86.62/86.85 (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5275, 5268])).
% 86.62/86.85 tff(5277,plain,
% 86.62/86.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5278,plain,
% 86.62/86.85 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5279,plain,
% 86.62/86.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3))))),
% 86.62/86.85 inference(monotonicity,[status(thm)],[5278])).
% 86.62/86.85 tff(5280,plain,
% 86.62/86.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(transitivity,[status(thm)],[5279, 5277])).
% 86.62/86.85 tff(5281,plain,
% 86.62/86.85 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5282,plain,
% 86.62/86.85 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3))),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5281, 5280])).
% 86.62/86.85 tff(5283,plain,
% 86.62/86.85 (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5282, 209, 5236])).
% 86.62/86.85 tff(5284,plain,
% 86.62/86.85 ($false),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5283, 5276, 5268])).
% 86.62/86.85 tff(5285,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.85 tff(5286,plain,
% 86.62/86.85 (node14(c_e_h_1, c_e, s3, s4)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5285, 5216, 5215])).
% 86.62/86.85 tff(5287,assumption,(node14(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 86.62/86.85 tff(5288,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5289,plain,
% 86.62/86.85 (((~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))) <=> ((~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5290,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 86.62/86.85 inference(monotonicity,[status(thm)],[5289])).
% 86.62/86.85 tff(5291,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 86.62/86.85 inference(transitivity,[status(thm)],[5290, 5288])).
% 86.62/86.85 tff(5292,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5293,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5292, 5291])).
% 86.62/86.85 tff(5294,plain,
% 86.62/86.85 ($false),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5293, 283, 5215, 5287, 5251])).
% 86.62/86.85 tff(5295,plain,((~node14(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.85 tff(5296,plain,
% 86.62/86.85 (m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5295, 5286, 5215])).
% 86.62/86.85 tff(5297,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s3)), introduced(assumption)).
% 86.62/86.85 tff(5298,plain,
% 86.62/86.85 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | (~node17(c_e_h_1, c_e, s3))),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5282, 209, 5297])).
% 86.62/86.85 tff(5299,plain,
% 86.62/86.85 ($false),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5298, 5296, 5236])).
% 86.62/86.85 tff(5300,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.85 tff(5301,plain,
% 86.62/86.85 (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5300, 5114])).
% 86.62/86.85 tff(5302,plain,
% 86.62/86.85 (~m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5301, 5214])).
% 86.62/86.85 tff(5303,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), introduced(assumption)).
% 86.62/86.85 tff(5304,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s4)), introduced(assumption)).
% 86.62/86.85 tff(5305,plain,
% 86.62/86.85 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5306,plain,
% 86.62/86.85 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5307,plain,
% 86.62/86.85 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5306, 5305])).
% 86.62/86.85 tff(5308,plain,
% 86.62/86.85 ($false),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5307, 976, 5304, 5303])).
% 86.62/86.85 tff(5309,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s4) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.85 tff(5310,plain,
% 86.62/86.85 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5309, 5302])).
% 86.62/86.85 tff(5311,plain,
% 86.62/86.85 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5312,plain,
% 86.62/86.85 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5313,plain,
% 86.62/86.85 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5312, 5311])).
% 86.62/86.85 tff(5314,plain,
% 86.62/86.85 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5313, 1142, 5004])).
% 86.62/86.85 tff(5315,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), introduced(assumption)).
% 86.62/86.85 tff(5316,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)), introduced(assumption)).
% 86.62/86.85 tff(5317,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), introduced(assumption)).
% 86.62/86.85 tff(5318,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), introduced(assumption)).
% 86.62/86.85 tff(5319,assumption,(node11(c_e_h_1, c_n, s4, s5)), introduced(assumption)).
% 86.62/86.85 tff(5320,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5321,plain,
% 86.62/86.85 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5322,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5))))),
% 86.62/86.85 inference(monotonicity,[status(thm)],[5321])).
% 86.62/86.85 tff(5323,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 86.62/86.85 inference(transitivity,[status(thm)],[5322, 5320])).
% 86.62/86.85 tff(5324,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5325,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~node11(c_e_h_1, c_n, s4, s5))),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5324, 5323])).
% 86.62/86.85 tff(5326,plain,
% 86.62/86.85 ($false),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5325, 1161, 5318, 5319, 5317])).
% 86.62/86.85 tff(5327,plain,((~node11(c_e_h_1, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.85 tff(5328,plain,
% 86.62/86.85 (~node11(c_e_h_1, c_n, s4, s5)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5327, 5318, 5317])).
% 86.62/86.85 tff(5329,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5330,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5331,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5330, 5329])).
% 86.62/86.85 tff(5332,plain,
% 86.62/86.85 (node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5331, 1092, 1432])).
% 86.62/86.85 tff(5333,plain,
% 86.62/86.85 (node10(c_e_h_1, c_n, s4, s5)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5332, 5328])).
% 86.62/86.85 tff(5334,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5335,plain,
% 86.62/86.85 (((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5336,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5))))),
% 86.62/86.85 inference(monotonicity,[status(thm)],[5335])).
% 86.62/86.85 tff(5337,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)))),
% 86.62/86.85 inference(transitivity,[status(thm)],[5336, 5334])).
% 86.62/86.85 tff(5338,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5339,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5))),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 86.62/86.85 tff(5340,plain,
% 86.62/86.85 ($false),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5339, 1191, 5318, 5333, 5316, 5315])).
% 86.62/86.85 tff(5341,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.85 tff(5342,plain,
% 86.62/86.85 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4))),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5341, 5147])).
% 86.62/86.85 tff(5343,plain,
% 86.62/86.85 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4))),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5342, 5314])).
% 86.62/86.85 tff(5344,plain,
% 86.62/86.85 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5343, 5310])).
% 86.62/86.85 tff(5345,plain,
% 86.62/86.85 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5346,plain,
% 86.62/86.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5347,plain,
% 86.62/86.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5346, 5345])).
% 86.62/86.85 tff(5348,plain,
% 86.62/86.85 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5347, 1048, 5344])).
% 86.62/86.85 tff(5349,plain,
% 86.62/86.85 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5350,plain,
% 86.62/86.85 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5351,plain,
% 86.62/86.85 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 86.62/86.85 tff(5352,plain,
% 86.62/86.85 (~node9(c_e_h_1, c_m, s5)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5351, 1062, 5348])).
% 86.62/86.85 tff(5353,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), introduced(assumption)).
% 86.62/86.85 tff(5354,assumption,(~node9(c_e_h_1, c_m, s5)), introduced(assumption)).
% 86.62/86.85 tff(5355,assumption,(node10(c_e_h_1, c_m, s5, s6)), introduced(assumption)).
% 86.62/86.85 tff(5356,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5357,plain,
% 86.62/86.85 ((node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5358,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6))))),
% 86.62/86.85 inference(monotonicity,[status(thm)],[5357])).
% 86.62/86.85 tff(5359,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)))),
% 86.62/86.85 inference(transitivity,[status(thm)],[5358, 5356])).
% 86.62/86.85 tff(5360,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5361,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6))),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5360, 5359])).
% 86.62/86.85 tff(5362,plain,
% 86.62/86.85 ($false),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5361, 1076, 5355, 5354, 5353])).
% 86.62/86.85 tff(5363,plain,((~node10(c_e_h_1, c_m, s5, s6)) | node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.85 tff(5364,plain,
% 86.62/86.85 (~node10(c_e_h_1, c_m, s5, s6)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5363, 5353, 5354])).
% 86.62/86.85 tff(5365,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5366,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5367,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5366, 5365])).
% 86.62/86.85 tff(5368,plain,
% 86.62/86.85 (node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5367, 1092, 1499])).
% 86.62/86.85 tff(5369,plain,
% 86.62/86.85 (node11(c_e_h_1, c_m, s5, s6)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5368, 5364])).
% 86.62/86.85 tff(5370,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), introduced(assumption)).
% 86.62/86.85 tff(5371,plain,
% 86.62/86.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5372,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5373,plain,
% 86.62/86.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5372, 5371])).
% 86.62/86.85 tff(5374,plain,
% 86.62/86.85 ($false),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5373, 1130, 5370, 5369, 5353])).
% 86.62/86.85 tff(5375,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5) | node9(c_e_h_1, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.85 tff(5376,plain,
% 86.62/86.85 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5375, 5178])).
% 86.62/86.85 tff(5377,plain,
% 86.62/86.85 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5376, 5352])).
% 86.62/86.85 tff(5378,plain,
% 86.62/86.85 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5379,plain,
% 86.62/86.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5380,plain,
% 86.62/86.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5379, 5378])).
% 86.62/86.85 tff(5381,plain,
% 86.62/86.85 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5380, 1521, 5377])).
% 86.62/86.85 tff(5382,plain,
% 86.62/86.85 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6))),
% 86.62/86.85 inference(rewrite,[status(thm)],[])).
% 86.62/86.85 tff(5383,plain,
% 86.62/86.85 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6))),
% 86.62/86.85 inference(quant_inst,[status(thm)],[])).
% 86.62/86.85 tff(5384,plain,
% 86.62/86.85 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6)),
% 86.62/86.85 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 86.62/86.85 tff(5385,plain,
% 86.62/86.85 (~node20(c_e_h_1, c_r, s6)),
% 86.62/86.85 inference(unit_resolution,[status(thm)],[5384, 1535, 5381])).
% 86.62/86.86 tff(5386,assumption,(node21(c_e_h_1, c_r, s6, s7)), introduced(assumption)).
% 86.62/86.86 tff(5387,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5388,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5389,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7))),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5388, 5387])).
% 86.62/86.86 tff(5390,plain,
% 86.62/86.86 ($false),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5389, 51, 5210, 5386, 5385])).
% 86.62/86.86 tff(5391,plain,((~node21(c_e_h_1, c_r, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.86 tff(5392,plain,
% 86.62/86.86 (~node21(c_e_h_1, c_r, s6, s7)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5391, 5210])).
% 86.62/86.86 tff(5393,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5394,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5395,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5394, 5393])).
% 86.62/86.86 tff(5396,plain,
% 86.62/86.86 (node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5395, 81, 1552])).
% 86.62/86.86 tff(5397,plain,
% 86.62/86.86 (node22(c_e_h_1, c_r, s6, s7)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5396, 5392])).
% 86.62/86.86 tff(5398,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s6)), introduced(assumption)).
% 86.62/86.86 tff(5399,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5400,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5401,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5400, 5399])).
% 86.62/86.86 tff(5402,plain,
% 86.62/86.86 ($false),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5401, 107, 5398, 5210, 5397])).
% 86.62/86.86 tff(5403,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.86 tff(5404,plain,
% 86.62/86.86 (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5403, 5209])).
% 86.62/86.86 tff(5405,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s8)), introduced(assumption)).
% 86.62/86.86 tff(5406,assumption,(node21(c_e_h_1, c_r, s7, s8)), introduced(assumption)).
% 86.62/86.86 tff(5407,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s4)), introduced(assumption)).
% 86.62/86.86 tff(5408,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s2)), introduced(assumption)).
% 86.62/86.86 tff(5409,assumption,(node6(c_e_h_1, c_j, s1, s2)), introduced(assumption)).
% 86.62/86.86 tff(5410,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s1)), introduced(assumption)).
% 86.62/86.86 tff(5411,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5412,plain,
% 86.62/86.86 (((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5413,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2))))),
% 86.62/86.86 inference(monotonicity,[status(thm)],[5412])).
% 86.62/86.86 tff(5414,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 86.62/86.86 inference(transitivity,[status(thm)],[5413, 5411])).
% 86.62/86.86 tff(5415,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5416,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2))),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5415, 5414])).
% 86.62/86.86 tff(5417,plain,
% 86.62/86.86 ($false),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5416, 899, 5408, 5410, 5409])).
% 86.62/86.86 tff(5418,plain,((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.86 tff(5419,plain,
% 86.62/86.86 ((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5418, 3913])).
% 86.62/86.86 tff(5420,plain,
% 86.62/86.86 (~node6(c_e_h_1, c_j, s1, s2)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5419, 5408])).
% 86.62/86.86 tff(5421,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s1)), introduced(assumption)).
% 86.62/86.86 tff(5422,assumption,(node21(c_e_h_3, c_q, s0, s1)), introduced(assumption)).
% 86.62/86.86 tff(5423,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s0)), introduced(assumption)).
% 86.62/86.86 tff(5424,plain,
% 86.62/86.86 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5425,plain,
% 86.62/86.86 ($false),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5424, 13, 5423])).
% 86.62/86.86 tff(5426,plain,(~m_c_h_element_v_out(c_e_h_3, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.86 tff(5427,plain,
% 86.62/86.86 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s0)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s0)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5428,plain,
% 86.62/86.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s0)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5429,plain,
% 86.62/86.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s0)) | m_c_h_element_v_out(c_e_h_3, c_f, s0)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5428, 5427])).
% 86.62/86.86 tff(5430,plain,
% 86.62/86.86 (~m_and_h_gate_v_in1(c_e_h_3, c_q, s0)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5429, 1666, 5426])).
% 86.62/86.86 tff(5431,plain,
% 86.62/86.86 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s0))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5432,plain,
% 86.62/86.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s0))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5433,plain,
% 86.62/86.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s0)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5432, 5431])).
% 86.62/86.86 tff(5434,plain,
% 86.62/86.86 (~node20(c_e_h_3, c_q, s0)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5433, 37, 5430])).
% 86.62/86.86 tff(5435,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1)))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5436,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1)))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5437,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1))),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5436, 5435])).
% 86.62/86.86 tff(5438,plain,
% 86.62/86.86 ($false),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5437, 51, 5434, 5421, 5422])).
% 86.62/86.86 tff(5439,plain,((~node21(c_e_h_3, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.86 tff(5440,plain,
% 86.62/86.86 (~node21(c_e_h_3, c_q, s0, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5439, 5421])).
% 86.62/86.86 tff(5441,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5442,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5443,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5442, 5441])).
% 86.62/86.86 tff(5444,plain,
% 86.62/86.86 (node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5443, 81, 71])).
% 86.62/86.86 tff(5445,plain,
% 86.62/86.86 (node22(c_e_h_3, c_q, s0, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5444, 5440])).
% 86.62/86.86 tff(5446,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5447,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5448,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5447, 5446])).
% 86.62/86.86 tff(5449,plain,
% 86.62/86.86 ($false),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5448, 107, 3869, 5421, 5445])).
% 86.62/86.86 tff(5450,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.86 tff(5451,plain,
% 86.62/86.86 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5452,plain,
% 86.62/86.86 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5453,plain,
% 86.62/86.86 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5452, 5451])).
% 86.62/86.86 tff(5454,plain,
% 86.62/86.86 (node3(c_e_h_3, c_e_h_1, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5453, 3860, 814])).
% 86.62/86.86 tff(5455,plain,
% 86.62/86.86 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s1)) | (~node3(c_e_h_3, c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s1)) | (~node3(c_e_h_3, c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5456,plain,
% 86.62/86.86 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s1)) | (~node3(c_e_h_3, c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5457,plain,
% 86.62/86.86 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s1)) | (~node3(c_e_h_3, c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5456, 5455])).
% 86.62/86.86 tff(5458,plain,
% 86.62/86.86 ((~m_cell_v_ack(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5457, 836, 5454])).
% 86.62/86.86 tff(5459,plain,
% 86.62/86.86 (~m_cell_v_ack(c_e_h_1, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5458, 5450])).
% 86.62/86.86 tff(5460,plain,
% 86.62/86.86 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)) | m_cell_v_ack(c_e_h_1, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)) | m_cell_v_ack(c_e_h_1, s1))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5461,plain,
% 86.62/86.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)) | m_cell_v_ack(c_e_h_1, s1))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5462,plain,
% 86.62/86.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)) | m_cell_v_ack(c_e_h_1, s1)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5461, 5460])).
% 86.62/86.86 tff(5463,plain,
% 86.62/86.86 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5462, 848, 5459])).
% 86.62/86.86 tff(5464,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s1)), introduced(assumption)).
% 86.62/86.86 tff(5465,assumption,(node22(c_e_h_1, c_l, s0, s1)), introduced(assumption)).
% 86.62/86.86 tff(5466,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5467,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5468,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5467, 5466])).
% 86.62/86.86 tff(5469,plain,
% 86.62/86.86 ($false),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5468, 107, 5465, 3882, 5464])).
% 86.62/86.86 tff(5470,plain,((~node22(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.86 tff(5471,plain,
% 86.62/86.86 (~node22(c_e_h_1, c_l, s0, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5470, 5464])).
% 86.62/86.86 tff(5472,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5473,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5474,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5473, 5472])).
% 86.62/86.86 tff(5475,plain,
% 86.62/86.86 (node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5474, 81, 71])).
% 86.62/86.86 tff(5476,plain,
% 86.62/86.86 (node21(c_e_h_1, c_l, s0, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5475, 5471])).
% 86.62/86.86 tff(5477,plain,
% 86.62/86.86 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5478,plain,
% 86.62/86.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5479,plain,
% 86.62/86.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5478, 5477])).
% 86.62/86.86 tff(5480,plain,
% 86.62/86.86 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5479, 1638, 4538])).
% 86.62/86.86 tff(5481,plain,
% 86.62/86.86 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s0))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5482,plain,
% 86.62/86.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s0))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5483,plain,
% 86.62/86.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s0)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5482, 5481])).
% 86.62/86.86 tff(5484,plain,
% 86.62/86.86 (~node20(c_e_h_1, c_l, s0)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5483, 1535, 5480])).
% 86.62/86.86 tff(5485,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5486,plain,
% 86.62/86.86 ((node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1))) <=> (node20(c_e_h_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5487,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1))))),
% 86.62/86.86 inference(monotonicity,[status(thm)],[5486])).
% 86.62/86.86 tff(5488,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)))),
% 86.62/86.86 inference(transitivity,[status(thm)],[5487, 5485])).
% 86.62/86.86 tff(5489,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1)))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5490,plain,
% 86.62/86.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s0) | (~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5489, 5488])).
% 86.62/86.86 tff(5491,plain,
% 86.62/86.86 ($false),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5490, 51, 5484, 5476, 5464])).
% 86.62/86.86 tff(5492,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.86 tff(5493,plain,
% 86.62/86.86 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5494,plain,
% 86.62/86.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 86.62/86.86 inference(quant_inst,[status(thm)],[])).
% 86.62/86.86 tff(5495,plain,
% 86.62/86.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1)),
% 86.62/86.86 inference(modus_ponens,[status(thm)],[5494, 5493])).
% 86.62/86.86 tff(5496,plain,
% 86.62/86.86 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)),
% 86.62/86.86 inference(unit_resolution,[status(thm)],[5495, 801, 5492])).
% 86.62/86.86 tff(5497,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)), introduced(assumption)).
% 86.62/86.86 tff(5498,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)), introduced(assumption)).
% 86.62/86.86 tff(5499,assumption,(node5(c_e_h_1, c_j, s1, s2)), introduced(assumption)).
% 86.62/86.86 tff(5500,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5501,plain,
% 86.62/86.86 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2))) <=> (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 86.62/86.86 inference(rewrite,[status(thm)],[])).
% 86.62/86.86 tff(5502,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2))))),
% 86.62/86.86 inference(monotonicity,[status(thm)],[5501])).
% 86.62/86.86 tff(5503,plain,
% 86.62/86.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 86.62/86.87 inference(transitivity,[status(thm)],[5502, 5500])).
% 86.62/86.87 tff(5504,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5505,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2))),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5504, 5503])).
% 86.62/86.87 tff(5506,plain,
% 86.62/86.87 ($false),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5505, 862, 5408, 5499, 5498, 5497])).
% 86.62/86.87 tff(5507,plain,((~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.87 tff(5508,plain,
% 86.62/86.87 ((~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5507, 5496])).
% 86.62/86.87 tff(5509,plain,
% 86.62/86.87 (~node5(c_e_h_1, c_j, s1, s2)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5508, 5408, 5463])).
% 86.62/86.87 tff(5510,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_1, c_j, s1, s2) | node6(c_e_h_1, c_j, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_1, c_j, s1, s2) | node6(c_e_h_1, c_j, s1, s2))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5511,plain,
% 86.62/86.87 ((node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node5(c_e_h_1, c_j, s1, s2) | node6(c_e_h_1, c_j, s1, s2))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5512,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_1, c_j, s1, s2) | node6(c_e_h_1, c_j, s1, s2)))),
% 86.62/86.87 inference(monotonicity,[status(thm)],[5511])).
% 86.62/86.87 tff(5513,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_1, c_j, s1, s2) | node6(c_e_h_1, c_j, s1, s2))),
% 86.62/86.87 inference(transitivity,[status(thm)],[5512, 5510])).
% 86.62/86.87 tff(5514,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2) | (~trans(s1, s2)))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5515,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_1, c_j, s1, s2) | node6(c_e_h_1, c_j, s1, s2)),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5514, 5513])).
% 86.62/86.87 tff(5516,plain,
% 86.62/86.87 (node5(c_e_h_1, c_j, s1, s2) | node6(c_e_h_1, c_j, s1, s2)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5515, 881, 344])).
% 86.62/86.87 tff(5517,plain,
% 86.62/86.87 ($false),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5516, 5509, 5420])).
% 86.62/86.87 tff(5518,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.87 tff(5519,plain,
% 86.62/86.87 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5520,plain,
% 86.62/86.87 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5521,plain,
% 86.62/86.87 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2)),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5520, 5519])).
% 86.62/86.87 tff(5522,plain,
% 86.62/86.87 (~m_c_h_element_v_in2(c_e_h_1, c_h, s2)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5521, 309, 5518])).
% 86.62/86.87 tff(5523,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s2)), introduced(assumption)).
% 86.62/86.87 tff(5524,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s3)), introduced(assumption)).
% 86.62/86.87 tff(5525,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s2)), introduced(assumption)).
% 86.62/86.87 tff(5526,assumption,(node15(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 86.62/86.87 tff(5527,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5528,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5529,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5528, 5527])).
% 86.62/86.87 tff(5530,plain,
% 86.62/86.87 ($false),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5529, 173, 5525, 5524, 5526])).
% 86.62/86.87 tff(5531,plain,((~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.87 tff(5532,plain,
% 86.62/86.87 (~node15(c_e_h_1, c_h, s2, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5531, 5525, 5524])).
% 86.62/86.87 tff(5533,assumption,(~node15(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 86.62/86.87 tff(5534,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s2)), introduced(assumption)).
% 86.62/86.87 tff(5535,plain,
% 86.62/86.87 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | m_c_h_element_v_in2(c_e_h_1, c_h, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | m_c_h_element_v_in2(c_e_h_1, c_h, s2))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5536,plain,
% 86.62/86.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | m_c_h_element_v_in2(c_e_h_1, c_h, s2))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5537,plain,
% 86.62/86.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | m_c_h_element_v_in2(c_e_h_1, c_h, s2)),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5536, 5535])).
% 86.62/86.87 tff(5538,plain,
% 86.62/86.87 ((~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5537, 228, 5523])).
% 86.62/86.87 tff(5539,plain,
% 86.62/86.87 (~node16(c_e_h_1, c_h, s2)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5538, 5534])).
% 86.62/86.87 tff(5540,assumption,(node14(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 86.62/86.87 tff(5541,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node14(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node14(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5542,plain,
% 86.62/86.87 (((~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node14(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5543,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node14(c_e_h_1, c_h, s2, s3))))),
% 86.62/86.87 inference(monotonicity,[status(thm)],[5542])).
% 86.62/86.87 tff(5544,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node14(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(transitivity,[status(thm)],[5543, 5541])).
% 86.62/86.87 tff(5545,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5546,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node14(c_e_h_1, c_h, s2, s3))),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5545, 5544])).
% 86.62/86.87 tff(5547,plain,
% 86.62/86.87 ($false),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5546, 283, 5524, 5534, 5540])).
% 86.62/86.87 tff(5548,plain,((~node14(c_e_h_1, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.87 tff(5549,plain,
% 86.62/86.87 (~node14(c_e_h_1, c_h, s2, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5548, 5534, 5524])).
% 86.62/86.87 tff(5550,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_h, s2, s3))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5551,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_h, s2, s3))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5552,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_h, s2, s3)),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5551, 5550])).
% 86.62/86.87 tff(5553,plain,
% 86.62/86.87 (node19(c_e_h_1, c_h, s2, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5552, 141, 582])).
% 86.62/86.87 tff(5554,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5555,plain,
% 86.62/86.87 ((node16(c_e_h_1, c_h, s2) | node14(c_e_h_1, c_h, s2, s3) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))) <=> (node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5556,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s2) | node14(c_e_h_1, c_h, s2, s3) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))))),
% 86.62/86.87 inference(monotonicity,[status(thm)],[5555])).
% 86.62/86.87 tff(5557,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s2) | node14(c_e_h_1, c_h, s2, s3) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(transitivity,[status(thm)],[5556, 5554])).
% 86.62/86.87 tff(5558,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s2) | node14(c_e_h_1, c_h, s2, s3) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5559,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 86.62/86.87 tff(5560,plain,
% 86.62/86.87 (node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | node14(c_e_h_1, c_h, s2, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5559, 189, 5553])).
% 86.62/86.87 tff(5561,plain,
% 86.62/86.87 ($false),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5560, 5549, 5539, 5533])).
% 86.62/86.87 tff(5562,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.87 tff(5563,plain,
% 86.62/86.87 (m_c_h_element_v_in1(c_e_h_1, c_h, s2)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5562, 5532, 5524, 5523])).
% 86.62/86.87 tff(5564,plain,
% 86.62/86.87 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | (~node17(c_e_h_1, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | (~node17(c_e_h_1, c_h, s2)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5565,plain,
% 86.62/86.87 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | (~node17(c_e_h_1, c_h, s2)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5566,plain,
% 86.62/86.87 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | (~node17(c_e_h_1, c_h, s2))))),
% 86.62/86.87 inference(monotonicity,[status(thm)],[5565])).
% 86.62/86.87 tff(5567,plain,
% 86.62/86.87 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | (~node17(c_e_h_1, c_h, s2)))),
% 86.62/86.87 inference(transitivity,[status(thm)],[5566, 5564])).
% 86.62/86.87 tff(5568,plain,
% 86.62/86.87 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5569,plain,
% 86.62/86.87 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | (~node17(c_e_h_1, c_h, s2))),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5568, 5567])).
% 86.62/86.87 tff(5570,plain,
% 86.62/86.87 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | (~node17(c_e_h_1, c_h, s2))),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5569, 209, 5523])).
% 86.62/86.87 tff(5571,plain,
% 86.62/86.87 (~node17(c_e_h_1, c_h, s2)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5570, 5563])).
% 86.62/86.87 tff(5572,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5573,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5574,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5573, 5572])).
% 86.62/86.87 tff(5575,plain,
% 86.62/86.87 (node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5574, 156, 5553])).
% 86.62/86.87 tff(5576,plain,
% 86.62/86.87 (node18(c_e_h_1, c_h, s2, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5575, 5571])).
% 86.62/86.87 tff(5577,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5578,plain,
% 86.62/86.87 (((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5579,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3))))),
% 86.62/86.87 inference(monotonicity,[status(thm)],[5578])).
% 86.62/86.87 tff(5580,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(transitivity,[status(thm)],[5579, 5577])).
% 86.62/86.87 tff(5581,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5582,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node18(c_e_h_1, c_h, s2, s3))),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5581, 5580])).
% 86.62/86.87 tff(5583,plain,
% 86.62/86.87 ($false),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5582, 124, 5525, 5524, 5576])).
% 86.62/86.87 tff(5584,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.87 tff(5585,plain,
% 86.62/86.87 (m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5584, 5522])).
% 86.62/86.87 tff(5586,plain,
% 86.62/86.87 (~m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5585, 3975])).
% 86.62/86.87 tff(5587,plain,
% 86.62/86.87 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5588,plain,
% 86.62/86.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5589,plain,
% 86.62/86.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5588, 5587])).
% 86.62/86.87 tff(5590,plain,
% 86.62/86.87 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5589, 23, 5586])).
% 86.62/86.87 tff(5591,plain,
% 86.62/86.87 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5592,plain,
% 86.62/86.87 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5593,plain,
% 86.62/86.87 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3)),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5592, 5591])).
% 86.62/86.87 tff(5594,plain,
% 86.62/86.87 (~node20(c_e_h_1, c_i, s3)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5593, 37, 5590])).
% 86.62/86.87 tff(5595,assumption,(~node20(c_e_h_1, c_i, s3)), introduced(assumption)).
% 86.62/86.87 tff(5596,assumption,(node21(c_e_h_1, c_i, s3, s4)), introduced(assumption)).
% 86.62/86.87 tff(5597,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4)))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5598,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4)))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5599,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4))),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5598, 5597])).
% 86.62/86.87 tff(5600,plain,
% 86.62/86.87 ($false),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5599, 51, 5407, 5596, 5595])).
% 86.62/86.87 tff(5601,plain,((~node21(c_e_h_1, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.87 tff(5602,plain,
% 86.62/86.87 ((~node21(c_e_h_1, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5601, 5594])).
% 86.62/86.87 tff(5603,plain,
% 86.62/86.87 (~node21(c_e_h_1, c_i, s3, s4)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5602, 5407])).
% 86.62/86.87 tff(5604,plain,
% 86.62/86.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4))),
% 86.62/86.87 inference(rewrite,[status(thm)],[])).
% 86.62/86.87 tff(5605,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4))),
% 86.62/86.87 inference(quant_inst,[status(thm)],[])).
% 86.62/86.87 tff(5606,plain,
% 86.62/86.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4)),
% 86.62/86.87 inference(modus_ponens,[status(thm)],[5605, 5604])).
% 86.62/86.87 tff(5607,plain,
% 86.62/86.87 (node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4)),
% 86.62/86.87 inference(unit_resolution,[status(thm)],[5606, 81, 679])).
% 86.62/86.87 tff(5608,plain,
% 86.62/86.87 (node22(c_e_h_1, c_i, s3, s4)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5607, 5603])).
% 86.62/86.88 tff(5609,plain,
% 86.62/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5610,plain,
% 86.62/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 86.62/86.88 inference(quant_inst,[status(thm)],[])).
% 86.62/86.88 tff(5611,plain,
% 86.62/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 86.62/86.88 inference(modus_ponens,[status(thm)],[5610, 5609])).
% 86.62/86.88 tff(5612,plain,
% 86.62/86.88 ($false),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5611, 107, 5407, 5608, 3989])).
% 86.62/86.88 tff(5613,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 86.62/86.88 tff(5614,plain,
% 86.62/86.88 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5615,plain,
% 86.62/86.88 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 86.62/86.88 inference(quant_inst,[status(thm)],[])).
% 86.62/86.88 tff(5616,plain,
% 86.62/86.88 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 86.62/86.88 inference(modus_ponens,[status(thm)],[5615, 5614])).
% 86.62/86.88 tff(5617,plain,
% 86.62/86.88 (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5616, 365, 5613])).
% 86.62/86.88 tff(5618,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s5)), introduced(assumption)).
% 86.62/86.88 tff(5619,assumption,(node18(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 86.62/86.88 tff(5620,plain,
% 86.62/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node18(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5621,plain,
% 86.62/86.88 (((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5622,plain,
% 86.62/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node18(c_e_h_1, c_e, s4, s5))))),
% 86.62/86.88 inference(monotonicity,[status(thm)],[5621])).
% 86.62/86.88 tff(5623,plain,
% 86.62/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 86.62/86.88 inference(transitivity,[status(thm)],[5622, 5620])).
% 86.62/86.88 tff(5624,plain,
% 86.62/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 86.62/86.88 inference(quant_inst,[status(thm)],[])).
% 86.62/86.88 tff(5625,plain,
% 86.62/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node18(c_e_h_1, c_e, s4, s5))),
% 86.62/86.88 inference(modus_ponens,[status(thm)],[5624, 5623])).
% 86.62/86.88 tff(5626,plain,
% 86.62/86.88 ($false),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5625, 124, 5304, 5618, 5619])).
% 86.62/86.88 tff(5627,plain,((~node18(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.88 tff(5628,plain,
% 86.62/86.88 (~node18(c_e_h_1, c_e, s4, s5)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5627, 5304, 5618])).
% 86.62/86.88 tff(5629,plain,
% 86.62/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_e, s4, s5))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5630,plain,
% 86.62/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_e, s4, s5))),
% 86.62/86.88 inference(quant_inst,[status(thm)],[])).
% 86.62/86.88 tff(5631,plain,
% 86.62/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_e, s4, s5)),
% 86.62/86.88 inference(modus_ponens,[status(thm)],[5630, 5629])).
% 86.62/86.88 tff(5632,plain,
% 86.62/86.88 (node19(c_e_h_1, c_e, s4, s5)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5631, 141, 1432])).
% 86.62/86.88 tff(5633,plain,
% 86.62/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5634,plain,
% 86.62/86.88 ((node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5))) <=> (node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5635,plain,
% 86.62/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5)))),
% 86.62/86.88 inference(monotonicity,[status(thm)],[5634])).
% 86.62/86.88 tff(5636,plain,
% 86.62/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5))),
% 86.62/86.88 inference(transitivity,[status(thm)],[5635, 5633])).
% 86.62/86.88 tff(5637,plain,
% 86.62/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 86.62/86.88 inference(quant_inst,[status(thm)],[])).
% 86.62/86.88 tff(5638,plain,
% 86.62/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5)),
% 86.62/86.88 inference(modus_ponens,[status(thm)],[5637, 5636])).
% 86.62/86.88 tff(5639,plain,
% 86.62/86.88 (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5638, 156, 5632])).
% 86.62/86.88 tff(5640,plain,
% 86.62/86.88 (node17(c_e_h_1, c_e, s4)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5639, 5628])).
% 86.62/86.88 tff(5641,assumption,(node17(c_e_h_1, c_e, s4)), introduced(assumption)).
% 86.62/86.88 tff(5642,assumption,(node16(c_e_h_1, c_e, s4)), introduced(assumption)).
% 86.62/86.88 tff(5643,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s4)), introduced(assumption)).
% 86.62/86.88 tff(5644,plain,
% 86.62/86.88 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5645,plain,
% 86.62/86.88 ((m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5646,plain,
% 86.62/86.88 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4)))),
% 86.62/86.88 inference(monotonicity,[status(thm)],[5645])).
% 86.62/86.88 tff(5647,plain,
% 86.62/86.88 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 86.62/86.88 inference(transitivity,[status(thm)],[5646, 5644])).
% 86.62/86.88 tff(5648,plain,
% 86.62/86.88 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)))),
% 86.62/86.88 inference(quant_inst,[status(thm)],[])).
% 86.62/86.88 tff(5649,plain,
% 86.62/86.88 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 86.62/86.88 inference(modus_ponens,[status(thm)],[5648, 5647])).
% 86.62/86.88 tff(5650,plain,
% 86.62/86.88 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5649, 245, 5641])).
% 86.62/86.88 tff(5651,plain,
% 86.62/86.88 (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5650, 5643])).
% 86.62/86.88 tff(5652,plain,
% 86.62/86.88 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5653,plain,
% 86.62/86.88 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4))),
% 86.62/86.88 inference(quant_inst,[status(thm)],[])).
% 86.62/86.88 tff(5654,plain,
% 86.62/86.88 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 86.62/86.88 inference(modus_ponens,[status(thm)],[5653, 5652])).
% 86.62/86.88 tff(5655,plain,
% 86.62/86.88 (m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5654, 228, 5642])).
% 86.62/86.88 tff(5656,plain,
% 86.62/86.88 ($false),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5655, 5651, 5643])).
% 86.62/86.88 tff(5657,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node16(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 86.62/86.88 tff(5658,plain,
% 86.62/86.88 (m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 86.62/86.88 inference(unit_resolution,[status(thm)],[5657, 5642, 5641])).
% 86.62/86.88 tff(5659,plain,
% 86.62/86.88 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5660,plain,
% 86.62/86.88 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)))),
% 86.62/86.88 inference(rewrite,[status(thm)],[])).
% 86.62/86.88 tff(5661,plain,
% 86.62/86.88 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4))))),
% 86.62/86.88 inference(monotonicity,[status(thm)],[5660])).
% 86.62/86.88 tff(5662,plain,
% 86.62/86.88 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)))),
% 86.62/86.88 inference(transitivity,[status(thm)],[5661, 5659])).
% 86.62/86.88 tff(5663,plain,
% 86.62/86.88 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)))),
% 86.62/86.88 inference(quant_inst,[status(thm)],[])).
% 86.62/86.88 tff(5664,plain,
% 86.62/86.88 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 86.70/86.88 inference(modus_ponens,[status(thm)],[5663, 5662])).
% 86.70/86.88 tff(5665,plain,
% 86.70/86.88 (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5664, 209, 5641])).
% 86.70/86.88 tff(5666,plain,
% 86.70/86.88 (m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5665, 5658])).
% 86.70/86.88 tff(5667,plain,
% 86.70/86.88 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)))),
% 86.70/86.88 inference(rewrite,[status(thm)],[])).
% 86.70/86.88 tff(5668,plain,
% 86.70/86.88 (((~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4))) <=> ((~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)))),
% 86.70/86.88 inference(rewrite,[status(thm)],[])).
% 86.70/86.88 tff(5669,plain,
% 86.70/86.88 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4))))),
% 86.70/86.88 inference(monotonicity,[status(thm)],[5668])).
% 86.70/86.88 tff(5670,plain,
% 86.70/86.88 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)))),
% 86.70/86.88 inference(transitivity,[status(thm)],[5669, 5667])).
% 86.70/86.88 tff(5671,plain,
% 86.70/86.88 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)))),
% 86.70/86.88 inference(quant_inst,[status(thm)],[])).
% 86.70/86.88 tff(5672,plain,
% 86.70/86.88 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 86.70/86.88 inference(modus_ponens,[status(thm)],[5671, 5670])).
% 86.70/86.88 tff(5673,plain,
% 86.70/86.88 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5672, 263, 5642])).
% 86.70/86.88 tff(5674,plain,
% 86.70/86.88 ($false),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5673, 5666, 5658])).
% 86.70/86.88 tff(5675,plain,((~node16(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.88 tff(5676,plain,
% 86.70/86.88 (~node16(c_e_h_1, c_e, s4)),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5675, 5640])).
% 86.70/86.88 tff(5677,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s4)), introduced(assumption)).
% 86.70/86.88 tff(5678,plain,
% 86.70/86.88 ((~node17(c_e_h_1, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5664, 209, 5677])).
% 86.70/86.88 tff(5679,plain,
% 86.70/86.88 (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5678, 5640])).
% 86.70/86.88 tff(5680,assumption,(node14(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 86.70/86.88 tff(5681,plain,
% 86.70/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 86.70/86.88 inference(rewrite,[status(thm)],[])).
% 86.70/86.88 tff(5682,plain,
% 86.70/86.88 (((~node14(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 86.70/86.88 inference(rewrite,[status(thm)],[])).
% 86.70/86.88 tff(5683,plain,
% 86.70/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5))))),
% 86.70/86.88 inference(monotonicity,[status(thm)],[5682])).
% 86.70/86.88 tff(5684,plain,
% 86.70/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 86.70/86.88 inference(transitivity,[status(thm)],[5683, 5681])).
% 86.70/86.88 tff(5685,plain,
% 86.70/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)))),
% 86.70/86.88 inference(quant_inst,[status(thm)],[])).
% 86.70/86.88 tff(5686,plain,
% 86.70/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5))),
% 86.70/86.88 inference(modus_ponens,[status(thm)],[5685, 5684])).
% 86.70/86.88 tff(5687,plain,
% 86.70/86.88 ($false),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5686, 283, 5618, 5680, 5643])).
% 86.70/86.88 tff(5688,plain,((~node14(c_e_h_1, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.88 tff(5689,plain,
% 86.70/86.88 (~node14(c_e_h_1, c_e, s4, s5)),
% 86.70/86.88 inference(unit_resolution,[status(thm)],[5688, 5679, 5618])).
% 86.70/86.88 tff(5690,plain,
% 86.70/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5) | node14(c_e_h_1, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5) | node14(c_e_h_1, c_e, s4, s5))),
% 86.70/86.88 inference(rewrite,[status(thm)],[])).
% 86.70/86.88 tff(5691,plain,
% 86.70/86.88 ((node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5))) <=> (node16(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5) | node14(c_e_h_1, c_e, s4, s5))),
% 86.70/86.88 inference(rewrite,[status(thm)],[])).
% 86.70/86.88 tff(5692,plain,
% 86.70/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5) | node14(c_e_h_1, c_e, s4, s5)))),
% 86.70/86.88 inference(monotonicity,[status(thm)],[5691])).
% 86.70/86.88 tff(5693,plain,
% 86.70/86.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5) | node14(c_e_h_1, c_e, s4, s5))),
% 86.70/86.88 inference(transitivity,[status(thm)],[5692, 5690])).
% 86.70/86.88 tff(5694,plain,
% 86.70/86.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5695,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5) | node14(c_e_h_1, c_e, s4, s5)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5694, 5693])).
% 86.70/86.89 tff(5696,plain,
% 86.70/86.89 (node16(c_e_h_1, c_e, s4) | node15(c_e_h_1, c_e, s4, s5) | node14(c_e_h_1, c_e, s4, s5)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5695, 189, 5632])).
% 86.70/86.89 tff(5697,plain,
% 86.70/86.89 (node15(c_e_h_1, c_e, s4, s5)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5696, 5689, 5676])).
% 86.70/86.89 tff(5698,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5699,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5700,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5699, 5698])).
% 86.70/86.89 tff(5701,plain,
% 86.70/86.89 ($false),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5700, 173, 5304, 5618, 5697])).
% 86.70/86.89 tff(5702,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.89 tff(5703,plain,
% 86.70/86.89 (~m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5702, 5617, 5302])).
% 86.70/86.89 tff(5704,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)), introduced(assumption)).
% 86.70/86.89 tff(5705,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s5)), introduced(assumption)).
% 86.70/86.89 tff(5706,plain,
% 86.70/86.89 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5707,plain,
% 86.70/86.89 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5708,plain,
% 86.70/86.89 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5707, 5706])).
% 86.70/86.89 tff(5709,plain,
% 86.70/86.89 ($false),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5708, 976, 5705, 5704])).
% 86.70/86.89 tff(5710,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.89 tff(5711,plain,
% 86.70/86.89 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5710, 5703])).
% 86.70/86.89 tff(5712,plain,
% 86.70/86.89 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5713,plain,
% 86.70/86.89 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5714,plain,
% 86.70/86.89 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5713, 5712])).
% 86.70/86.89 tff(5715,plain,
% 86.70/86.89 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5714, 1142, 5178])).
% 86.70/86.89 tff(5716,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)), introduced(assumption)).
% 86.70/86.89 tff(5717,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)), introduced(assumption)).
% 86.70/86.89 tff(5718,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)), introduced(assumption)).
% 86.70/86.89 tff(5719,assumption,(node10(c_e_h_1, c_n, s5, s6)), introduced(assumption)).
% 86.70/86.89 tff(5720,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5721,plain,
% 86.70/86.89 (((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5722,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6))))),
% 86.70/86.89 inference(monotonicity,[status(thm)],[5721])).
% 86.70/86.89 tff(5723,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 86.70/86.89 inference(transitivity,[status(thm)],[5722, 5720])).
% 86.70/86.89 tff(5724,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5725,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6))),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5724, 5723])).
% 86.70/86.89 tff(5726,plain,
% 86.70/86.89 ($false),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5725, 1191, 5718, 5719, 5717, 5716])).
% 86.70/86.89 tff(5727,plain,((~node10(c_e_h_1, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.89 tff(5728,plain,
% 86.70/86.89 (~node10(c_e_h_1, c_n, s5, s6)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5727, 5718, 5717, 5716])).
% 86.70/86.89 tff(5729,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5730,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5731,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5730, 5729])).
% 86.70/86.89 tff(5732,plain,
% 86.70/86.89 (node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5731, 1092, 1499])).
% 86.70/86.89 tff(5733,plain,
% 86.70/86.89 (node11(c_e_h_1, c_n, s5, s6)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5732, 5728])).
% 86.70/86.89 tff(5734,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), introduced(assumption)).
% 86.70/86.89 tff(5735,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5736,plain,
% 86.70/86.89 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5737,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6))))),
% 86.70/86.89 inference(monotonicity,[status(thm)],[5736])).
% 86.70/86.89 tff(5738,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 86.70/86.89 inference(transitivity,[status(thm)],[5737, 5735])).
% 86.70/86.89 tff(5739,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5740,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~node11(c_e_h_1, c_n, s5, s6))),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5739, 5738])).
% 86.70/86.89 tff(5741,plain,
% 86.70/86.89 ($false),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5740, 1161, 5734, 5718, 5733])).
% 86.70/86.89 tff(5742,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.89 tff(5743,plain,
% 86.70/86.89 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5))),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5742, 5715])).
% 86.70/86.89 tff(5744,plain,
% 86.70/86.89 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5743, 5711, 5344])).
% 86.70/86.89 tff(5745,plain,
% 86.70/86.89 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5746,plain,
% 86.70/86.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5747,plain,
% 86.70/86.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5746, 5745])).
% 86.70/86.89 tff(5748,plain,
% 86.70/86.89 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5747, 1048, 5744])).
% 86.70/86.89 tff(5749,plain,
% 86.70/86.89 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5750,plain,
% 86.70/86.89 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5751,plain,
% 86.70/86.89 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5750, 5749])).
% 86.70/86.89 tff(5752,plain,
% 86.70/86.89 (~node9(c_e_h_1, c_m, s6)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5751, 1062, 5748])).
% 86.70/86.89 tff(5753,assumption,(~node9(c_e_h_1, c_m, s6)), introduced(assumption)).
% 86.70/86.89 tff(5754,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), introduced(assumption)).
% 86.70/86.89 tff(5755,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), introduced(assumption)).
% 86.70/86.89 tff(5756,assumption,(node11(c_e_h_1, c_m, s6, s7)), introduced(assumption)).
% 86.70/86.89 tff(5757,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5758,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5759,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5758, 5757])).
% 86.70/86.89 tff(5760,plain,
% 86.70/86.89 ($false),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5759, 1130, 5755, 5754, 5756])).
% 86.70/86.89 tff(5761,plain,((~node11(c_e_h_1, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.89 tff(5762,plain,
% 86.70/86.89 (~node11(c_e_h_1, c_m, s6, s7)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5761, 5755, 5754])).
% 86.70/86.89 tff(5763,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5764,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5765,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5764, 5763])).
% 86.70/86.89 tff(5766,plain,
% 86.70/86.89 (node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5765, 1092, 1552])).
% 86.70/86.89 tff(5767,plain,
% 86.70/86.89 (node10(c_e_h_1, c_m, s6, s7)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5766, 5762])).
% 86.70/86.89 tff(5768,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5769,plain,
% 86.70/86.89 ((node9(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node10(c_e_h_1, c_m, s6, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5770,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node10(c_e_h_1, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7))))),
% 86.70/86.89 inference(monotonicity,[status(thm)],[5769])).
% 86.70/86.89 tff(5771,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node10(c_e_h_1, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7)))),
% 86.70/86.89 inference(transitivity,[status(thm)],[5770, 5768])).
% 86.70/86.89 tff(5772,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node10(c_e_h_1, c_m, s6, s7)))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5773,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7))),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5772, 5771])).
% 86.70/86.89 tff(5774,plain,
% 86.70/86.89 ($false),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5773, 1076, 5755, 5767, 5753])).
% 86.70/86.89 tff(5775,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.89 tff(5776,plain,
% 86.70/86.89 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5775, 5752, 5377])).
% 86.70/86.89 tff(5777,plain,
% 86.70/86.89 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5778,plain,
% 86.70/86.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5779,plain,
% 86.70/86.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5778, 5777])).
% 86.70/86.89 tff(5780,plain,
% 86.70/86.89 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5779, 1521])).
% 86.70/86.89 tff(5781,plain,
% 86.70/86.89 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5780, 5776])).
% 86.70/86.89 tff(5782,plain,
% 86.70/86.89 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s7))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5783,plain,
% 86.70/86.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s7))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5784,plain,
% 86.70/86.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s7)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5783, 5782])).
% 86.70/86.89 tff(5785,plain,
% 86.70/86.89 (~node20(c_e_h_1, c_r, s7)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5784, 1535, 5781])).
% 86.70/86.89 tff(5786,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5787,plain,
% 86.70/86.89 ((node20(c_e_h_1, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5788,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8))))),
% 86.70/86.89 inference(monotonicity,[status(thm)],[5787])).
% 86.70/86.89 tff(5789,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 86.70/86.89 inference(transitivity,[status(thm)],[5788, 5786])).
% 86.70/86.89 tff(5790,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5791,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8))),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5790, 5789])).
% 86.70/86.89 tff(5792,plain,
% 86.70/86.89 ($false),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5791, 51, 5405, 5785, 5406])).
% 86.70/86.89 tff(5793,plain,((~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.89 tff(5794,plain,
% 86.70/86.89 (~node21(c_e_h_1, c_r, s7, s8)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5793, 5405])).
% 86.70/86.89 tff(5795,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5796,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5797,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5796, 5795])).
% 86.70/86.89 tff(5798,plain,
% 86.70/86.89 (node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5797, 81, 2152])).
% 86.70/86.89 tff(5799,plain,
% 86.70/86.89 (node22(c_e_h_1, c_r, s7, s8)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5798, 5794])).
% 86.70/86.89 tff(5800,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s7)), introduced(assumption)).
% 86.70/86.89 tff(5801,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5802,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))),
% 86.70/86.89 inference(quant_inst,[status(thm)],[])).
% 86.70/86.89 tff(5803,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 86.70/86.89 inference(modus_ponens,[status(thm)],[5802, 5801])).
% 86.70/86.89 tff(5804,plain,
% 86.70/86.89 ($false),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5803, 107, 5800, 5405, 5799])).
% 86.70/86.89 tff(5805,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.89 tff(5806,plain,
% 86.70/86.89 (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 86.70/86.89 inference(unit_resolution,[status(thm)],[5805, 5404])).
% 86.70/86.89 tff(5807,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s9)), introduced(assumption)).
% 86.70/86.89 tff(5808,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s2)), introduced(assumption)).
% 86.70/86.89 tff(5809,assumption,(node22(c_e_h_3, c_q, s1, s2)), introduced(assumption)).
% 86.70/86.89 tff(5810,plain,
% 86.70/86.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 86.70/86.89 inference(rewrite,[status(thm)],[])).
% 86.70/86.89 tff(5811,plain,
% 86.70/86.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5812,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5811, 5810])).
% 86.70/86.90 tff(5813,plain,
% 86.70/86.90 ($false),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5812, 107, 5450, 5808, 5809])).
% 86.70/86.90 tff(5814,plain,((~node22(c_e_h_3, c_q, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.90 tff(5815,plain,
% 86.70/86.90 (~node22(c_e_h_3, c_q, s1, s2)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5814, 5808])).
% 86.70/86.90 tff(5816,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5817,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5818,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2)),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5817, 5816])).
% 86.70/86.90 tff(5819,plain,
% 86.70/86.90 (node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5818, 81, 344])).
% 86.70/86.90 tff(5820,plain,
% 86.70/86.90 (node21(c_e_h_3, c_q, s1, s2)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5819, 5815])).
% 86.70/86.90 tff(5821,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s0)), introduced(assumption)).
% 86.70/86.90 tff(5822,plain,
% 86.70/86.90 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5823,plain,
% 86.70/86.90 ($false),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5822, 94, 5821])).
% 86.70/86.90 tff(5824,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.90 tff(5825,plain,
% 86.70/86.90 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X)))),
% 86.70/86.90 inference(bind,[status(th)],[])).
% 86.70/86.90 tff(5826,plain,
% 86.70/86.90 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 86.70/86.90 inference(quant_intro,[status(thm)],[5825])).
% 86.70/86.90 tff(5827,plain,
% 86.70/86.90 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5828,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_24')).
% 86.70/86.90 tff(5829,plain,
% 86.70/86.90 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5828, 5827])).
% 86.70/86.90 tff(5830,plain,(
% 86.70/86.90 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 86.70/86.90 inference(skolemize,[status(sab)],[5829])).
% 86.70/86.90 tff(5831,plain,
% 86.70/86.90 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5830, 5826])).
% 86.70/86.90 tff(5832,plain,
% 86.70/86.90 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5833,plain,
% 86.70/86.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5834,plain,
% 86.70/86.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0)),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5833, 5832])).
% 86.70/86.90 tff(5835,plain,
% 86.70/86.90 (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5834, 5831, 5824])).
% 86.70/86.90 tff(5836,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s1)), introduced(assumption)).
% 86.70/86.90 tff(5837,assumption,(node15(c_e_h_3, c_f, s0, s1)), introduced(assumption)).
% 86.70/86.90 tff(5838,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5839,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5840,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5839, 5838])).
% 86.70/86.90 tff(5841,plain,
% 86.70/86.90 ($false),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5840, 173, 5837, 5836, 5426])).
% 86.70/86.90 tff(5842,plain,((~node15(c_e_h_3, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.90 tff(5843,plain,
% 86.70/86.90 (~node15(c_e_h_3, c_f, s0, s1)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5842, 5836])).
% 86.70/86.90 tff(5844,assumption,(node18(c_e_h_3, c_f, s0, s1)), introduced(assumption)).
% 86.70/86.90 tff(5845,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5846,plain,
% 86.70/86.90 (((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1))) <=> ((~node18(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5847,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))))),
% 86.70/86.90 inference(monotonicity,[status(thm)],[5846])).
% 86.70/86.90 tff(5848,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))),
% 86.70/86.90 inference(transitivity,[status(thm)],[5847, 5845])).
% 86.70/86.90 tff(5849,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5850,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5849, 5848])).
% 86.70/86.90 tff(5851,plain,
% 86.70/86.90 ($false),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5850, 124, 5844, 5836, 5426])).
% 86.70/86.90 tff(5852,plain,((~node18(c_e_h_3, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.90 tff(5853,plain,
% 86.70/86.90 (~node18(c_e_h_3, c_f, s0, s1)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5852, 5836])).
% 86.70/86.90 tff(5854,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_f, s0, s1))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5855,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_f, s0, s1))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5856,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_f, s0, s1)),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5855, 5854])).
% 86.70/86.90 tff(5857,plain,
% 86.70/86.90 (node19(c_e_h_3, c_f, s0, s1)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5856, 141, 71])).
% 86.70/86.90 tff(5858,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5859,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5860,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5859, 5858])).
% 86.70/86.90 tff(5861,plain,
% 86.70/86.90 (node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5860, 156, 5857])).
% 86.70/86.90 tff(5862,plain,
% 86.70/86.90 (node17(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5861, 5853])).
% 86.70/86.90 tff(5863,assumption,(node17(c_e_h_3, c_f, s0)), introduced(assumption)).
% 86.70/86.90 tff(5864,assumption,(node16(c_e_h_3, c_f, s0)), introduced(assumption)).
% 86.70/86.90 tff(5865,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s0)), introduced(assumption)).
% 86.70/86.90 tff(5866,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5867,plain,
% 86.70/86.90 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0))) <=> ((~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5868,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0))))),
% 86.70/86.90 inference(monotonicity,[status(thm)],[5867])).
% 86.70/86.90 tff(5869,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(transitivity,[status(thm)],[5868, 5866])).
% 86.70/86.90 tff(5870,plain,
% 86.70/86.90 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5871,plain,
% 86.70/86.90 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5870, 5869])).
% 86.70/86.90 tff(5872,plain,
% 86.70/86.90 (m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5871, 209, 5863])).
% 86.70/86.90 tff(5873,plain,
% 86.70/86.90 (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5872, 5865])).
% 86.70/86.90 tff(5874,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5875,plain,
% 86.70/86.90 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5876,plain,
% 86.70/86.90 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5875, 5874])).
% 86.70/86.90 tff(5877,plain,
% 86.70/86.90 (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5876, 228, 5864])).
% 86.70/86.90 tff(5878,plain,
% 86.70/86.90 ($false),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5877, 5873, 5865])).
% 86.70/86.90 tff(5879,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node16(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.90 tff(5880,plain,
% 86.70/86.90 (m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5879, 5864, 5863])).
% 86.70/86.90 tff(5881,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5882,plain,
% 86.70/86.90 ((m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0))) <=> ((~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5883,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))))),
% 86.70/86.90 inference(monotonicity,[status(thm)],[5882])).
% 86.70/86.90 tff(5884,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(transitivity,[status(thm)],[5883, 5881])).
% 86.70/86.90 tff(5885,plain,
% 86.70/86.90 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5886,plain,
% 86.70/86.90 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5885, 5884])).
% 86.70/86.90 tff(5887,plain,
% 86.70/86.90 (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5886, 245, 5863])).
% 86.70/86.90 tff(5888,plain,
% 86.70/86.90 (m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5887, 5880])).
% 86.70/86.90 tff(5889,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5890,plain,
% 86.70/86.90 (((~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5891,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))))),
% 86.70/86.90 inference(monotonicity,[status(thm)],[5890])).
% 86.70/86.90 tff(5892,plain,
% 86.70/86.90 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(transitivity,[status(thm)],[5891, 5889])).
% 86.70/86.90 tff(5893,plain,
% 86.70/86.90 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5894,plain,
% 86.70/86.90 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node16(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5893, 5892])).
% 86.70/86.90 tff(5895,plain,
% 86.70/86.90 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5894, 263, 5864])).
% 86.70/86.90 tff(5896,plain,
% 86.70/86.90 ($false),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5895, 5888, 5880])).
% 86.70/86.90 tff(5897,plain,((~node16(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.90 tff(5898,plain,
% 86.70/86.90 (~node16(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5897, 5862])).
% 86.70/86.90 tff(5899,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5900,plain,
% 86.70/86.90 ((node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1))) <=> (node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5901,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1))))),
% 86.70/86.90 inference(monotonicity,[status(thm)],[5900])).
% 86.70/86.90 tff(5902,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(transitivity,[status(thm)],[5901, 5899])).
% 86.70/86.90 tff(5903,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5904,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5903, 5902])).
% 86.70/86.90 tff(5905,plain,
% 86.70/86.90 (node15(c_e_h_3, c_f, s0, s1) | node14(c_e_h_3, c_f, s0, s1) | node16(c_e_h_3, c_f, s0)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5904, 189, 5857])).
% 86.70/86.90 tff(5906,plain,
% 86.70/86.90 (node14(c_e_h_3, c_f, s0, s1)),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5905, 5898, 5843])).
% 86.70/86.90 tff(5907,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5908,plain,
% 86.70/86.90 (((~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(rewrite,[status(thm)],[])).
% 86.70/86.90 tff(5909,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1))))),
% 86.70/86.90 inference(monotonicity,[status(thm)],[5908])).
% 86.70/86.90 tff(5910,plain,
% 86.70/86.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)))),
% 86.70/86.90 inference(transitivity,[status(thm)],[5909, 5907])).
% 86.70/86.90 tff(5911,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))),
% 86.70/86.90 inference(quant_inst,[status(thm)],[])).
% 86.70/86.90 tff(5912,plain,
% 86.70/86.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1))),
% 86.70/86.90 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 86.70/86.90 tff(5913,plain,
% 86.70/86.90 ($false),
% 86.70/86.90 inference(unit_resolution,[status(thm)],[5912, 283, 5906, 5836, 5835])).
% 86.70/86.90 tff(5914,plain,(~m_c_h_element_v_out(c_e_h_3, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.91 tff(5915,plain,
% 86.70/86.91 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5916,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5917,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5916, 5915])).
% 86.70/86.91 tff(5918,plain,
% 86.70/86.91 (~m_and_h_gate_v_in1(c_e_h_3, c_q, s1)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5917, 1666, 5914])).
% 86.70/86.91 tff(5919,plain,
% 86.70/86.91 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s1))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5920,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s1))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5921,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s1)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5920, 5919])).
% 86.70/86.91 tff(5922,plain,
% 86.70/86.91 (~node20(c_e_h_3, c_q, s1)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5921, 37, 5918])).
% 86.70/86.91 tff(5923,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2)))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5924,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2)))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5925,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2))),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5924, 5923])).
% 86.70/86.91 tff(5926,plain,
% 86.70/86.91 ($false),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5925, 51, 5808, 5922, 5820])).
% 86.70/86.91 tff(5927,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.91 tff(5928,plain,
% 86.70/86.91 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5929,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5930,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5929, 5928])).
% 86.70/86.91 tff(5931,plain,
% 86.70/86.91 (node3(c_e_h_3, c_e_h_1, s2)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5930, 3860, 814])).
% 86.70/86.91 tff(5932,plain,
% 86.70/86.91 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s2)) | (~node3(c_e_h_3, c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s2)) | (~node3(c_e_h_3, c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5933,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s2)) | (~node3(c_e_h_3, c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5934,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s2)) | (~node3(c_e_h_3, c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5933, 5932])).
% 86.70/86.91 tff(5935,plain,
% 86.70/86.91 ((~m_cell_v_ack(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5934, 836, 5931])).
% 86.70/86.91 tff(5936,plain,
% 86.70/86.91 (~m_cell_v_ack(c_e_h_1, s2)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5935, 5927])).
% 86.70/86.91 tff(5937,plain,
% 86.70/86.91 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5938,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5939,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5938, 5937])).
% 86.70/86.91 tff(5940,plain,
% 86.70/86.91 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5939, 848, 5936])).
% 86.70/86.91 tff(5941,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s2)), introduced(assumption)).
% 86.70/86.91 tff(5942,assumption,(node22(c_e_h_1, c_l, s1, s2)), introduced(assumption)).
% 86.70/86.91 tff(5943,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5944,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5945,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5944, 5943])).
% 86.70/86.91 tff(5946,plain,
% 86.70/86.91 ($false),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5945, 107, 5492, 5942, 5941])).
% 86.70/86.91 tff(5947,plain,((~node22(c_e_h_1, c_l, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.91 tff(5948,plain,
% 86.70/86.91 (~node22(c_e_h_1, c_l, s1, s2)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5947, 5941])).
% 86.70/86.91 tff(5949,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5950,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5951,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5950, 5949])).
% 86.70/86.91 tff(5952,plain,
% 86.70/86.91 (node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5951, 81, 344])).
% 86.70/86.91 tff(5953,plain,
% 86.70/86.91 (node21(c_e_h_1, c_l, s1, s2)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5952, 5948])).
% 86.70/86.91 tff(5954,plain,
% 86.70/86.91 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5955,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5956,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5955, 5954])).
% 86.70/86.91 tff(5957,plain,
% 86.70/86.91 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5956, 1638, 4595])).
% 86.70/86.91 tff(5958,plain,
% 86.70/86.91 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s1))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5959,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s1))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5960,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s1)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5959, 5958])).
% 86.70/86.91 tff(5961,plain,
% 86.70/86.91 (~node20(c_e_h_1, c_l, s1)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5960, 1535, 5957])).
% 86.70/86.91 tff(5962,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2)))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5963,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2)))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5964,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2))),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5963, 5962])).
% 86.70/86.91 tff(5965,plain,
% 86.70/86.91 ($false),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5964, 51, 5961, 5953, 5941])).
% 86.70/86.91 tff(5966,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.91 tff(5967,plain,
% 86.70/86.91 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5968,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5969,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5968, 5967])).
% 86.70/86.91 tff(5970,plain,
% 86.70/86.91 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5969, 801, 5966])).
% 86.70/86.91 tff(5971,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s3)), introduced(assumption)).
% 86.70/86.91 tff(5972,assumption,(node6(c_e_h_1, c_j, s2, s3)), introduced(assumption)).
% 86.70/86.91 tff(5973,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s2)), introduced(assumption)).
% 86.70/86.91 tff(5974,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~node6(c_e_h_1, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~node6(c_e_h_1, c_j, s2, s3)))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5975,plain,
% 86.70/86.91 (((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~node6(c_e_h_1, c_j, s2, s3)))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5976,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~node6(c_e_h_1, c_j, s2, s3))))),
% 86.70/86.91 inference(monotonicity,[status(thm)],[5975])).
% 86.70/86.91 tff(5977,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~node6(c_e_h_1, c_j, s2, s3)))),
% 86.70/86.91 inference(transitivity,[status(thm)],[5976, 5974])).
% 86.70/86.91 tff(5978,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5979,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~node6(c_e_h_1, c_j, s2, s3))),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 86.70/86.91 tff(5980,plain,
% 86.70/86.91 ($false),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5979, 899, 5971, 5973, 5972])).
% 86.70/86.91 tff(5981,plain,((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.91 tff(5982,plain,
% 86.70/86.91 ((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5981, 5518])).
% 86.70/86.91 tff(5983,plain,
% 86.70/86.91 (~node6(c_e_h_1, c_j, s2, s3)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5982, 5971])).
% 86.70/86.91 tff(5984,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_1, c_j, s2, s3) | node6(c_e_h_1, c_j, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_1, c_j, s2, s3) | node6(c_e_h_1, c_j, s2, s3))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5985,plain,
% 86.70/86.91 ((node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node5(c_e_h_1, c_j, s2, s3) | node6(c_e_h_1, c_j, s2, s3))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5986,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_1, c_j, s2, s3) | node6(c_e_h_1, c_j, s2, s3)))),
% 86.70/86.91 inference(monotonicity,[status(thm)],[5985])).
% 86.70/86.91 tff(5987,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_1, c_j, s2, s3) | node6(c_e_h_1, c_j, s2, s3))),
% 86.70/86.91 inference(transitivity,[status(thm)],[5986, 5984])).
% 86.70/86.91 tff(5988,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3)))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5989,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_1, c_j, s2, s3) | node6(c_e_h_1, c_j, s2, s3)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5988, 5987])).
% 86.70/86.91 tff(5990,plain,
% 86.70/86.91 (node5(c_e_h_1, c_j, s2, s3) | node6(c_e_h_1, c_j, s2, s3)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5989, 881, 582])).
% 86.70/86.91 tff(5991,plain,
% 86.70/86.91 (node5(c_e_h_1, c_j, s2, s3)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5990, 5983])).
% 86.70/86.91 tff(5992,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5993,plain,
% 86.70/86.91 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(5994,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2)))),
% 86.70/86.91 inference(monotonicity,[status(thm)],[5993])).
% 86.70/86.91 tff(5995,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2))),
% 86.70/86.91 inference(transitivity,[status(thm)],[5994, 5992])).
% 86.70/86.91 tff(5996,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(5997,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[5996, 5995])).
% 86.70/86.91 tff(5998,plain,
% 86.70/86.91 ($false),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[5997, 862, 5971, 5991, 5970, 5940])).
% 86.70/86.91 tff(5999,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.91 tff(6000,plain,
% 86.70/86.91 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(6001,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(6002,plain,
% 86.70/86.91 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[6001, 6000])).
% 86.70/86.91 tff(6003,plain,
% 86.70/86.91 (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[6002, 309, 5999])).
% 86.70/86.91 tff(6004,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s4)), introduced(assumption)).
% 86.70/86.91 tff(6005,assumption,(node18(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 86.70/86.91 tff(6006,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s3)), introduced(assumption)).
% 86.70/86.91 tff(6007,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(6008,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(6009,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4))),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[6008, 6007])).
% 86.70/86.91 tff(6010,plain,
% 86.70/86.91 ($false),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[6009, 124, 6004, 6006, 6005])).
% 86.70/86.91 tff(6011,plain,((~node18(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.91 tff(6012,plain,
% 86.70/86.91 (~node18(c_e_h_1, c_h, s3, s4)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[6011, 6004, 5586])).
% 86.70/86.91 tff(6013,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s3)), introduced(assumption)).
% 86.70/86.91 tff(6014,assumption,(node15(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 86.70/86.91 tff(6015,plain,
% 86.70/86.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(6016,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 86.70/86.91 inference(quant_inst,[status(thm)],[])).
% 86.70/86.91 tff(6017,plain,
% 86.70/86.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 86.70/86.91 inference(modus_ponens,[status(thm)],[6016, 6015])).
% 86.70/86.91 tff(6018,plain,
% 86.70/86.91 ($false),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[6017, 173, 6004, 6006, 6014])).
% 86.70/86.91 tff(6019,plain,((~node15(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.91 tff(6020,plain,
% 86.70/86.91 (~node15(c_e_h_1, c_h, s3, s4)),
% 86.70/86.91 inference(unit_resolution,[status(thm)],[6019, 6004, 5586])).
% 86.70/86.91 tff(6021,assumption,(~node15(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 86.70/86.91 tff(6022,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s3)), introduced(assumption)).
% 86.70/86.91 tff(6023,plain,
% 86.70/86.91 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 86.70/86.91 inference(rewrite,[status(thm)],[])).
% 86.70/86.91 tff(6024,plain,
% 86.70/86.91 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6025,plain,
% 86.70/86.92 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6024, 6023])).
% 86.70/86.92 tff(6026,plain,
% 86.70/86.92 ((~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6025, 228, 6022])).
% 86.70/86.92 tff(6027,plain,
% 86.70/86.92 (~node16(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6026, 6013])).
% 86.70/86.92 tff(6028,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6029,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6030,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6029, 6028])).
% 86.70/86.92 tff(6031,plain,
% 86.70/86.92 (node19(c_e_h_1, c_h, s3, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6030, 141, 679])).
% 86.70/86.92 tff(6032,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6033,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6034,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4))),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6033, 6032])).
% 86.70/86.92 tff(6035,plain,
% 86.70/86.92 (node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6034, 189, 6031])).
% 86.70/86.92 tff(6036,plain,
% 86.70/86.92 (node14(c_e_h_1, c_h, s3, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6035, 6027, 6021])).
% 86.70/86.92 tff(6037,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6038,plain,
% 86.70/86.92 (((~node14(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6039,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4))))),
% 86.70/86.92 inference(monotonicity,[status(thm)],[6038])).
% 86.70/86.92 tff(6040,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.92 inference(transitivity,[status(thm)],[6039, 6037])).
% 86.70/86.92 tff(6041,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6042,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4))),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6041, 6040])).
% 86.70/86.92 tff(6043,plain,
% 86.70/86.92 ($false),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6042, 283, 6004, 6013, 6036])).
% 86.70/86.92 tff(6044,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | node15(c_e_h_1, c_h, s3, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.92 tff(6045,plain,
% 86.70/86.92 (m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6044, 6013, 6021, 6004])).
% 86.70/86.92 tff(6046,assumption,(node17(c_e_h_1, c_h, s3)), introduced(assumption)).
% 86.70/86.92 tff(6047,plain,
% 86.70/86.92 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6048,plain,
% 86.70/86.92 ((m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6049,plain,
% 86.70/86.92 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3)))),
% 86.70/86.92 inference(monotonicity,[status(thm)],[6048])).
% 86.70/86.92 tff(6050,plain,
% 86.70/86.92 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3))),
% 86.70/86.92 inference(transitivity,[status(thm)],[6049, 6047])).
% 86.70/86.92 tff(6051,plain,
% 86.70/86.92 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6052,plain,
% 86.70/86.92 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6051, 6050])).
% 86.70/86.92 tff(6053,plain,
% 86.70/86.92 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6052, 245, 6046])).
% 86.70/86.92 tff(6054,plain,
% 86.70/86.92 ($false),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6053, 6045, 6013])).
% 86.70/86.92 tff(6055,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)) | node15(c_e_h_1, c_h, s3, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.92 tff(6056,plain,
% 86.70/86.92 (~node17(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6055, 6020, 6004, 6013])).
% 86.70/86.92 tff(6057,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6058,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6059,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4))),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6058, 6057])).
% 86.70/86.92 tff(6060,plain,
% 86.70/86.92 (node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6059, 156, 6031])).
% 86.70/86.92 tff(6061,plain,
% 86.70/86.92 ($false),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6060, 6056, 6012])).
% 86.70/86.92 tff(6062,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.92 tff(6063,plain,
% 86.70/86.92 (m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6062, 6004])).
% 86.70/86.92 tff(6064,plain,
% 86.70/86.92 ((~node18(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6011, 5586])).
% 86.70/86.92 tff(6065,plain,
% 86.70/86.92 (~node18(c_e_h_1, c_h, s3, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6064, 6004])).
% 86.70/86.92 tff(6066,plain,
% 86.70/86.92 (node17(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6060, 6065])).
% 86.70/86.92 tff(6067,plain,
% 86.70/86.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6068,plain,
% 86.70/86.92 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6069,plain,
% 86.70/86.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)))),
% 86.70/86.92 inference(monotonicity,[status(thm)],[6068])).
% 86.70/86.92 tff(6070,plain,
% 86.70/86.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 86.70/86.92 inference(transitivity,[status(thm)],[6069, 6067])).
% 86.70/86.92 tff(6071,plain,
% 86.70/86.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6072,plain,
% 86.70/86.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6071, 6070])).
% 86.70/86.92 tff(6073,plain,
% 86.70/86.92 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3))),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6072, 209, 6022])).
% 86.70/86.92 tff(6074,plain,
% 86.70/86.92 ($false),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6073, 6066, 6063])).
% 86.70/86.92 tff(6075,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.92 tff(6076,plain,
% 86.70/86.92 (~m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6075, 6003])).
% 86.70/86.92 tff(6077,plain,
% 86.70/86.92 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6078,plain,
% 86.70/86.92 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6079,plain,
% 86.70/86.92 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6078, 6077])).
% 86.70/86.92 tff(6080,plain,
% 86.70/86.92 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6079, 23, 6076])).
% 86.70/86.92 tff(6081,plain,
% 86.70/86.92 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6082,plain,
% 86.70/86.92 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6083,plain,
% 86.70/86.92 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6082, 6081])).
% 86.70/86.92 tff(6084,plain,
% 86.70/86.92 (~node20(c_e_h_1, c_i, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6083, 37, 6080])).
% 86.70/86.92 tff(6085,assumption,(~node20(c_e_h_1, c_i, s4)), introduced(assumption)).
% 86.70/86.92 tff(6086,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s4)), introduced(assumption)).
% 86.70/86.92 tff(6087,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s5)), introduced(assumption)).
% 86.70/86.92 tff(6088,assumption,(node22(c_e_h_1, c_i, s4, s5)), introduced(assumption)).
% 86.70/86.92 tff(6089,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6090,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6091,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6090, 6089])).
% 86.70/86.92 tff(6092,plain,
% 86.70/86.92 ($false),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6091, 107, 6087, 6088, 6086])).
% 86.70/86.92 tff(6093,plain,((~node22(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.92 tff(6094,plain,
% 86.70/86.92 (~node22(c_e_h_1, c_i, s4, s5)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6093, 6087, 6086])).
% 86.70/86.92 tff(6095,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6096,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6097,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6096, 6095])).
% 86.70/86.92 tff(6098,plain,
% 86.70/86.92 (node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6097, 81, 1432])).
% 86.70/86.92 tff(6099,plain,
% 86.70/86.92 (node21(c_e_h_1, c_i, s4, s5)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6098, 6094])).
% 86.70/86.92 tff(6100,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6101,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6102,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5))),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6101, 6100])).
% 86.70/86.92 tff(6103,plain,
% 86.70/86.92 ($false),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6102, 51, 6087, 6099, 6085])).
% 86.70/86.92 tff(6104,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.92 tff(6105,plain,
% 86.70/86.92 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6104, 5613])).
% 86.70/86.92 tff(6106,plain,
% 86.70/86.92 (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6105, 6084])).
% 86.70/86.92 tff(6107,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s5)), introduced(assumption)).
% 86.70/86.92 tff(6108,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s5)), introduced(assumption)).
% 86.70/86.92 tff(6109,plain,
% 86.70/86.92 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6110,plain,
% 86.70/86.92 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6111,plain,
% 86.70/86.92 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6110, 6109])).
% 86.70/86.92 tff(6112,plain,
% 86.70/86.92 ($false),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6111, 365, 6108, 6107])).
% 86.70/86.92 tff(6113,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.92 tff(6114,plain,
% 86.70/86.92 (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6113, 6106])).
% 86.70/86.92 tff(6115,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s5)), introduced(assumption)).
% 86.70/86.92 tff(6116,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s6)), introduced(assumption)).
% 86.70/86.92 tff(6117,assumption,(node18(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 86.70/86.92 tff(6118,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6119,plain,
% 86.70/86.92 (((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6120,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6))))),
% 86.70/86.92 inference(monotonicity,[status(thm)],[6119])).
% 86.70/86.92 tff(6121,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.92 inference(transitivity,[status(thm)],[6120, 6118])).
% 86.70/86.92 tff(6122,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6123,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6))),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6122, 6121])).
% 86.70/86.92 tff(6124,plain,
% 86.70/86.92 ($false),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6123, 124, 6116, 5705, 6117])).
% 86.70/86.92 tff(6125,plain,((~node18(c_e_h_1, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.92 tff(6126,plain,
% 86.70/86.92 (~node18(c_e_h_1, c_e, s5, s6)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6125, 5705, 6116])).
% 86.70/86.92 tff(6127,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_e, s5, s6))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6128,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_e, s5, s6))),
% 86.70/86.92 inference(quant_inst,[status(thm)],[])).
% 86.70/86.92 tff(6129,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_e, s5, s6)),
% 86.70/86.92 inference(modus_ponens,[status(thm)],[6128, 6127])).
% 86.70/86.92 tff(6130,plain,
% 86.70/86.92 (node19(c_e_h_1, c_e, s5, s6)),
% 86.70/86.92 inference(unit_resolution,[status(thm)],[6129, 141, 1499])).
% 86.70/86.92 tff(6131,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6132,plain,
% 86.70/86.92 ((node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6))) <=> (node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.92 inference(rewrite,[status(thm)],[])).
% 86.70/86.92 tff(6133,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6))))),
% 86.70/86.92 inference(monotonicity,[status(thm)],[6132])).
% 86.70/86.92 tff(6134,plain,
% 86.70/86.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.92 inference(transitivity,[status(thm)],[6133, 6131])).
% 86.70/86.92 tff(6135,plain,
% 86.70/86.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6136,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6))),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6135, 6134])).
% 86.70/86.93 tff(6137,plain,
% 86.70/86.93 (node18(c_e_h_1, c_e, s5, s6) | node17(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6136, 156, 6130])).
% 86.70/86.93 tff(6138,plain,
% 86.70/86.93 (node17(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6137, 6126])).
% 86.70/86.93 tff(6139,assumption,(node16(c_e_h_1, c_e, s5)), introduced(assumption)).
% 86.70/86.93 tff(6140,assumption,(node17(c_e_h_1, c_e, s5)), introduced(assumption)).
% 86.70/86.93 tff(6141,assumption,(m_c_h_element_v_in1(c_e_h_1, c_e, s5)), introduced(assumption)).
% 86.70/86.93 tff(6142,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6143,plain,
% 86.70/86.93 (((~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6144,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5))))),
% 86.70/86.93 inference(monotonicity,[status(thm)],[6143])).
% 86.70/86.93 tff(6145,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(transitivity,[status(thm)],[6144, 6142])).
% 86.70/86.93 tff(6146,plain,
% 86.70/86.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6147,plain,
% 86.70/86.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6146, 6145])).
% 86.70/86.93 tff(6148,plain,
% 86.70/86.93 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6147, 263, 6139])).
% 86.70/86.93 tff(6149,plain,
% 86.70/86.93 (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6148, 6141])).
% 86.70/86.93 tff(6150,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6151,plain,
% 86.70/86.93 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6152,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))))),
% 86.70/86.93 inference(monotonicity,[status(thm)],[6151])).
% 86.70/86.93 tff(6153,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(transitivity,[status(thm)],[6152, 6150])).
% 86.70/86.93 tff(6154,plain,
% 86.70/86.93 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6155,plain,
% 86.70/86.93 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6154, 6153])).
% 86.70/86.93 tff(6156,plain,
% 86.70/86.93 (m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6155, 209, 6140])).
% 86.70/86.93 tff(6157,plain,
% 86.70/86.93 ($false),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6156, 6149, 6141])).
% 86.70/86.93 tff(6158,plain,((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.93 tff(6159,plain,
% 86.70/86.93 (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6158, 6140, 6139])).
% 86.70/86.93 tff(6160,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6161,plain,
% 86.70/86.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6162,plain,
% 86.70/86.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6161, 6160])).
% 86.70/86.93 tff(6163,plain,
% 86.70/86.93 (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6162, 228, 6139])).
% 86.70/86.93 tff(6164,plain,
% 86.70/86.93 (m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6163, 6159])).
% 86.70/86.93 tff(6165,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6166,plain,
% 86.70/86.93 ((m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))) <=> ((~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6167,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5))))),
% 86.70/86.93 inference(monotonicity,[status(thm)],[6166])).
% 86.70/86.93 tff(6168,plain,
% 86.70/86.93 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(transitivity,[status(thm)],[6167, 6165])).
% 86.70/86.93 tff(6169,plain,
% 86.70/86.93 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6170,plain,
% 86.70/86.93 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6169, 6168])).
% 86.70/86.93 tff(6171,plain,
% 86.70/86.93 (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6170, 245, 6140])).
% 86.70/86.93 tff(6172,plain,
% 86.70/86.93 ($false),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6171, 6164, 6159])).
% 86.70/86.93 tff(6173,plain,((~node17(c_e_h_1, c_e, s5)) | (~node16(c_e_h_1, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.93 tff(6174,plain,
% 86.70/86.93 (~node16(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6173, 6138])).
% 86.70/86.93 tff(6175,plain,
% 86.70/86.93 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6155, 209, 6115])).
% 86.70/86.93 tff(6176,plain,
% 86.70/86.93 (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6175, 6138])).
% 86.70/86.93 tff(6177,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s5)), introduced(assumption)).
% 86.70/86.93 tff(6178,assumption,(node14(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 86.70/86.93 tff(6179,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6180,plain,
% 86.70/86.93 (((~node14(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6181,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6))))),
% 86.70/86.93 inference(monotonicity,[status(thm)],[6180])).
% 86.70/86.93 tff(6182,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.93 inference(transitivity,[status(thm)],[6181, 6179])).
% 86.70/86.93 tff(6183,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6184,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6))),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6183, 6182])).
% 86.70/86.93 tff(6185,plain,
% 86.70/86.93 ($false),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6184, 283, 6116, 6178, 6177])).
% 86.70/86.93 tff(6186,plain,((~node14(c_e_h_1, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.93 tff(6187,plain,
% 86.70/86.93 (~node14(c_e_h_1, c_e, s5, s6)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6186, 6176, 6116])).
% 86.70/86.93 tff(6188,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s5, s6) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node16(c_e_h_1, c_e, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s5, s6) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node16(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6189,plain,
% 86.70/86.93 ((node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6))) <=> (node15(c_e_h_1, c_e, s5, s6) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node16(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6190,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s5, s6) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node16(c_e_h_1, c_e, s5)))),
% 86.70/86.93 inference(monotonicity,[status(thm)],[6189])).
% 86.70/86.93 tff(6191,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s5, s6) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node16(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(transitivity,[status(thm)],[6190, 6188])).
% 86.70/86.93 tff(6192,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6193,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s5, s6) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node16(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6192, 6191])).
% 86.70/86.93 tff(6194,plain,
% 86.70/86.93 (node15(c_e_h_1, c_e, s5, s6) | node14(c_e_h_1, c_e, s5, s6) | node16(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6193, 189, 6130])).
% 86.70/86.93 tff(6195,plain,
% 86.70/86.93 (node15(c_e_h_1, c_e, s5, s6)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6194, 6187, 6174])).
% 86.70/86.93 tff(6196,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6197,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6198,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6197, 6196])).
% 86.70/86.93 tff(6199,plain,
% 86.70/86.93 ($false),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6198, 173, 6116, 5705, 6195])).
% 86.70/86.93 tff(6200,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.93 tff(6201,plain,
% 86.70/86.93 (~m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6200, 5705, 6115])).
% 86.70/86.93 tff(6202,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)), introduced(assumption)).
% 86.70/86.93 tff(6203,plain,
% 86.70/86.93 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[5710, 5705])).
% 86.70/86.93 tff(6204,plain,
% 86.70/86.93 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[5313, 1142, 5156])).
% 86.70/86.93 tff(6205,plain,
% 86.70/86.93 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[5342, 6204, 5315])).
% 86.70/86.93 tff(6206,plain,
% 86.70/86.93 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[5347, 1048, 6205])).
% 86.70/86.93 tff(6207,plain,
% 86.70/86.93 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[5177, 5156])).
% 86.70/86.93 tff(6208,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)), introduced(assumption)).
% 86.70/86.93 tff(6209,plain,
% 86.70/86.93 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[5714, 1142, 6207])).
% 86.70/86.93 tff(6210,plain,
% 86.70/86.93 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[5742, 6209, 5717, 6205])).
% 86.70/86.93 tff(6211,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)), introduced(assumption)).
% 86.70/86.93 tff(6212,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)), introduced(assumption)).
% 86.70/86.93 tff(6213,assumption,(node11(c_e_h_1, c_n, s6, s7)), introduced(assumption)).
% 86.70/86.93 tff(6214,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6215,plain,
% 86.70/86.93 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6216,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7))))),
% 86.70/86.93 inference(monotonicity,[status(thm)],[6215])).
% 86.70/86.93 tff(6217,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 86.70/86.93 inference(transitivity,[status(thm)],[6216, 6214])).
% 86.70/86.93 tff(6218,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6219,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7))),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6218, 6217])).
% 86.70/86.93 tff(6220,plain,
% 86.70/86.93 ($false),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6219, 1161, 6212, 6202, 6213])).
% 86.70/86.93 tff(6221,plain,((~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.93 tff(6222,plain,
% 86.70/86.93 (~node11(c_e_h_1, c_n, s6, s7)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6221, 6202, 6212])).
% 86.70/86.93 tff(6223,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6224,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7))),
% 86.70/86.93 inference(quant_inst,[status(thm)],[])).
% 86.70/86.93 tff(6225,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7)),
% 86.70/86.93 inference(modus_ponens,[status(thm)],[6224, 6223])).
% 86.70/86.93 tff(6226,plain,
% 86.70/86.93 (node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6225, 1092, 1552])).
% 86.70/86.93 tff(6227,plain,
% 86.70/86.93 (node10(c_e_h_1, c_n, s6, s7)),
% 86.70/86.93 inference(unit_resolution,[status(thm)],[6226, 6222])).
% 86.70/86.93 tff(6228,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6229,plain,
% 86.70/86.93 (((~node10(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 86.70/86.93 inference(rewrite,[status(thm)],[])).
% 86.70/86.93 tff(6230,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7))))),
% 86.70/86.93 inference(monotonicity,[status(thm)],[6229])).
% 86.70/86.93 tff(6231,plain,
% 86.70/86.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 86.70/86.93 inference(transitivity,[status(thm)],[6230, 6228])).
% 86.70/86.93 tff(6232,plain,
% 86.70/86.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6233,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7))),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6232, 6231])).
% 86.70/86.94 tff(6234,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6233, 1191, 6202, 6227, 6208, 6211])).
% 86.70/86.94 tff(6235,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6236,plain,
% 86.70/86.94 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6235, 6210, 6202, 6208])).
% 86.70/86.94 tff(6237,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)), introduced(assumption)).
% 86.70/86.94 tff(6238,plain,
% 86.70/86.94 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6239,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6240,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6239, 6238])).
% 86.70/86.94 tff(6241,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6240, 1142, 5754, 6237])).
% 86.70/86.94 tff(6242,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6243,plain,
% 86.70/86.94 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6242, 6236])).
% 86.70/86.94 tff(6244,plain,
% 86.70/86.94 (node9(c_e_h_1, c_m, s5)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[5375, 6243, 6207])).
% 86.70/86.94 tff(6245,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[5351, 1062, 6244, 6206])).
% 86.70/86.94 tff(6246,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6247,plain,
% 86.70/86.94 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4))),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6246, 5004])).
% 86.70/86.94 tff(6248,plain,
% 86.70/86.94 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6247, 6203, 5310, 6202])).
% 86.70/86.94 tff(6249,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)), introduced(assumption)).
% 86.70/86.94 tff(6250,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s6)), introduced(assumption)).
% 86.70/86.94 tff(6251,plain,
% 86.70/86.94 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6252,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6253,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6252, 6251])).
% 86.70/86.94 tff(6254,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6253, 976, 6250, 6249])).
% 86.70/86.94 tff(6255,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6256,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6255, 6248, 6201])).
% 86.70/86.94 tff(6257,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6258,plain,
% 86.70/86.94 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6257, 5703])).
% 86.70/86.94 tff(6259,plain,
% 86.70/86.94 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6258, 6114])).
% 86.70/86.94 tff(6260,plain,
% 86.70/86.94 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6261,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6262,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6261, 6260])).
% 86.70/86.94 tff(6263,plain,
% 86.70/86.94 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6262, 1048, 6259])).
% 86.70/86.94 tff(6264,plain,
% 86.70/86.94 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6265,plain,
% 86.70/86.94 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6266,plain,
% 86.70/86.94 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6265, 6264])).
% 86.70/86.94 tff(6267,plain,
% 86.70/86.94 (~node9(c_e_h_1, c_m, s7)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6266, 1062, 6263])).
% 86.70/86.94 tff(6268,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), introduced(assumption)).
% 86.70/86.94 tff(6269,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), introduced(assumption)).
% 86.70/86.94 tff(6270,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6271,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6272,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6271, 6270])).
% 86.70/86.94 tff(6273,plain,
% 86.70/86.94 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6272, 1130])).
% 86.70/86.94 tff(6274,plain,
% 86.70/86.94 (~node11(c_e_h_1, c_m, s7, s8)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6273, 6269, 6268])).
% 86.70/86.94 tff(6275,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6276,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6277,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6276, 6275])).
% 86.70/86.94 tff(6278,plain,
% 86.70/86.94 (node10(c_e_h_1, c_m, s7, s8)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6277, 1092, 2152, 6274])).
% 86.70/86.94 tff(6279,assumption,(~node9(c_e_h_1, c_m, s7)), introduced(assumption)).
% 86.70/86.94 tff(6280,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node10(c_e_h_1, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6281,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6282,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node10(c_e_h_1, c_m, s7, s8))),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6281, 6280])).
% 86.70/86.94 tff(6283,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6282, 1076, 6269, 6279, 6278])).
% 86.70/86.94 tff(6284,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6285,plain,
% 86.70/86.94 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6284, 5776])).
% 86.70/86.94 tff(6286,plain,
% 86.70/86.94 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6285, 6267])).
% 86.70/86.94 tff(6287,plain,
% 86.70/86.94 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6288,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6289,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6288, 6287])).
% 86.70/86.94 tff(6290,plain,
% 86.70/86.94 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6289, 1521, 6286])).
% 86.70/86.94 tff(6291,plain,
% 86.70/86.94 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s8))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6292,plain,
% 86.70/86.94 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s8))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6293,plain,
% 86.70/86.94 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s8)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6292, 6291])).
% 86.70/86.94 tff(6294,plain,
% 86.70/86.94 (~node20(c_e_h_1, c_r, s8)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6293, 1535, 6290])).
% 86.70/86.94 tff(6295,assumption,(node21(c_e_h_1, c_r, s8, s9)), introduced(assumption)).
% 86.70/86.94 tff(6296,assumption,(~node20(c_e_h_1, c_r, s8)), introduced(assumption)).
% 86.70/86.94 tff(6297,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8) | (~node21(c_e_h_1, c_r, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8) | (~node21(c_e_h_1, c_r, s8, s9)))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6298,plain,
% 86.70/86.94 ((node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8) | (~node21(c_e_h_1, c_r, s8, s9)))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6299,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8) | (~node21(c_e_h_1, c_r, s8, s9))))),
% 86.70/86.94 inference(monotonicity,[status(thm)],[6298])).
% 86.70/86.94 tff(6300,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8) | (~node21(c_e_h_1, c_r, s8, s9)))),
% 86.70/86.94 inference(transitivity,[status(thm)],[6299, 6297])).
% 86.70/86.94 tff(6301,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9)))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6302,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8) | (~node21(c_e_h_1, c_r, s8, s9))),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6301, 6300])).
% 86.70/86.94 tff(6303,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6302, 51, 5807, 6296, 6295])).
% 86.70/86.94 tff(6304,plain,((~node21(c_e_h_1, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | node20(c_e_h_1, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6305,plain,
% 86.70/86.94 ((~node21(c_e_h_1, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6304, 6294])).
% 86.70/86.94 tff(6306,plain,
% 86.70/86.94 (~node21(c_e_h_1, c_r, s8, s9)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6305, 5807])).
% 86.70/86.94 tff(6307,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s8)), introduced(assumption)).
% 86.70/86.94 tff(6308,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6309,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6310,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6309, 6308])).
% 86.70/86.94 tff(6311,plain,
% 86.70/86.94 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6310, 107])).
% 86.70/86.94 tff(6312,plain,
% 86.70/86.94 (~node22(c_e_h_1, c_r, s8, s9)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6311, 5807, 6307])).
% 86.70/86.94 tff(6313,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6314,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6315,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6314, 6313])).
% 86.70/86.94 tff(6316,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6315, 81, 2636, 6312, 6306])).
% 86.70/86.94 tff(6317,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6318,plain,
% 86.70/86.94 (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6317, 5806])).
% 86.70/86.94 tff(6319,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s9)), introduced(assumption)).
% 86.70/86.94 tff(6320,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s10)), introduced(assumption)).
% 86.70/86.94 tff(6321,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6322,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6323,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6322, 6321])).
% 86.70/86.94 tff(6324,plain,
% 86.70/86.94 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6323, 107])).
% 86.70/86.94 tff(6325,plain,
% 86.70/86.94 (~node22(c_e_h_1, c_r, s9, s10)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6324, 6320, 6319])).
% 86.70/86.94 tff(6326,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6327,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6328,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6327, 6326])).
% 86.70/86.94 tff(6329,plain,
% 86.70/86.94 (node21(c_e_h_1, c_r, s9, s10)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6328, 81, 3175, 6325])).
% 86.70/86.94 tff(6330,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s3)), introduced(assumption)).
% 86.70/86.94 tff(6331,assumption,(node22(c_e_h_3, c_q, s2, s3)), introduced(assumption)).
% 86.70/86.94 tff(6332,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node22(c_e_h_3, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node22(c_e_h_3, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6333,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node22(c_e_h_3, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6334,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node22(c_e_h_3, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6333, 6332])).
% 86.70/86.94 tff(6335,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6334, 107, 6330, 5927, 6331])).
% 86.70/86.94 tff(6336,plain,((~node22(c_e_h_3, c_q, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6337,plain,
% 86.70/86.94 (~node22(c_e_h_3, c_q, s2, s3)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6336, 6330])).
% 86.70/86.94 tff(6338,plain,
% 86.70/86.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6339,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6340,plain,
% 86.70/86.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6339, 6338])).
% 86.70/86.94 tff(6341,plain,
% 86.70/86.94 (node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6340, 81, 582])).
% 86.70/86.94 tff(6342,plain,
% 86.70/86.94 (node21(c_e_h_3, c_q, s2, s3)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6341, 6337])).
% 86.70/86.94 tff(6343,assumption,(~m_cell_v_token(c_e_h_3, s0)), introduced(assumption)).
% 86.70/86.94 tff(6344,plain,
% 86.70/86.94 (^[X: $i] : refl(m_cell_v_token(c_e_h_3, X) <=> m_cell_v_token(c_e_h_3, X))),
% 86.70/86.94 inference(bind,[status(th)],[])).
% 86.70/86.94 tff(6345,plain,
% 86.70/86.94 (![X: $i] : m_cell_v_token(c_e_h_3, X) <=> ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 86.70/86.94 inference(quant_intro,[status(thm)],[6344])).
% 86.70/86.94 tff(6346,plain,
% 86.70/86.94 (![X: $i] : m_cell_v_token(c_e_h_3, X) <=> ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6347,axiom,(![X: $i] : m_cell_v_token(c_e_h_3, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_9')).
% 86.70/86.94 tff(6348,plain,
% 86.70/86.94 (![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6347, 6346])).
% 86.70/86.94 tff(6349,plain,(
% 86.70/86.94 ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 86.70/86.94 inference(skolemize,[status(sab)],[6348])).
% 86.70/86.94 tff(6350,plain,
% 86.70/86.94 (![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6349, 6345])).
% 86.70/86.94 tff(6351,plain,
% 86.70/86.94 ((~![X: $i] : m_cell_v_token(c_e_h_3, X)) | m_cell_v_token(c_e_h_3, s0)),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6352,plain,
% 86.70/86.94 ($false),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6351, 6350, 6343])).
% 86.70/86.94 tff(6353,plain,(m_cell_v_token(c_e_h_3, s0)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.94 tff(6354,plain,
% 86.70/86.94 (^[I0: $i, X: $i] : refl(((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) <=> ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))))),
% 86.70/86.94 inference(bind,[status(th)],[])).
% 86.70/86.94 tff(6355,plain,
% 86.70/86.94 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.70/86.94 inference(quant_intro,[status(thm)],[6354])).
% 86.70/86.94 tff(6356,plain,
% 86.70/86.94 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6357,plain,
% 86.70/86.94 (^[I0: $i, X: $i] : rewrite(((~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) | (~m_cell_v_token(I0, X))) <=> ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))))),
% 86.70/86.94 inference(bind,[status(th)],[])).
% 86.70/86.94 tff(6358,plain,
% 86.70/86.94 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) | (~m_cell_v_token(I0, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.70/86.94 inference(quant_intro,[status(thm)],[6357])).
% 86.70/86.94 tff(6359,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) | (~m_cell_v_token(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_62')).
% 86.70/86.94 tff(6360,plain,
% 86.70/86.94 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6359, 6358])).
% 86.70/86.94 tff(6361,plain,
% 86.70/86.94 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6360, 6356])).
% 86.70/86.94 tff(6362,plain,(
% 86.70/86.94 ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.70/86.94 inference(skolemize,[status(sab)],[6361])).
% 86.70/86.94 tff(6363,plain,
% 86.70/86.94 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6362, 6355])).
% 86.70/86.94 tff(6364,plain,
% 86.70/86.94 (((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))) | ((~m_cell_v_token(c_e_h_3, s0)) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))) | (~m_cell_v_token(c_e_h_3, s0)) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6365,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))) | ((~m_cell_v_token(c_e_h_3, s0)) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6366,plain,
% 86.70/86.94 ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))) | (~m_cell_v_token(c_e_h_3, s0)) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6365, 6364])).
% 86.70/86.94 tff(6367,plain,
% 86.70/86.94 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6366, 6363, 6353])).
% 86.70/86.94 tff(6368,plain,
% 86.70/86.94 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6369,plain,
% 86.70/86.94 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))),
% 86.70/86.94 inference(quant_inst,[status(thm)],[])).
% 86.70/86.94 tff(6370,plain,
% 86.70/86.94 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)),
% 86.70/86.94 inference(modus_ponens,[status(thm)],[6369, 6368])).
% 86.70/86.94 tff(6371,plain,
% 86.70/86.94 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 86.70/86.94 inference(unit_resolution,[status(thm)],[6370, 1116, 6367])).
% 86.70/86.94 tff(6372,plain,
% 86.70/86.94 (^[I0: $i, X: $i] : refl((m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 86.70/86.94 inference(bind,[status(th)],[])).
% 86.70/86.94 tff(6373,plain,
% 86.70/86.94 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.94 inference(quant_intro,[status(thm)],[6372])).
% 86.70/86.94 tff(6374,plain,
% 86.70/86.94 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.94 inference(rewrite,[status(thm)],[])).
% 86.70/86.94 tff(6375,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_53')).
% 86.70/86.95 tff(6376,plain,
% 86.70/86.95 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6375, 6374])).
% 86.70/86.95 tff(6377,plain,(
% 86.70/86.95 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.95 inference(skolemize,[status(sab)],[6376])).
% 86.70/86.95 tff(6378,plain,
% 86.70/86.95 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6377, 6373])).
% 86.70/86.95 tff(6379,plain,
% 86.70/86.95 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6380,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6381,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6380, 6379])).
% 86.70/86.95 tff(6382,plain,
% 86.70/86.95 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6381, 6378, 6371])).
% 86.70/86.95 tff(6383,plain,
% 86.70/86.95 (^[I0: $i, X: $i] : refl((m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X)) <=> (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X)))),
% 86.70/86.95 inference(bind,[status(th)],[])).
% 86.70/86.95 tff(6384,plain,
% 86.70/86.95 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 86.70/86.95 inference(quant_intro,[status(thm)],[6383])).
% 86.70/86.95 tff(6385,plain,
% 86.70/86.95 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6386,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_51')).
% 86.70/86.95 tff(6387,plain,
% 86.70/86.95 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6386, 6385])).
% 86.70/86.95 tff(6388,plain,(
% 86.70/86.95 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 86.70/86.95 inference(skolemize,[status(sab)],[6387])).
% 86.70/86.95 tff(6389,plain,
% 86.70/86.95 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6388, 6384])).
% 86.70/86.95 tff(6390,plain,
% 86.70/86.95 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6391,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6392,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6391, 6390])).
% 86.70/86.95 tff(6393,plain,
% 86.70/86.95 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6392, 6389, 5426])).
% 86.70/86.95 tff(6394,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)), introduced(assumption)).
% 86.70/86.95 tff(6395,assumption,(node11(c_e_h_3, c_m, s0, s1)), introduced(assumption)).
% 86.70/86.95 tff(6396,plain,
% 86.70/86.95 (^[I0: $i, X: $i] : refl(((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) <=> ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)))),
% 86.70/86.95 inference(bind,[status(th)],[])).
% 86.70/86.95 tff(6397,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 86.70/86.95 inference(quant_intro,[status(thm)],[6396])).
% 86.70/86.95 tff(6398,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6399,plain,
% 86.70/86.95 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_h_init_v_init_h_out(I0, c_m, X) | (~m_cell_v_token(I0, X))) <=> ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)))),
% 86.70/86.95 inference(bind,[status(th)],[])).
% 86.70/86.95 tff(6400,plain,
% 86.70/86.95 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_init_h_out(I0, c_m, X) | (~m_cell_v_token(I0, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 86.70/86.95 inference(quant_intro,[status(thm)],[6399])).
% 86.70/86.95 tff(6401,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_init_h_out(I0, c_m, X) | (~m_cell_v_token(I0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_55')).
% 86.70/86.95 tff(6402,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6401, 6400])).
% 86.70/86.95 tff(6403,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6402, 6398])).
% 86.70/86.95 tff(6404,plain,(
% 86.70/86.95 ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 86.70/86.95 inference(skolemize,[status(sab)],[6403])).
% 86.70/86.95 tff(6405,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6404, 6397])).
% 86.70/86.95 tff(6406,plain,
% 86.70/86.95 (((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))) | ((~m_cell_v_token(c_e_h_3, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))) | (~m_cell_v_token(c_e_h_3, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6407,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))) | ((~m_cell_v_token(c_e_h_3, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6408,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))) | (~m_cell_v_token(c_e_h_3, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6407, 6406])).
% 86.70/86.95 tff(6409,plain,
% 86.70/86.95 (m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6408, 6405, 6353])).
% 86.70/86.95 tff(6410,plain,
% 86.70/86.95 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6411,plain,
% 86.70/86.95 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6412,plain,
% 86.70/86.95 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6411, 6410])).
% 86.70/86.95 tff(6413,plain,
% 86.70/86.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6412, 1037, 6409])).
% 86.70/86.95 tff(6414,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6415,plain,
% 86.70/86.95 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6416,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1))))),
% 86.70/86.95 inference(monotonicity,[status(thm)],[6415])).
% 86.70/86.95 tff(6417,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)))),
% 86.70/86.95 inference(transitivity,[status(thm)],[6416, 6414])).
% 86.70/86.95 tff(6418,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6419,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6418, 6417])).
% 86.70/86.95 tff(6420,plain,
% 86.70/86.95 ($false),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6419, 1161, 6413, 6394, 6395])).
% 86.70/86.95 tff(6421,plain,((~node11(c_e_h_3, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.95 tff(6422,plain,
% 86.70/86.95 (~node11(c_e_h_3, c_m, s0, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6421, 6394])).
% 86.70/86.95 tff(6423,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6424,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6425,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6424, 6423])).
% 86.70/86.95 tff(6426,plain,
% 86.70/86.95 (node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6425, 1092, 71])).
% 86.70/86.95 tff(6427,plain,
% 86.70/86.95 (node10(c_e_h_3, c_m, s0, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6426, 6422])).
% 86.70/86.95 tff(6428,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6429,plain,
% 86.70/86.95 (((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6430,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1))))),
% 86.70/86.95 inference(monotonicity,[status(thm)],[6429])).
% 86.70/86.95 tff(6431,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1)))),
% 86.70/86.95 inference(transitivity,[status(thm)],[6430, 6428])).
% 86.70/86.95 tff(6432,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6433,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6432, 6431])).
% 86.70/86.95 tff(6434,plain,
% 86.70/86.95 ($false),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6433, 1191, 6394, 6427, 6393, 6382])).
% 86.70/86.95 tff(6435,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.95 tff(6436,plain,
% 86.70/86.95 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))))),
% 86.70/86.95 inference(bind,[status(th)],[])).
% 86.70/86.95 tff(6437,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 86.70/86.95 inference(quant_intro,[status(thm)],[6436])).
% 86.70/86.95 tff(6438,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6439,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_60')).
% 86.70/86.95 tff(6440,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6439, 6438])).
% 86.70/86.95 tff(6441,plain,(
% 86.70/86.95 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 86.70/86.95 inference(skolemize,[status(sab)],[6440])).
% 86.70/86.95 tff(6442,plain,
% 86.70/86.95 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6441, 6437])).
% 86.70/86.95 tff(6443,plain,
% 86.70/86.95 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6444,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6445,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6444, 6443])).
% 86.70/86.95 tff(6446,plain,
% 86.70/86.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6445, 6442, 6435])).
% 86.70/86.95 tff(6447,plain,
% 86.70/86.95 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6448,plain,
% 86.70/86.95 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6449,plain,
% 86.70/86.95 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6448, 6447])).
% 86.70/86.95 tff(6450,plain,
% 86.70/86.95 (~node9(c_e_h_3, c_n, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6449, 1062, 6446])).
% 86.70/86.95 tff(6451,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)), introduced(assumption)).
% 86.70/86.95 tff(6452,assumption,(node11(c_e_h_3, c_n, s1, s2)), introduced(assumption)).
% 86.70/86.95 tff(6453,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)), introduced(assumption)).
% 86.70/86.95 tff(6454,plain,
% 86.70/86.95 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6455,plain,
% 86.70/86.95 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6456,plain,
% 86.70/86.95 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6455, 6454])).
% 86.70/86.95 tff(6457,plain,
% 86.70/86.95 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6456, 1037, 6453])).
% 86.70/86.95 tff(6458,plain,
% 86.70/86.95 (((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_3, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_3, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6459,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_3, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6460,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_3, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6459, 6458])).
% 86.70/86.95 tff(6461,plain,
% 86.70/86.95 (m_cell_v_token(c_e_h_3, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6460, 1023, 6457])).
% 86.70/86.95 tff(6462,plain,
% 86.70/86.95 (m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6408, 6405, 6461])).
% 86.70/86.95 tff(6463,plain,
% 86.70/86.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6412, 1037, 6462])).
% 86.70/86.95 tff(6464,plain,
% 86.70/86.95 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6465,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6466,plain,
% 86.70/86.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6465, 6464])).
% 86.70/86.95 tff(6467,plain,
% 86.70/86.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6466, 6442, 6463])).
% 86.70/86.95 tff(6468,plain,
% 86.70/86.95 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6469,plain,
% 86.70/86.95 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6470,plain,
% 86.70/86.95 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6469, 6468])).
% 86.70/86.95 tff(6471,plain,
% 86.70/86.95 (~node9(c_e_h_3, c_n, s0)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6470, 1062, 6467])).
% 86.70/86.95 tff(6472,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)), introduced(assumption)).
% 86.70/86.95 tff(6473,assumption,(node11(c_e_h_3, c_n, s0, s1)), introduced(assumption)).
% 86.70/86.95 tff(6474,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6475,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6476,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6475, 6474])).
% 86.70/86.95 tff(6477,plain,
% 86.70/86.95 ($false),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6476, 1130, 6453, 6473, 6472])).
% 86.70/86.95 tff(6478,plain,((~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.95 tff(6479,plain,
% 86.70/86.95 (~node11(c_e_h_3, c_n, s0, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6478, 6453, 6472])).
% 86.70/86.95 tff(6480,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6481,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6482,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6481, 6480])).
% 86.70/86.95 tff(6483,plain,
% 86.70/86.95 (node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6482, 1092, 71])).
% 86.70/86.95 tff(6484,plain,
% 86.70/86.95 (node10(c_e_h_3, c_n, s0, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6483, 6479])).
% 86.70/86.95 tff(6485,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node10(c_e_h_3, c_n, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node10(c_e_h_3, c_n, s0, s1)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6486,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node10(c_e_h_3, c_n, s0, s1)))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6487,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node10(c_e_h_3, c_n, s0, s1))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6486, 6485])).
% 86.70/86.95 tff(6488,plain,
% 86.70/86.95 ($false),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6487, 1076, 6484, 6472, 6471])).
% 86.70/86.95 tff(6489,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.95 tff(6490,plain,
% 86.70/86.95 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6489, 6371])).
% 86.70/86.95 tff(6491,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node11(c_e_h_3, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node11(c_e_h_3, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6492,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node11(c_e_h_3, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6493,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node11(c_e_h_3, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6492, 6491])).
% 86.70/86.95 tff(6494,plain,
% 86.70/86.95 ($false),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6493, 1130, 6451, 6490, 6452])).
% 86.70/86.95 tff(6495,plain,((~node11(c_e_h_3, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.95 tff(6496,plain,
% 86.70/86.95 (~node11(c_e_h_3, c_n, s1, s2)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6495, 6451])).
% 86.70/86.95 tff(6497,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6498,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6499,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2)),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6498, 6497])).
% 86.70/86.95 tff(6500,plain,
% 86.70/86.95 (node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6499, 1092, 344])).
% 86.70/86.95 tff(6501,plain,
% 86.70/86.95 (node10(c_e_h_3, c_n, s1, s2)),
% 86.70/86.95 inference(unit_resolution,[status(thm)],[6500, 6496])).
% 86.70/86.95 tff(6502,plain,
% 86.70/86.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node10(c_e_h_3, c_n, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node10(c_e_h_3, c_n, s1, s2)))),
% 86.70/86.95 inference(rewrite,[status(thm)],[])).
% 86.70/86.95 tff(6503,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node10(c_e_h_3, c_n, s1, s2)))),
% 86.70/86.95 inference(quant_inst,[status(thm)],[])).
% 86.70/86.95 tff(6504,plain,
% 86.70/86.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node10(c_e_h_3, c_n, s1, s2))),
% 86.70/86.95 inference(modus_ponens,[status(thm)],[6503, 6502])).
% 86.70/86.95 tff(6505,plain,
% 86.70/86.95 ($false),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6504, 1076, 6451, 6501, 6450])).
% 86.70/86.96 tff(6506,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.96 tff(6507,plain,
% 86.70/86.96 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 86.70/86.96 inference(bind,[status(th)],[])).
% 86.70/86.96 tff(6508,plain,
% 86.70/86.96 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.96 inference(quant_intro,[status(thm)],[6507])).
% 86.70/86.96 tff(6509,plain,
% 86.70/86.96 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6510,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_70')).
% 86.70/86.96 tff(6511,plain,
% 86.70/86.96 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6510, 6509])).
% 86.70/86.96 tff(6512,plain,(
% 86.70/86.96 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.96 inference(skolemize,[status(sab)],[6511])).
% 86.70/86.96 tff(6513,plain,
% 86.70/86.96 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6512, 6508])).
% 86.70/86.96 tff(6514,plain,
% 86.70/86.96 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6515,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6516,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6515, 6514])).
% 86.70/86.96 tff(6517,plain,
% 86.70/86.96 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6516, 6513, 6506])).
% 86.70/86.96 tff(6518,plain,
% 86.70/86.96 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s2)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s2)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s2))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6519,plain,
% 86.70/86.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s2)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s2))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6520,plain,
% 86.70/86.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s2)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s2)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6519, 6518])).
% 86.70/86.96 tff(6521,plain,
% 86.70/86.96 (~node20(c_e_h_3, c_q, s2)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6520, 1535, 6517])).
% 86.70/86.96 tff(6522,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6523,plain,
% 86.70/86.96 ((node20(c_e_h_3, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node21(c_e_h_3, c_q, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6524,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node21(c_e_h_3, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3))))),
% 86.70/86.96 inference(monotonicity,[status(thm)],[6523])).
% 86.70/86.96 tff(6525,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node21(c_e_h_3, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3)))),
% 86.70/86.96 inference(transitivity,[status(thm)],[6524, 6522])).
% 86.70/86.96 tff(6526,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node21(c_e_h_3, c_q, s2, s3)))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6527,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3))),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6526, 6525])).
% 86.70/86.96 tff(6528,plain,
% 86.70/86.96 ($false),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6527, 51, 6330, 6521, 6342])).
% 86.70/86.96 tff(6529,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.96 tff(6530,assumption,(~node3(c_e_h_3, c_e_h_1, s3)), introduced(assumption)).
% 86.70/86.96 tff(6531,plain,
% 86.70/86.96 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s3))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6532,plain,
% 86.70/86.96 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s3))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6533,plain,
% 86.70/86.96 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s3)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6532, 6531])).
% 86.70/86.96 tff(6534,plain,
% 86.70/86.96 ($false),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6533, 3860, 814, 6530])).
% 86.70/86.96 tff(6535,plain,(node3(c_e_h_3, c_e_h_1, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.96 tff(6536,plain,
% 86.70/86.96 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6537,plain,
% 86.70/86.96 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6538,plain,
% 86.70/86.96 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6537, 6536])).
% 86.70/86.96 tff(6539,plain,
% 86.70/86.96 ((~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6538, 836])).
% 86.70/86.96 tff(6540,plain,
% 86.70/86.96 ((~m_cell_v_ack(c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6539, 6535])).
% 86.70/86.96 tff(6541,plain,
% 86.70/86.96 (~m_cell_v_ack(c_e_h_1, s3)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6540, 6529])).
% 86.70/86.96 tff(6542,plain,
% 86.70/86.96 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)) | m_cell_v_ack(c_e_h_1, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)) | m_cell_v_ack(c_e_h_1, s3))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6543,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)) | m_cell_v_ack(c_e_h_1, s3))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6544,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)) | m_cell_v_ack(c_e_h_1, s3)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6543, 6542])).
% 86.70/86.96 tff(6545,plain,
% 86.70/86.96 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6544, 848, 6541])).
% 86.70/86.96 tff(6546,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s3)), introduced(assumption)).
% 86.70/86.96 tff(6547,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6548,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6549,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6548, 6547])).
% 86.70/86.96 tff(6550,plain,
% 86.70/86.96 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3))),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6549, 107, 5966])).
% 86.70/86.96 tff(6551,plain,
% 86.70/86.96 (~node22(c_e_h_1, c_l, s2, s3)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6550, 6546])).
% 86.70/86.96 tff(6552,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6553,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6554,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6553, 6552])).
% 86.70/86.96 tff(6555,plain,
% 86.70/86.96 (node21(c_e_h_1, c_l, s2, s3)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6554, 81, 582, 6551])).
% 86.70/86.96 tff(6556,plain,
% 86.70/86.96 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6557,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6558,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6557, 6556])).
% 86.70/86.96 tff(6559,plain,
% 86.70/86.96 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6558, 1638, 4682])).
% 86.70/86.96 tff(6560,plain,
% 86.70/86.96 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s2))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6561,plain,
% 86.70/86.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s2))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6562,plain,
% 86.70/86.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s2)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6561, 6560])).
% 86.70/86.96 tff(6563,plain,
% 86.70/86.96 (~node20(c_e_h_1, c_l, s2)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6562, 1535, 6559])).
% 86.70/86.96 tff(6564,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node21(c_e_h_1, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node21(c_e_h_1, c_l, s2, s3)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6565,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node21(c_e_h_1, c_l, s2, s3)))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6566,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node21(c_e_h_1, c_l, s2, s3))),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6565, 6564])).
% 86.70/86.96 tff(6567,plain,
% 86.70/86.96 ($false),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6566, 51, 6563, 6546, 6555])).
% 86.70/86.96 tff(6568,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.96 tff(6569,plain,
% 86.70/86.96 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6570,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6571,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6570, 6569])).
% 86.70/86.96 tff(6572,plain,
% 86.70/86.96 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6571, 801, 6568])).
% 86.70/86.96 tff(6573,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)), introduced(assumption)).
% 86.70/86.96 tff(6574,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s4)), introduced(assumption)).
% 86.70/86.96 tff(6575,assumption,(node6(c_e_h_1, c_j, s3, s4)), introduced(assumption)).
% 86.70/86.96 tff(6576,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s3)), introduced(assumption)).
% 86.70/86.96 tff(6577,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6578,plain,
% 86.70/86.96 (((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6579,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4))))),
% 86.70/86.96 inference(monotonicity,[status(thm)],[6578])).
% 86.70/86.96 tff(6580,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4)))),
% 86.70/86.96 inference(transitivity,[status(thm)],[6579, 6577])).
% 86.70/86.96 tff(6581,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6582,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4))),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6581, 6580])).
% 86.70/86.96 tff(6583,plain,
% 86.70/86.96 ($false),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6582, 899, 6576, 6574, 6575])).
% 86.70/86.96 tff(6584,plain,((~node6(c_e_h_1, c_j, s3, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.96 tff(6585,plain,
% 86.70/86.96 ((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6584, 5999])).
% 86.70/86.96 tff(6586,plain,
% 86.70/86.96 (~node6(c_e_h_1, c_j, s3, s4)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6585, 6574])).
% 86.70/86.96 tff(6587,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node5(c_e_h_1, c_j, s3, s4) | node6(c_e_h_1, c_j, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_1, c_j, s3, s4) | node6(c_e_h_1, c_j, s3, s4))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6588,plain,
% 86.70/86.96 ((node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node5(c_e_h_1, c_j, s3, s4) | node6(c_e_h_1, c_j, s3, s4))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6589,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node5(c_e_h_1, c_j, s3, s4) | node6(c_e_h_1, c_j, s3, s4)))),
% 86.70/86.96 inference(monotonicity,[status(thm)],[6588])).
% 86.70/86.96 tff(6590,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_1, c_j, s3, s4) | node6(c_e_h_1, c_j, s3, s4))),
% 86.70/86.96 inference(transitivity,[status(thm)],[6589, 6587])).
% 86.70/86.96 tff(6591,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4) | (~trans(s3, s4)))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6592,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_1, c_j, s3, s4) | node6(c_e_h_1, c_j, s3, s4)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6591, 6590])).
% 86.70/86.96 tff(6593,plain,
% 86.70/86.96 (node5(c_e_h_1, c_j, s3, s4) | node6(c_e_h_1, c_j, s3, s4)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6592, 881, 679])).
% 86.70/86.96 tff(6594,plain,
% 86.70/86.96 (node5(c_e_h_1, c_j, s3, s4)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6593, 6586])).
% 86.70/86.96 tff(6595,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6596,plain,
% 86.70/86.96 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6597,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4))))),
% 86.70/86.96 inference(monotonicity,[status(thm)],[6596])).
% 86.70/86.96 tff(6598,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)))),
% 86.70/86.96 inference(transitivity,[status(thm)],[6597, 6595])).
% 86.70/86.96 tff(6599,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6600,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4))),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6599, 6598])).
% 86.70/86.96 tff(6601,plain,
% 86.70/86.96 ($false),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6600, 862, 6574, 6594, 6573, 6572])).
% 86.70/86.96 tff(6602,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.96 tff(6603,plain,
% 86.70/86.96 (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6602, 6545])).
% 86.70/86.96 tff(6604,plain,
% 86.70/86.96 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6605,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6606,plain,
% 86.70/86.96 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4)),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6605, 6604])).
% 86.70/86.96 tff(6607,plain,
% 86.70/86.96 (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6606, 309, 6603])).
% 86.70/86.96 tff(6608,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s4)), introduced(assumption)).
% 86.70/86.96 tff(6609,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s5)), introduced(assumption)).
% 86.70/86.96 tff(6610,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s4)), introduced(assumption)).
% 86.70/86.96 tff(6611,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6612,plain,
% 86.70/86.96 (((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~node18(c_e_h_1, c_h, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)))),
% 86.70/86.96 inference(rewrite,[status(thm)],[])).
% 86.70/86.96 tff(6613,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~node18(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5))))),
% 86.70/86.96 inference(monotonicity,[status(thm)],[6612])).
% 86.70/86.96 tff(6614,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~node18(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)))),
% 86.70/86.96 inference(transitivity,[status(thm)],[6613, 6611])).
% 86.70/86.96 tff(6615,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~node18(c_e_h_1, c_h, s4, s5)))),
% 86.70/86.96 inference(quant_inst,[status(thm)],[])).
% 86.70/86.96 tff(6616,plain,
% 86.70/86.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5))),
% 86.70/86.96 inference(modus_ponens,[status(thm)],[6615, 6614])).
% 86.70/86.96 tff(6617,plain,
% 86.70/86.96 (m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5))),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6616, 124])).
% 86.70/86.96 tff(6618,plain,
% 86.70/86.96 (~node18(c_e_h_1, c_h, s4, s5)),
% 86.70/86.96 inference(unit_resolution,[status(thm)],[6617, 6609, 6608])).
% 86.70/86.96 tff(6619,assumption,(~node19(c_e_h_1, c_h, s4, s5)), introduced(assumption)).
% 86.70/86.96 tff(6620,plain,
% 86.70/86.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_h, s4, s5))),
% 86.70/86.97 inference(rewrite,[status(thm)],[])).
% 86.70/86.97 tff(6621,plain,
% 86.70/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_h, s4, s5))),
% 86.70/86.97 inference(quant_inst,[status(thm)],[])).
% 86.70/86.97 tff(6622,plain,
% 86.70/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_h, s4, s5)),
% 86.70/86.97 inference(modus_ponens,[status(thm)],[6621, 6620])).
% 86.70/86.97 tff(6623,plain,
% 86.70/86.97 ($false),
% 86.70/86.97 inference(unit_resolution,[status(thm)],[6622, 141, 1432, 6619])).
% 86.70/86.97 tff(6624,plain,(node19(c_e_h_1, c_h, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 86.70/86.97 tff(6625,plain,
% 86.70/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))),
% 86.70/86.97 inference(rewrite,[status(thm)],[])).
% 86.70/86.97 tff(6626,plain,
% 86.70/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))),
% 86.70/86.97 inference(quant_inst,[status(thm)],[])).
% 86.70/86.97 tff(6627,plain,
% 86.70/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5))),
% 86.70/86.97 inference(modus_ponens,[status(thm)],[6626, 6625])).
% 86.70/86.97 tff(6628,plain,
% 86.70/86.97 (node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5)),
% 86.70/86.97 inference(unit_resolution,[status(thm)],[6627, 156, 6624])).
% 86.70/86.97 tff(6629,plain,
% 86.70/86.97 (node17(c_e_h_1, c_h, s4)),
% 86.70/86.97 inference(unit_resolution,[status(thm)],[6628, 6618])).
% 86.70/86.97 tff(6630,assumption,(~node14(c_e_h_1, c_h, s4, s5)), introduced(assumption)).
% 86.70/86.97 tff(6631,assumption,(node15(c_e_h_1, c_h, s4, s5)), introduced(assumption)).
% 86.70/86.97 tff(6632,plain,
% 86.70/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 86.70/86.97 inference(rewrite,[status(thm)],[])).
% 86.70/86.97 tff(6633,plain,
% 86.70/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 86.70/86.97 inference(quant_inst,[status(thm)],[])).
% 86.70/86.97 tff(6634,plain,
% 86.70/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 86.70/86.97 inference(modus_ponens,[status(thm)],[6633, 6632])).
% 86.70/86.97 tff(6635,plain,
% 86.70/86.97 ($false),
% 86.70/86.97 inference(unit_resolution,[status(thm)],[6634, 173, 6608, 6609, 6631])).
% 86.70/86.97 tff(6636,plain,((~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5))), inference(lemma,lemma(discharge,[]))).
% 86.70/86.97 tff(6637,plain,
% 86.70/86.97 (~node15(c_e_h_1, c_h, s4, s5)),
% 86.70/86.97 inference(unit_resolution,[status(thm)],[6636, 6609, 6608])).
% 86.70/86.97 tff(6638,plain,
% 86.70/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))),
% 86.70/86.97 inference(rewrite,[status(thm)],[])).
% 86.70/86.97 tff(6639,plain,
% 86.70/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))),
% 86.70/86.97 inference(quant_inst,[status(thm)],[])).
% 86.70/86.97 tff(6640,plain,
% 86.70/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5))),
% 86.70/86.97 inference(modus_ponens,[status(thm)],[6639, 6638])).
% 86.70/86.97 tff(6641,plain,
% 86.70/86.97 (node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5)),
% 86.70/86.97 inference(unit_resolution,[status(thm)],[6640, 189, 6624])).
% 86.70/86.97 tff(6642,plain,
% 86.70/86.97 (node16(c_e_h_1, c_h, s4)),
% 86.70/86.97 inference(unit_resolution,[status(thm)],[6641, 6637, 6630])).
% 86.70/86.97 tff(6643,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s4)), introduced(assumption)).
% 86.70/86.97 tff(6644,assumption,(node17(c_e_h_1, c_h, s4)), introduced(assumption)).
% 86.70/86.97 tff(6645,plain,
% 86.70/86.97 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))),
% 86.70/86.97 inference(rewrite,[status(thm)],[])).
% 86.70/86.97 tff(6646,plain,
% 86.70/86.97 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))),
% 86.70/86.97 inference(rewrite,[status(thm)],[])).
% 86.70/86.97 tff(6647,plain,
% 86.70/86.97 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4))))),
% 86.70/86.97 inference(monotonicity,[status(thm)],[6646])).
% 86.70/86.97 tff(6648,plain,
% 86.70/86.97 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))),
% 86.70/86.97 inference(transitivity,[status(thm)],[6647, 6645])).
% 86.70/86.97 tff(6649,plain,
% 86.70/86.97 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))),
% 86.70/86.97 inference(quant_inst,[status(thm)],[])).
% 86.70/86.97 tff(6650,plain,
% 86.70/86.97 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4))),
% 86.70/86.97 inference(modus_ponens,[status(thm)],[6649, 6648])).
% 86.70/86.97 tff(6651,plain,
% 86.70/86.97 (m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4))),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6650, 209, 6644])).
% 86.78/86.97 tff(6652,plain,
% 86.78/86.97 (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6651, 6643])).
% 86.78/86.97 tff(6653,assumption,(node16(c_e_h_1, c_h, s4)), introduced(assumption)).
% 86.78/86.97 tff(6654,plain,
% 86.78/86.97 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6655,plain,
% 86.78/86.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6656,plain,
% 86.78/86.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6655, 6654])).
% 86.78/86.97 tff(6657,plain,
% 86.78/86.97 (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6656, 228, 6653])).
% 86.78/86.97 tff(6658,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6657, 6652, 6643])).
% 86.78/86.97 tff(6659,plain,(m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node16(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 86.78/86.97 tff(6660,plain,
% 86.78/86.97 (m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6659, 6642, 6629])).
% 86.78/86.97 tff(6661,plain,
% 86.78/86.97 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6662,plain,
% 86.78/86.97 ((m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6663,plain,
% 86.78/86.97 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4))))),
% 86.78/86.97 inference(monotonicity,[status(thm)],[6662])).
% 86.78/86.97 tff(6664,plain,
% 86.78/86.97 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))),
% 86.78/86.97 inference(transitivity,[status(thm)],[6663, 6661])).
% 86.78/86.97 tff(6665,plain,
% 86.78/86.97 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6666,plain,
% 86.78/86.97 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4))),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6665, 6664])).
% 86.78/86.97 tff(6667,plain,
% 86.78/86.97 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6666, 245, 6629])).
% 86.78/86.97 tff(6668,plain,
% 86.78/86.97 (m_c_h_element_v_in1(c_e_h_1, c_h, s4)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6667, 6660])).
% 86.78/86.97 tff(6669,plain,
% 86.78/86.97 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6670,plain,
% 86.78/86.97 (((~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6671,plain,
% 86.78/86.97 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4))))),
% 86.78/86.97 inference(monotonicity,[status(thm)],[6670])).
% 86.78/86.97 tff(6672,plain,
% 86.78/86.97 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)))),
% 86.78/86.97 inference(transitivity,[status(thm)],[6671, 6669])).
% 86.78/86.97 tff(6673,plain,
% 86.78/86.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6674,plain,
% 86.78/86.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4))),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6673, 6672])).
% 86.78/86.97 tff(6675,plain,
% 86.78/86.97 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4))),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6674, 263, 6642])).
% 86.78/86.97 tff(6676,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6675, 6668, 6660])).
% 86.78/86.97 tff(6677,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | node14(c_e_h_1, c_h, s4, s5) | m_c_h_element_v_out(c_e_h_1, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.97 tff(6678,plain,
% 86.78/86.97 (node14(c_e_h_1, c_h, s4, s5)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6677, 6609, 6608])).
% 86.78/86.97 tff(6679,assumption,(node14(c_e_h_1, c_h, s4, s5)), introduced(assumption)).
% 86.78/86.97 tff(6680,plain,
% 86.78/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node14(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node14(c_e_h_1, c_h, s4, s5)))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6681,plain,
% 86.78/86.97 (((~node14(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node14(c_e_h_1, c_h, s4, s5)))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6682,plain,
% 86.78/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node14(c_e_h_1, c_h, s4, s5))))),
% 86.78/86.97 inference(monotonicity,[status(thm)],[6681])).
% 86.78/86.97 tff(6683,plain,
% 86.78/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node14(c_e_h_1, c_h, s4, s5)))),
% 86.78/86.97 inference(transitivity,[status(thm)],[6682, 6680])).
% 86.78/86.97 tff(6684,plain,
% 86.78/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6685,plain,
% 86.78/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node14(c_e_h_1, c_h, s4, s5))),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6684, 6683])).
% 86.78/86.97 tff(6686,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6685, 283, 6609, 6679, 6610])).
% 86.78/86.97 tff(6687,plain,((~node14(c_e_h_1, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.97 tff(6688,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6687, 6678, 6609, 6610])).
% 86.78/86.97 tff(6689,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_out(c_e_h_1, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.97 tff(6690,plain,
% 86.78/86.97 (m_c_h_element_v_in1(c_e_h_1, c_h, s4)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6689, 6609, 6608])).
% 86.78/86.97 tff(6691,plain,
% 86.78/86.97 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4))),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6650, 209, 6643])).
% 86.78/86.97 tff(6692,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6691, 6629, 6690])).
% 86.78/86.97 tff(6693,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | m_c_h_element_v_out(c_e_h_1, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.97 tff(6694,plain,
% 86.78/86.97 ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6693, 6076])).
% 86.78/86.97 tff(6695,plain,
% 86.78/86.97 (~m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6694, 6607])).
% 86.78/86.97 tff(6696,plain,
% 86.78/86.97 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6697,plain,
% 86.78/86.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6698,plain,
% 86.78/86.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6697, 6696])).
% 86.78/86.97 tff(6699,plain,
% 86.78/86.97 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6698, 23, 6695])).
% 86.78/86.97 tff(6700,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)), introduced(assumption)).
% 86.78/86.97 tff(6701,assumption,(node20(c_e_h_1, c_i, s5)), introduced(assumption)).
% 86.78/86.97 tff(6702,plain,
% 86.78/86.97 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s5))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6703,plain,
% 86.78/86.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s5))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6704,plain,
% 86.78/86.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s5)),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6703, 6702])).
% 86.78/86.97 tff(6705,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6704, 37, 6701, 6700])).
% 86.78/86.97 tff(6706,plain,(m_and_h_gate_v_in1(c_e_h_1, c_i, s5) | (~node20(c_e_h_1, c_i, s5))), inference(lemma,lemma(discharge,[]))).
% 86.78/86.97 tff(6707,plain,
% 86.78/86.97 (~node20(c_e_h_1, c_i, s5)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6706, 6699])).
% 86.78/86.97 tff(6708,assumption,(~node20(c_e_h_1, c_i, s5)), introduced(assumption)).
% 86.78/86.97 tff(6709,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s6)), introduced(assumption)).
% 86.78/86.97 tff(6710,assumption,(node21(c_e_h_1, c_i, s5, s6)), introduced(assumption)).
% 86.78/86.97 tff(6711,plain,
% 86.78/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node21(c_e_h_1, c_i, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node21(c_e_h_1, c_i, s5, s6)))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6712,plain,
% 86.78/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node21(c_e_h_1, c_i, s5, s6)))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6713,plain,
% 86.78/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node21(c_e_h_1, c_i, s5, s6))),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6712, 6711])).
% 86.78/86.97 tff(6714,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6713, 51, 6709, 6708, 6710])).
% 86.78/86.97 tff(6715,plain,((~node21(c_e_h_1, c_i, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | node20(c_e_h_1, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.97 tff(6716,plain,
% 86.78/86.97 (~node21(c_e_h_1, c_i, s5, s6)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6715, 6709, 6708])).
% 86.78/86.97 tff(6717,plain,
% 86.78/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6718,plain,
% 86.78/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6719,plain,
% 86.78/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6)),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6718, 6717])).
% 86.78/86.97 tff(6720,plain,
% 86.78/86.97 (node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6719, 81, 1499])).
% 86.78/86.97 tff(6721,plain,
% 86.78/86.97 (node22(c_e_h_1, c_i, s5, s6)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6720, 6716])).
% 86.78/86.97 tff(6722,plain,
% 86.78/86.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node22(c_e_h_1, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node22(c_e_h_1, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6723,plain,
% 86.78/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node22(c_e_h_1, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6724,plain,
% 86.78/86.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node22(c_e_h_1, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6723, 6722])).
% 86.78/86.97 tff(6725,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6724, 107, 6108, 6709, 6721])).
% 86.78/86.97 tff(6726,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5) | node20(c_e_h_1, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.97 tff(6727,plain,
% 86.78/86.97 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | node20(c_e_h_1, c_i, s5)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6726, 6106])).
% 86.78/86.97 tff(6728,plain,
% 86.78/86.97 (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6727, 6707])).
% 86.78/86.97 tff(6729,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s6)), introduced(assumption)).
% 86.78/86.97 tff(6730,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s6)), introduced(assumption)).
% 86.78/86.97 tff(6731,plain,
% 86.78/86.97 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 86.78/86.97 inference(rewrite,[status(thm)],[])).
% 86.78/86.97 tff(6732,plain,
% 86.78/86.97 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 86.78/86.97 inference(quant_inst,[status(thm)],[])).
% 86.78/86.97 tff(6733,plain,
% 86.78/86.97 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 86.78/86.97 inference(modus_ponens,[status(thm)],[6732, 6731])).
% 86.78/86.97 tff(6734,plain,
% 86.78/86.97 ($false),
% 86.78/86.97 inference(unit_resolution,[status(thm)],[6733, 365, 6730, 6729])).
% 86.78/86.98 tff(6735,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.98 tff(6736,plain,
% 86.78/86.98 (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6735, 6728])).
% 86.78/86.98 tff(6737,plain,
% 86.78/86.98 ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6200, 5703])).
% 86.78/86.98 tff(6738,plain,
% 86.78/86.98 (~m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6737, 6114])).
% 86.78/86.98 tff(6739,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s6)), introduced(assumption)).
% 86.78/86.98 tff(6740,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s7)), introduced(assumption)).
% 86.78/86.98 tff(6741,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s6)), introduced(assumption)).
% 86.78/86.98 tff(6742,assumption,(~node16(c_e_h_1, c_e, s6)), introduced(assumption)).
% 86.78/86.98 tff(6743,assumption,(node14(c_e_h_1, c_e, s6, s7)), introduced(assumption)).
% 86.78/86.98 tff(6744,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6745,plain,
% 86.78/86.98 (((~node14(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6746,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7))))),
% 86.78/86.98 inference(monotonicity,[status(thm)],[6745])).
% 86.78/86.98 tff(6747,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))),
% 86.78/86.98 inference(transitivity,[status(thm)],[6746, 6744])).
% 86.78/86.98 tff(6748,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6749,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6748, 6747])).
% 86.78/86.98 tff(6750,plain,
% 86.78/86.98 ($false),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6749, 283, 6740, 6743, 6741])).
% 86.78/86.98 tff(6751,plain,((~node14(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.98 tff(6752,plain,
% 86.78/86.98 (~node14(c_e_h_1, c_e, s6, s7)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6751, 6740, 6741])).
% 86.78/86.98 tff(6753,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_e, s6, s7))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6754,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_e, s6, s7))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6755,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_e, s6, s7)),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6754, 6753])).
% 86.78/86.98 tff(6756,plain,
% 86.78/86.98 (node19(c_e_h_1, c_e, s6, s7)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6755, 141, 1552])).
% 86.78/86.98 tff(6757,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node15(c_e_h_1, c_e, s6, s7) | node16(c_e_h_1, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node15(c_e_h_1, c_e, s6, s7) | node16(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6758,plain,
% 86.78/86.98 ((node16(c_e_h_1, c_e, s6) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7))) <=> (node14(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node15(c_e_h_1, c_e, s6, s7) | node16(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6759,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s6) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node15(c_e_h_1, c_e, s6, s7) | node16(c_e_h_1, c_e, s6)))),
% 86.78/86.98 inference(monotonicity,[status(thm)],[6758])).
% 86.78/86.98 tff(6760,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s6) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node15(c_e_h_1, c_e, s6, s7) | node16(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(transitivity,[status(thm)],[6759, 6757])).
% 86.78/86.98 tff(6761,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s6) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6762,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node15(c_e_h_1, c_e, s6, s7) | node16(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6761, 6760])).
% 86.78/86.98 tff(6763,plain,
% 86.78/86.98 (node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | node16(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6762, 189, 6756])).
% 86.78/86.98 tff(6764,plain,
% 86.78/86.98 (node15(c_e_h_1, c_e, s6, s7)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6763, 6752, 6742])).
% 86.78/86.98 tff(6765,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node15(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node15(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6766,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node15(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6767,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node15(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6766, 6765])).
% 86.78/86.98 tff(6768,plain,
% 86.78/86.98 ($false),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6767, 173, 6740, 6764, 6250])).
% 86.78/86.98 tff(6769,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | node16(c_e_h_1, c_e, s6) | m_c_h_element_v_in1(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.98 tff(6770,plain,
% 86.78/86.98 (node16(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6769, 6741, 6250, 6740])).
% 86.78/86.98 tff(6771,plain,
% 86.78/86.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6772,plain,
% 86.78/86.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6773,plain,
% 86.78/86.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6772, 6771])).
% 86.78/86.98 tff(6774,plain,
% 86.78/86.98 ((~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6773, 228, 6739])).
% 86.78/86.98 tff(6775,plain,
% 86.78/86.98 ($false),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6774, 6770, 6741])).
% 86.78/86.98 tff(6776,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 86.78/86.98 tff(6777,plain,
% 86.78/86.98 (m_c_h_element_v_in1(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6776, 6740, 6250, 6739])).
% 86.78/86.98 tff(6778,plain,
% 86.78/86.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6779,plain,
% 86.78/86.98 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | (~node17(c_e_h_1, c_e, s6))) <=> ((~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6780,plain,
% 86.78/86.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | (~node17(c_e_h_1, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)))),
% 86.78/86.98 inference(monotonicity,[status(thm)],[6779])).
% 86.78/86.98 tff(6781,plain,
% 86.78/86.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | (~node17(c_e_h_1, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(transitivity,[status(thm)],[6780, 6778])).
% 86.78/86.98 tff(6782,plain,
% 86.78/86.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | (~node17(c_e_h_1, c_e, s6)))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6783,plain,
% 86.78/86.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6782, 6781])).
% 86.78/86.98 tff(6784,plain,
% 86.78/86.98 ((~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6783, 209, 6739])).
% 86.78/86.98 tff(6785,plain,
% 86.78/86.98 (~node17(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6784, 6777])).
% 86.78/86.98 tff(6786,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node17(c_e_h_1, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node17(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6787,plain,
% 86.78/86.98 ((node17(c_e_h_1, c_e, s6) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7))) <=> (node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node17(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6788,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s6) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node17(c_e_h_1, c_e, s6)))),
% 86.78/86.98 inference(monotonicity,[status(thm)],[6787])).
% 86.78/86.98 tff(6789,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s6) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node17(c_e_h_1, c_e, s6))),
% 86.78/86.98 inference(transitivity,[status(thm)],[6788, 6786])).
% 86.78/86.98 tff(6790,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s6) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6791,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node17(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6790, 6789])).
% 86.78/86.98 tff(6792,plain,
% 86.78/86.98 (node18(c_e_h_1, c_e, s6, s7) | node17(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6791, 156, 6756])).
% 86.78/86.98 tff(6793,plain,
% 86.78/86.98 (node18(c_e_h_1, c_e, s6, s7)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6792, 6785])).
% 86.78/86.98 tff(6794,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node18(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node18(c_e_h_1, c_e, s6, s7)))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6795,plain,
% 86.78/86.98 (((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~node18(c_e_h_1, c_e, s6, s7))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node18(c_e_h_1, c_e, s6, s7)))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6796,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~node18(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node18(c_e_h_1, c_e, s6, s7))))),
% 86.78/86.98 inference(monotonicity,[status(thm)],[6795])).
% 86.78/86.98 tff(6797,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~node18(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node18(c_e_h_1, c_e, s6, s7)))),
% 86.78/86.98 inference(transitivity,[status(thm)],[6796, 6794])).
% 86.78/86.98 tff(6798,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~node18(c_e_h_1, c_e, s6, s7)))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6799,plain,
% 86.78/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node18(c_e_h_1, c_e, s6, s7))),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6798, 6797])).
% 86.78/86.98 tff(6800,plain,
% 86.78/86.98 ($false),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6799, 124, 6740, 6793, 6250])).
% 86.78/86.98 tff(6801,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.98 tff(6802,plain,
% 86.78/86.98 ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6801, 6738])).
% 86.78/86.98 tff(6803,plain,
% 86.78/86.98 (~m_c_h_element_v_out(c_e_h_1, c_e, s7)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6802, 6736])).
% 86.78/86.98 tff(6804,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)), introduced(assumption)).
% 86.78/86.98 tff(6805,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s7)), introduced(assumption)).
% 86.78/86.98 tff(6806,plain,
% 86.78/86.98 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6807,plain,
% 86.78/86.98 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6808,plain,
% 86.78/86.98 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7)),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6807, 6806])).
% 86.78/86.98 tff(6809,plain,
% 86.78/86.98 ($false),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6808, 976, 6805, 6804])).
% 86.78/86.98 tff(6810,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.98 tff(6811,plain,
% 86.78/86.98 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6810, 6803])).
% 86.78/86.98 tff(6812,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)), introduced(assumption)).
% 86.78/86.98 tff(6813,plain,
% 86.78/86.98 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6814,plain,
% 86.78/86.98 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 86.78/86.98 inference(quant_inst,[status(thm)],[])).
% 86.78/86.98 tff(6815,plain,
% 86.78/86.98 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 86.78/86.98 inference(modus_ponens,[status(thm)],[6814, 6813])).
% 86.78/86.98 tff(6816,plain,
% 86.78/86.98 ($false),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6815, 1142, 6268, 6812])).
% 86.78/86.98 tff(6817,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)), inference(lemma,lemma(discharge,[]))).
% 86.78/86.98 tff(6818,plain,
% 86.78/86.98 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)),
% 86.78/86.98 inference(unit_resolution,[status(thm)],[6817, 5776])).
% 86.78/86.98 tff(6819,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)), introduced(assumption)).
% 86.78/86.98 tff(6820,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)), introduced(assumption)).
% 86.78/86.98 tff(6821,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)), introduced(assumption)).
% 86.78/86.98 tff(6822,assumption,(node10(c_e_h_1, c_n, s7, s8)), introduced(assumption)).
% 86.78/86.98 tff(6823,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6824,plain,
% 86.78/86.98 (((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)))),
% 86.78/86.98 inference(rewrite,[status(thm)],[])).
% 86.78/86.98 tff(6825,plain,
% 86.78/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7))))),
% 86.80/86.98 inference(monotonicity,[status(thm)],[6824])).
% 86.80/86.98 tff(6826,plain,
% 86.80/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)))),
% 86.80/86.98 inference(transitivity,[status(thm)],[6825, 6823])).
% 86.80/86.98 tff(6827,plain,
% 86.80/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))),
% 86.80/86.98 inference(quant_inst,[status(thm)],[])).
% 86.80/86.98 tff(6828,plain,
% 86.80/86.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7))),
% 86.80/86.98 inference(modus_ponens,[status(thm)],[6827, 6826])).
% 86.80/86.98 tff(6829,plain,
% 86.80/86.98 ($false),
% 86.80/86.98 inference(unit_resolution,[status(thm)],[6828, 1191, 6821, 6822, 6820, 6819])).
% 86.80/86.98 tff(6830,plain,((~node10(c_e_h_1, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 86.80/86.98 tff(6831,plain,
% 86.80/86.98 (~node10(c_e_h_1, c_n, s7, s8)),
% 86.80/86.98 inference(unit_resolution,[status(thm)],[6830, 6821, 6820, 6819])).
% 86.80/86.98 tff(6832,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)), introduced(assumption)).
% 86.80/86.98 tff(6833,assumption,(node11(c_e_h_1, c_n, s7, s8)), introduced(assumption)).
% 86.80/86.98 tff(6834,plain,
% 86.80/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)))),
% 86.80/86.98 inference(rewrite,[status(thm)],[])).
% 86.80/86.98 tff(6835,plain,
% 86.80/86.98 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)))),
% 86.80/86.98 inference(rewrite,[status(thm)],[])).
% 86.80/86.98 tff(6836,plain,
% 86.80/86.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8))))),
% 86.80/86.99 inference(monotonicity,[status(thm)],[6835])).
% 86.80/86.99 tff(6837,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)))),
% 86.80/86.99 inference(transitivity,[status(thm)],[6836, 6834])).
% 86.80/86.99 tff(6838,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6839,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8))),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6838, 6837])).
% 86.80/86.99 tff(6840,plain,
% 86.80/86.99 ($false),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6839, 1161, 6821, 6832, 6833])).
% 86.80/86.99 tff(6841,plain,((~node11(c_e_h_1, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 86.80/86.99 tff(6842,plain,
% 86.80/86.99 (~node11(c_e_h_1, c_n, s7, s8)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6841, 6821, 6832])).
% 86.80/86.99 tff(6843,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6844,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6845,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6844, 6843])).
% 86.80/86.99 tff(6846,plain,
% 86.80/86.99 (node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6845, 1092, 2152])).
% 86.80/86.99 tff(6847,plain,
% 86.80/86.99 ($false),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6846, 6842, 6831])).
% 86.80/86.99 tff(6848,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 86.80/86.99 tff(6849,plain,
% 86.80/86.99 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6848, 6818])).
% 86.80/86.99 tff(6850,plain,
% 86.80/86.99 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6849, 6259])).
% 86.80/86.99 tff(6851,plain,
% 86.80/86.99 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6850, 6811])).
% 86.80/86.99 tff(6852,plain,
% 86.80/86.99 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6853,plain,
% 86.80/86.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6854,plain,
% 86.80/86.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6853, 6852])).
% 86.80/86.99 tff(6855,plain,
% 86.80/86.99 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6854, 1048, 6851])).
% 86.80/86.99 tff(6856,plain,
% 86.80/86.99 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6857,plain,
% 86.80/86.99 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6858,plain,
% 86.80/86.99 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6857, 6856])).
% 86.80/86.99 tff(6859,plain,
% 86.80/86.99 (~node9(c_e_h_1, c_m, s8)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6858, 1062, 6855])).
% 86.80/86.99 tff(6860,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), introduced(assumption)).
% 86.80/86.99 tff(6861,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)), introduced(assumption)).
% 86.80/86.99 tff(6862,assumption,(node11(c_e_h_1, c_m, s8, s9)), introduced(assumption)).
% 86.80/86.99 tff(6863,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node11(c_e_h_1, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node11(c_e_h_1, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6864,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node11(c_e_h_1, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6865,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node11(c_e_h_1, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6864, 6863])).
% 86.80/86.99 tff(6866,plain,
% 86.80/86.99 ($false),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6865, 1130, 6861, 6860, 6862])).
% 86.80/86.99 tff(6867,plain,((~node11(c_e_h_1, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 86.80/86.99 tff(6868,plain,
% 86.80/86.99 (~node11(c_e_h_1, c_m, s8, s9)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6867, 6861, 6860])).
% 86.80/86.99 tff(6869,assumption,(~node9(c_e_h_1, c_m, s8)), introduced(assumption)).
% 86.80/86.99 tff(6870,assumption,(node10(c_e_h_1, c_m, s8, s9)), introduced(assumption)).
% 86.80/86.99 tff(6871,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)) | node9(c_e_h_1, c_m, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)) | node9(c_e_h_1, c_m, s8))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6872,plain,
% 86.80/86.99 ((node9(c_e_h_1, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)) | node9(c_e_h_1, c_m, s8))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6873,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)) | node9(c_e_h_1, c_m, s8)))),
% 86.80/86.99 inference(monotonicity,[status(thm)],[6872])).
% 86.80/86.99 tff(6874,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)) | node9(c_e_h_1, c_m, s8))),
% 86.80/86.99 inference(transitivity,[status(thm)],[6873, 6871])).
% 86.80/86.99 tff(6875,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6876,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)) | node9(c_e_h_1, c_m, s8)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6875, 6874])).
% 86.80/86.99 tff(6877,plain,
% 86.80/86.99 ($false),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6876, 1076, 6861, 6870, 6869])).
% 86.80/86.99 tff(6878,plain,((~node10(c_e_h_1, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 86.80/86.99 tff(6879,plain,
% 86.80/86.99 (~node10(c_e_h_1, c_m, s8, s9)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6878, 6861, 6869])).
% 86.80/86.99 tff(6880,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6881,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6882,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6881, 6880])).
% 86.80/86.99 tff(6883,plain,
% 86.80/86.99 (node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6882, 1092, 2636])).
% 86.80/86.99 tff(6884,plain,
% 86.80/86.99 ($false),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6883, 6879, 6868])).
% 86.80/86.99 tff(6885,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 86.80/86.99 tff(6886,plain,
% 86.80/86.99 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6885, 6286])).
% 86.80/86.99 tff(6887,plain,
% 86.80/86.99 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6886, 6859])).
% 86.80/86.99 tff(6888,plain,
% 86.80/86.99 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6889,plain,
% 86.80/86.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6890,plain,
% 86.80/86.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6889, 6888])).
% 86.80/86.99 tff(6891,plain,
% 86.80/86.99 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6890, 1521])).
% 86.80/86.99 tff(6892,plain,
% 86.80/86.99 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6891, 6887])).
% 86.80/86.99 tff(6893,plain,
% 86.80/86.99 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s9))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6894,plain,
% 86.80/86.99 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s9))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6895,plain,
% 86.80/86.99 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s9)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6894, 6893])).
% 86.80/86.99 tff(6896,plain,
% 86.80/86.99 (~node20(c_e_h_1, c_r, s9)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6895, 1535, 6892])).
% 86.80/86.99 tff(6897,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | node20(c_e_h_1, c_r, s9) | (~node21(c_e_h_1, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | node20(c_e_h_1, c_r, s9) | (~node21(c_e_h_1, c_r, s9, s10)))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6898,plain,
% 86.80/86.99 ((node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node21(c_e_h_1, c_r, s9, s10))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | node20(c_e_h_1, c_r, s9) | (~node21(c_e_h_1, c_r, s9, s10)))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6899,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node21(c_e_h_1, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | node20(c_e_h_1, c_r, s9) | (~node21(c_e_h_1, c_r, s9, s10))))),
% 86.80/86.99 inference(monotonicity,[status(thm)],[6898])).
% 86.80/86.99 tff(6900,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node21(c_e_h_1, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | node20(c_e_h_1, c_r, s9) | (~node21(c_e_h_1, c_r, s9, s10)))),
% 86.80/86.99 inference(transitivity,[status(thm)],[6899, 6897])).
% 86.80/86.99 tff(6901,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node21(c_e_h_1, c_r, s9, s10)))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6902,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | node20(c_e_h_1, c_r, s9) | (~node21(c_e_h_1, c_r, s9, s10))),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6901, 6900])).
% 86.80/86.99 tff(6903,plain,
% 86.80/86.99 ($false),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6902, 51, 6320, 6896, 6329])).
% 86.80/86.99 tff(6904,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 86.80/86.99 tff(6905,plain,
% 86.80/86.99 (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6904, 6318])).
% 86.80/86.99 tff(6906,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s10)), introduced(assumption)).
% 86.80/86.99 tff(6907,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s11)), introduced(assumption)).
% 86.80/86.99 tff(6908,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6909,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6910,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6909, 6908])).
% 86.80/86.99 tff(6911,plain,
% 86.80/86.99 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6910, 107])).
% 86.80/86.99 tff(6912,plain,
% 86.80/86.99 (~node22(c_e_h_1, c_r, s10, s11)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6911, 6907, 6906])).
% 86.80/86.99 tff(6913,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6914,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6915,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6914, 6913])).
% 86.80/86.99 tff(6916,plain,
% 86.80/86.99 (node21(c_e_h_1, c_r, s10, s11)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6915, 81, 3778, 6912])).
% 86.80/86.99 tff(6917,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s3)), introduced(assumption)).
% 86.80/86.99 tff(6918,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s4)), introduced(assumption)).
% 86.80/86.99 tff(6919,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6920,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6921,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6920, 6919])).
% 86.80/86.99 tff(6922,plain,
% 86.80/86.99 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6921, 107])).
% 86.80/86.99 tff(6923,plain,
% 86.80/86.99 (~node22(c_e_h_3, c_q, s3, s4)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6922, 6918, 6917])).
% 86.80/86.99 tff(6924,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6925,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6926,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6925, 6924])).
% 86.80/86.99 tff(6927,plain,
% 86.80/86.99 (node21(c_e_h_3, c_q, s3, s4)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6926, 81, 679, 6923])).
% 86.80/86.99 tff(6928,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)), introduced(assumption)).
% 86.80/86.99 tff(6929,assumption,(node11(c_e_h_3, c_n, s2, s3)), introduced(assumption)).
% 86.80/86.99 tff(6930,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)), introduced(assumption)).
% 86.80/86.99 tff(6931,plain,
% 86.80/86.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node11(c_e_h_3, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node11(c_e_h_3, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6932,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node11(c_e_h_3, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6933,plain,
% 86.80/86.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node11(c_e_h_3, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6932, 6931])).
% 86.80/86.99 tff(6934,plain,
% 86.80/86.99 ($false),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6933, 1130, 6928, 6930, 6929])).
% 86.80/86.99 tff(6935,plain,((~node11(c_e_h_3, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 86.80/86.99 tff(6936,plain,
% 86.80/86.99 ((~node11(c_e_h_3, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6935, 6506])).
% 86.80/86.99 tff(6937,plain,
% 86.80/86.99 (~node11(c_e_h_3, c_n, s2, s3)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6936, 6928])).
% 86.80/86.99 tff(6938,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)), introduced(assumption)).
% 86.80/86.99 tff(6939,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s1)), introduced(assumption)).
% 86.80/86.99 tff(6940,plain,
% 86.80/86.99 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6941,plain,
% 86.80/86.99 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6942,plain,
% 86.80/86.99 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6941, 6940])).
% 86.80/86.99 tff(6943,plain,
% 86.80/86.99 ($false),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6942, 6389, 6939, 6938])).
% 86.80/86.99 tff(6944,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 86.80/86.99 tff(6945,plain,
% 86.80/86.99 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)),
% 86.80/86.99 inference(unit_resolution,[status(thm)],[6944, 5914])).
% 86.80/86.99 tff(6946,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)), introduced(assumption)).
% 86.80/86.99 tff(6947,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)), introduced(assumption)).
% 86.80/86.99 tff(6948,plain,
% 86.80/86.99 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 86.80/86.99 inference(rewrite,[status(thm)],[])).
% 86.80/86.99 tff(6949,plain,
% 86.80/86.99 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 86.80/86.99 inference(quant_inst,[status(thm)],[])).
% 86.80/86.99 tff(6950,plain,
% 86.80/86.99 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)),
% 86.80/86.99 inference(modus_ponens,[status(thm)],[6949, 6948])).
% 86.80/86.99 tff(6951,plain,
% 86.80/87.00 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6950, 6378, 6490])).
% 86.80/87.00 tff(6952,assumption,(node10(c_e_h_3, c_m, s1, s2)), introduced(assumption)).
% 86.80/87.00 tff(6953,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6954,plain,
% 86.80/87.00 (((~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6955,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1))))),
% 86.80/87.00 inference(monotonicity,[status(thm)],[6954])).
% 86.80/87.00 tff(6956,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)))),
% 86.80/87.00 inference(transitivity,[status(thm)],[6955, 6953])).
% 86.80/87.00 tff(6957,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(6958,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1))),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[6957, 6956])).
% 86.80/87.00 tff(6959,plain,
% 86.80/87.00 ($false),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6958, 1191, 6947, 6952, 6951, 6946])).
% 86.80/87.00 tff(6960,plain,((~node10(c_e_h_3, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 86.80/87.00 tff(6961,plain,
% 86.80/87.00 (~node10(c_e_h_3, c_m, s1, s2)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6960, 6947, 6946])).
% 86.80/87.00 tff(6962,assumption,(node11(c_e_h_3, c_m, s1, s2)), introduced(assumption)).
% 86.80/87.00 tff(6963,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)), introduced(assumption)).
% 86.80/87.00 tff(6964,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) | (~node11(c_e_h_3, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) | (~node11(c_e_h_3, c_m, s1, s2)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6965,plain,
% 86.80/87.00 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) | (~node11(c_e_h_3, c_m, s1, s2)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6966,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) | (~node11(c_e_h_3, c_m, s1, s2))))),
% 86.80/87.00 inference(monotonicity,[status(thm)],[6965])).
% 86.80/87.00 tff(6967,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) | (~node11(c_e_h_3, c_m, s1, s2)))),
% 86.80/87.00 inference(transitivity,[status(thm)],[6966, 6964])).
% 86.80/87.00 tff(6968,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(6969,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) | (~node11(c_e_h_3, c_m, s1, s2))),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[6968, 6967])).
% 86.80/87.00 tff(6970,plain,
% 86.80/87.00 ($false),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6969, 1161, 6947, 6963, 6962])).
% 86.80/87.00 tff(6971,plain,((~node11(c_e_h_3, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 86.80/87.00 tff(6972,plain,
% 86.80/87.00 ((~node11(c_e_h_3, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6971, 6435])).
% 86.80/87.00 tff(6973,plain,
% 86.80/87.00 (~node11(c_e_h_3, c_m, s1, s2)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6972, 6947])).
% 86.80/87.00 tff(6974,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6975,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(6976,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[6975, 6974])).
% 86.80/87.00 tff(6977,plain,
% 86.80/87.00 (node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6976, 1092, 344])).
% 86.80/87.00 tff(6978,plain,
% 86.80/87.00 ($false),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6977, 6973, 6961])).
% 86.80/87.00 tff(6979,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 86.80/87.00 tff(6980,plain,
% 86.80/87.00 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6979, 6945])).
% 86.80/87.00 tff(6981,plain,
% 86.80/87.00 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6982,plain,
% 86.80/87.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(6983,plain,
% 86.80/87.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[6982, 6981])).
% 86.80/87.00 tff(6984,plain,
% 86.80/87.00 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6983, 6442, 6980])).
% 86.80/87.00 tff(6985,plain,
% 86.80/87.00 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6986,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(6987,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[6986, 6985])).
% 86.80/87.00 tff(6988,plain,
% 86.80/87.00 (~node9(c_e_h_3, c_n, s2)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6987, 1062, 6984])).
% 86.80/87.00 tff(6989,assumption,(~node9(c_e_h_3, c_n, s2)), introduced(assumption)).
% 86.80/87.00 tff(6990,assumption,(node10(c_e_h_3, c_n, s2, s3)), introduced(assumption)).
% 86.80/87.00 tff(6991,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6992,plain,
% 86.80/87.00 ((node9(c_e_h_3, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node10(c_e_h_3, c_n, s2, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(6993,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node10(c_e_h_3, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3))))),
% 86.80/87.00 inference(monotonicity,[status(thm)],[6992])).
% 86.80/87.00 tff(6994,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node10(c_e_h_3, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3)))),
% 86.80/87.00 inference(transitivity,[status(thm)],[6993, 6991])).
% 86.80/87.00 tff(6995,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node10(c_e_h_3, c_n, s2, s3)))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(6996,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3))),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[6995, 6994])).
% 86.80/87.00 tff(6997,plain,
% 86.80/87.00 ($false),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6996, 1076, 6928, 6990, 6989])).
% 86.80/87.00 tff(6998,plain,((~node10(c_e_h_3, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 86.80/87.00 tff(6999,plain,
% 86.80/87.00 ((~node10(c_e_h_3, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6998, 6988])).
% 86.80/87.00 tff(7000,plain,
% 86.80/87.00 (~node10(c_e_h_3, c_n, s2, s3)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[6999, 6928])).
% 86.80/87.00 tff(7001,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7002,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7003,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7002, 7001])).
% 86.80/87.00 tff(7004,plain,
% 86.80/87.00 (node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7003, 1092, 582])).
% 86.80/87.00 tff(7005,plain,
% 86.80/87.00 ($false),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7004, 7000, 6937])).
% 86.80/87.00 tff(7006,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)), inference(lemma,lemma(discharge,[]))).
% 86.80/87.00 tff(7007,plain,
% 86.80/87.00 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7008,plain,
% 86.80/87.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7009,plain,
% 86.80/87.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7008, 7007])).
% 86.80/87.00 tff(7010,plain,
% 86.80/87.00 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7009, 6513, 7006])).
% 86.80/87.00 tff(7011,plain,
% 86.80/87.00 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s3)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s3)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s3))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7012,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s3)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s3))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7013,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s3)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s3)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7012, 7011])).
% 86.80/87.00 tff(7014,plain,
% 86.80/87.00 (~node20(c_e_h_3, c_q, s3)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7013, 1535, 7010])).
% 86.80/87.00 tff(7015,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node21(c_e_h_3, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node21(c_e_h_3, c_q, s3, s4)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7016,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node21(c_e_h_3, c_q, s3, s4)))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7017,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node21(c_e_h_3, c_q, s3, s4))),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7016, 7015])).
% 86.80/87.00 tff(7018,plain,
% 86.80/87.00 ($false),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7017, 51, 6918, 7014, 6927])).
% 86.80/87.00 tff(7019,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 86.80/87.00 tff(7020,plain,
% 86.80/87.00 (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7019, 6529])).
% 86.80/87.00 tff(7021,plain,
% 86.80/87.00 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s4))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7022,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s4))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7023,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s4)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7022, 7021])).
% 86.80/87.00 tff(7024,plain,
% 86.80/87.00 (node3(c_e_h_3, c_e_h_1, s4)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7023, 3860, 814])).
% 86.80/87.00 tff(7025,plain,
% 86.80/87.00 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s4)) | (~node3(c_e_h_3, c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s4)) | (~node3(c_e_h_3, c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7026,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s4)) | (~node3(c_e_h_3, c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7027,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s4)) | (~node3(c_e_h_3, c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7026, 7025])).
% 86.80/87.00 tff(7028,plain,
% 86.80/87.00 ((~m_cell_v_ack(c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7027, 836, 7024])).
% 86.80/87.00 tff(7029,plain,
% 86.80/87.00 (~m_cell_v_ack(c_e_h_1, s4)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7028, 7020])).
% 86.80/87.00 tff(7030,assumption,(m_or_h_gate_v_in2(c_e_h_1, c_j, s4)), introduced(assumption)).
% 86.80/87.00 tff(7031,assumption,(~m_cell_v_ack(c_e_h_1, s4)), introduced(assumption)).
% 86.80/87.00 tff(7032,plain,
% 86.80/87.00 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)) | m_cell_v_ack(c_e_h_1, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)) | m_cell_v_ack(c_e_h_1, s4))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7033,plain,
% 86.80/87.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)) | m_cell_v_ack(c_e_h_1, s4))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7034,plain,
% 86.80/87.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)) | m_cell_v_ack(c_e_h_1, s4)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7033, 7032])).
% 86.80/87.00 tff(7035,plain,
% 86.80/87.00 ($false),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7034, 848, 7031, 7030])).
% 86.80/87.00 tff(7036,plain,(m_cell_v_ack(c_e_h_1, s4) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s4))), inference(lemma,lemma(discharge,[]))).
% 86.80/87.00 tff(7037,plain,
% 86.80/87.00 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7036, 7029])).
% 86.80/87.00 tff(7038,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)), introduced(assumption)).
% 86.80/87.00 tff(7039,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s4)), introduced(assumption)).
% 86.80/87.00 tff(7040,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s4)), introduced(assumption)).
% 86.80/87.00 tff(7041,plain,
% 86.80/87.00 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7042,plain,
% 86.80/87.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7043,plain,
% 86.80/87.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7042, 7041])).
% 86.80/87.00 tff(7044,plain,
% 86.80/87.00 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7043, 1638, 4818])).
% 86.80/87.00 tff(7045,plain,
% 86.80/87.00 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s3))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7046,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s3))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7047,plain,
% 86.80/87.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s3)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7046, 7045])).
% 86.80/87.00 tff(7048,plain,
% 86.80/87.00 (~node20(c_e_h_1, c_l, s3)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7047, 1535, 7044])).
% 86.80/87.00 tff(7049,assumption,(~node20(c_e_h_1, c_l, s3)), introduced(assumption)).
% 86.80/87.00 tff(7050,assumption,(node21(c_e_h_1, c_l, s3, s4)), introduced(assumption)).
% 86.80/87.00 tff(7051,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node21(c_e_h_1, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node21(c_e_h_1, c_l, s3, s4)))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7052,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node21(c_e_h_1, c_l, s3, s4)))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7053,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node21(c_e_h_1, c_l, s3, s4))),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7052, 7051])).
% 86.80/87.00 tff(7054,plain,
% 86.80/87.00 ($false),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7053, 51, 7050, 7040, 7049])).
% 86.80/87.00 tff(7055,plain,((~node21(c_e_h_1, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | node20(c_e_h_1, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 86.80/87.00 tff(7056,plain,
% 86.80/87.00 ((~node21(c_e_h_1, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7055, 7048])).
% 86.80/87.00 tff(7057,plain,
% 86.80/87.00 (~node21(c_e_h_1, c_l, s3, s4)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7056, 7040])).
% 86.80/87.00 tff(7058,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4))),
% 86.80/87.00 inference(rewrite,[status(thm)],[])).
% 86.80/87.00 tff(7059,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4))),
% 86.80/87.00 inference(quant_inst,[status(thm)],[])).
% 86.80/87.00 tff(7060,plain,
% 86.80/87.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4)),
% 86.80/87.00 inference(modus_ponens,[status(thm)],[7059, 7058])).
% 86.80/87.00 tff(7061,plain,
% 86.80/87.00 (node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7060, 81, 679])).
% 86.80/87.00 tff(7062,plain,
% 86.80/87.00 (node22(c_e_h_1, c_l, s3, s4)),
% 86.80/87.00 inference(unit_resolution,[status(thm)],[7061, 7057])).
% 86.80/87.00 tff(7063,plain,
% 86.80/87.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node22(c_e_h_1, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node22(c_e_h_1, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7064,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node22(c_e_h_1, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))),
% 86.80/87.01 inference(quant_inst,[status(thm)],[])).
% 86.80/87.01 tff(7065,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node22(c_e_h_1, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3)),
% 86.80/87.01 inference(modus_ponens,[status(thm)],[7064, 7063])).
% 86.80/87.01 tff(7066,plain,
% 86.80/87.01 ($false),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7065, 107, 7062, 7040, 6568])).
% 86.80/87.01 tff(7067,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 86.80/87.01 tff(7068,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s4)), introduced(assumption)).
% 86.80/87.01 tff(7069,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s4)), introduced(assumption)).
% 86.80/87.01 tff(7070,plain,
% 86.80/87.01 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7071,plain,
% 86.80/87.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 86.80/87.01 inference(quant_inst,[status(thm)],[])).
% 86.80/87.01 tff(7072,plain,
% 86.80/87.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4)),
% 86.80/87.01 inference(modus_ponens,[status(thm)],[7071, 7070])).
% 86.80/87.01 tff(7073,plain,
% 86.80/87.01 ($false),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7072, 801, 7069, 7068])).
% 86.80/87.01 tff(7074,plain,(m_and_h_gate_v_out(c_e_h_1, c_l, s4) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s4))), inference(lemma,lemma(discharge,[]))).
% 86.80/87.01 tff(7075,plain,
% 86.80/87.01 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7074, 7067])).
% 86.80/87.01 tff(7076,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)), introduced(assumption)).
% 86.80/87.01 tff(7077,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s5)), introduced(assumption)).
% 86.80/87.01 tff(7078,assumption,(node5(c_e_h_1, c_j, s4, s5)), introduced(assumption)).
% 86.80/87.01 tff(7079,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7080,plain,
% 86.80/87.01 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7081,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5))))),
% 86.80/87.01 inference(monotonicity,[status(thm)],[7080])).
% 86.80/87.01 tff(7082,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)))),
% 86.80/87.01 inference(transitivity,[status(thm)],[7081, 7079])).
% 86.80/87.01 tff(7083,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)))),
% 86.80/87.01 inference(quant_inst,[status(thm)],[])).
% 86.80/87.01 tff(7084,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5))),
% 86.80/87.01 inference(modus_ponens,[status(thm)],[7083, 7082])).
% 86.80/87.01 tff(7085,plain,
% 86.80/87.01 ($false),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7084, 862, 7077, 7078, 7076, 7038])).
% 86.80/87.01 tff(7086,plain,((~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 86.80/87.01 tff(7087,plain,
% 86.80/87.01 (~node5(c_e_h_1, c_j, s4, s5)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7086, 7077, 7076, 7038])).
% 86.80/87.01 tff(7088,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_1, c_j, s4, s5) | node6(c_e_h_1, c_j, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_1, c_j, s4, s5) | node6(c_e_h_1, c_j, s4, s5))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7089,plain,
% 86.80/87.01 ((node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node5(c_e_h_1, c_j, s4, s5) | node6(c_e_h_1, c_j, s4, s5))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7090,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_1, c_j, s4, s5) | node6(c_e_h_1, c_j, s4, s5)))),
% 86.80/87.01 inference(monotonicity,[status(thm)],[7089])).
% 86.80/87.01 tff(7091,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_1, c_j, s4, s5) | node6(c_e_h_1, c_j, s4, s5))),
% 86.80/87.01 inference(transitivity,[status(thm)],[7090, 7088])).
% 86.80/87.01 tff(7092,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5) | (~trans(s4, s5)))),
% 86.80/87.01 inference(quant_inst,[status(thm)],[])).
% 86.80/87.01 tff(7093,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_1, c_j, s4, s5) | node6(c_e_h_1, c_j, s4, s5)),
% 86.80/87.01 inference(modus_ponens,[status(thm)],[7092, 7091])).
% 86.80/87.01 tff(7094,plain,
% 86.80/87.01 (node5(c_e_h_1, c_j, s4, s5) | node6(c_e_h_1, c_j, s4, s5)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7093, 881, 1432])).
% 86.80/87.01 tff(7095,plain,
% 86.80/87.01 (node6(c_e_h_1, c_j, s4, s5)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7094, 7087])).
% 86.80/87.01 tff(7096,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5)))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7097,plain,
% 86.80/87.01 (((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5)))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7098,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5))))),
% 86.80/87.01 inference(monotonicity,[status(thm)],[7097])).
% 86.80/87.01 tff(7099,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5)))),
% 86.80/87.01 inference(transitivity,[status(thm)],[7098, 7096])).
% 86.80/87.01 tff(7100,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 86.80/87.01 inference(quant_inst,[status(thm)],[])).
% 86.80/87.01 tff(7101,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5))),
% 86.80/87.01 inference(modus_ponens,[status(thm)],[7100, 7099])).
% 86.80/87.01 tff(7102,plain,
% 86.80/87.01 ($false),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7101, 899, 7039, 7077, 7095])).
% 86.80/87.01 tff(7103,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 86.80/87.01 tff(7104,plain,
% 86.80/87.01 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7103, 7075])).
% 86.80/87.01 tff(7105,plain,
% 86.80/87.01 (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7104, 7039, 7038])).
% 86.80/87.01 tff(7106,plain,
% 86.80/87.01 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7107,plain,
% 86.80/87.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))),
% 86.80/87.01 inference(quant_inst,[status(thm)],[])).
% 86.80/87.01 tff(7108,plain,
% 86.80/87.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5)),
% 86.80/87.01 inference(modus_ponens,[status(thm)],[7107, 7106])).
% 86.80/87.01 tff(7109,plain,
% 86.80/87.01 (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[7108, 309, 7105])).
% 86.80/87.01 tff(7110,plain,
% 86.80/87.01 (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[6606, 309, 7039])).
% 86.80/87.01 tff(7111,plain,
% 86.80/87.01 (~m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 86.80/87.01 inference(unit_resolution,[status(thm)],[6694, 7110])).
% 86.80/87.01 tff(7112,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s5)), introduced(assumption)).
% 86.80/87.01 tff(7113,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s6)), introduced(assumption)).
% 86.80/87.01 tff(7114,assumption,(node18(c_e_h_1, c_h, s5, s6)), introduced(assumption)).
% 86.80/87.01 tff(7115,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node18(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node18(c_e_h_1, c_h, s5, s6)))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7116,plain,
% 86.80/87.01 (((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node18(c_e_h_1, c_h, s5, s6)))),
% 86.80/87.01 inference(rewrite,[status(thm)],[])).
% 86.80/87.01 tff(7117,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node18(c_e_h_1, c_h, s5, s6))))),
% 86.80/87.01 inference(monotonicity,[status(thm)],[7116])).
% 86.80/87.01 tff(7118,plain,
% 86.80/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node18(c_e_h_1, c_h, s5, s6)))),
% 86.80/87.01 inference(transitivity,[status(thm)],[7117, 7115])).
% 86.80/87.01 tff(7119,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)))),
% 86.80/87.01 inference(quant_inst,[status(thm)],[])).
% 86.80/87.01 tff(7120,plain,
% 86.80/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node18(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(modus_ponens,[status(thm)],[7119, 7118])).
% 86.82/87.01 tff(7121,plain,
% 86.82/87.01 ($false),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7120, 124, 7112, 7113, 7114])).
% 86.82/87.01 tff(7122,plain,((~node18(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 86.82/87.01 tff(7123,plain,
% 86.82/87.01 (~node18(c_e_h_1, c_h, s5, s6)),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7122, 7113, 7112])).
% 86.82/87.01 tff(7124,plain,
% 86.82/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7125,plain,
% 86.82/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(quant_inst,[status(thm)],[])).
% 86.82/87.01 tff(7126,plain,
% 86.82/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_h, s5, s6)),
% 86.82/87.01 inference(modus_ponens,[status(thm)],[7125, 7124])).
% 86.82/87.01 tff(7127,plain,
% 86.82/87.01 (node19(c_e_h_1, c_h, s5, s6)),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7126, 141, 1499])).
% 86.82/87.01 tff(7128,plain,
% 86.82/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7129,plain,
% 86.82/87.01 ((node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6))) <=> (node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7130,plain,
% 86.82/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6)))),
% 86.82/87.01 inference(monotonicity,[status(thm)],[7129])).
% 86.82/87.01 tff(7131,plain,
% 86.82/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(transitivity,[status(thm)],[7130, 7128])).
% 86.82/87.01 tff(7132,plain,
% 86.82/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))),
% 86.82/87.01 inference(quant_inst,[status(thm)],[])).
% 86.82/87.01 tff(7133,plain,
% 86.82/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6)),
% 86.82/87.01 inference(modus_ponens,[status(thm)],[7132, 7131])).
% 86.82/87.01 tff(7134,plain,
% 86.82/87.01 (node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6)),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7133, 156, 7127])).
% 86.82/87.01 tff(7135,plain,
% 86.82/87.01 (node17(c_e_h_1, c_h, s5)),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7134, 7123])).
% 86.82/87.01 tff(7136,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s5)), introduced(assumption)).
% 86.82/87.01 tff(7137,plain,
% 86.82/87.01 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7138,plain,
% 86.82/87.01 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7139,plain,
% 86.82/87.01 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5))))),
% 86.82/87.01 inference(monotonicity,[status(thm)],[7138])).
% 86.82/87.01 tff(7140,plain,
% 86.82/87.01 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)))),
% 86.82/87.01 inference(transitivity,[status(thm)],[7139, 7137])).
% 86.82/87.01 tff(7141,plain,
% 86.82/87.01 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)))),
% 86.82/87.01 inference(quant_inst,[status(thm)],[])).
% 86.82/87.01 tff(7142,plain,
% 86.82/87.01 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5))),
% 86.82/87.01 inference(modus_ponens,[status(thm)],[7141, 7140])).
% 86.82/87.01 tff(7143,plain,
% 86.82/87.01 ((~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5))),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7142, 209, 7136])).
% 86.82/87.01 tff(7144,plain,
% 86.82/87.01 (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7143, 7135])).
% 86.82/87.01 tff(7145,assumption,(node15(c_e_h_1, c_h, s5, s6)), introduced(assumption)).
% 86.82/87.01 tff(7146,plain,
% 86.82/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7147,plain,
% 86.82/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 86.82/87.01 inference(quant_inst,[status(thm)],[])).
% 86.82/87.01 tff(7148,plain,
% 86.82/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 86.82/87.01 inference(modus_ponens,[status(thm)],[7147, 7146])).
% 86.82/87.01 tff(7149,plain,
% 86.82/87.01 ($false),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7148, 173, 7112, 7113, 7145])).
% 86.82/87.01 tff(7150,plain,((~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 86.82/87.01 tff(7151,plain,
% 86.82/87.01 (~node15(c_e_h_1, c_h, s5, s6)),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7150, 7113, 7112])).
% 86.82/87.01 tff(7152,plain,
% 86.82/87.01 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7153,plain,
% 86.82/87.01 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 86.82/87.01 inference(quant_inst,[status(thm)],[])).
% 86.82/87.01 tff(7154,plain,
% 86.82/87.01 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s5)),
% 86.82/87.01 inference(modus_ponens,[status(thm)],[7153, 7152])).
% 86.82/87.01 tff(7155,plain,
% 86.82/87.01 ((~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5)),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7154, 228, 7136])).
% 86.82/87.01 tff(7156,plain,
% 86.82/87.01 (~node16(c_e_h_1, c_h, s5)),
% 86.82/87.01 inference(unit_resolution,[status(thm)],[7155, 7144])).
% 86.82/87.01 tff(7157,plain,
% 86.82/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7158,plain,
% 86.82/87.01 ((node16(c_e_h_1, c_h, s5) | node14(c_e_h_1, c_h, s5, s6) | node15(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6))) <=> (node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(rewrite,[status(thm)],[])).
% 86.82/87.01 tff(7159,plain,
% 86.82/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | node14(c_e_h_1, c_h, s5, s6) | node15(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6)))),
% 86.82/87.01 inference(monotonicity,[status(thm)],[7158])).
% 86.82/87.01 tff(7160,plain,
% 86.82/87.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | node14(c_e_h_1, c_h, s5, s6) | node15(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6))),
% 86.82/87.01 inference(transitivity,[status(thm)],[7159, 7157])).
% 86.82/87.01 tff(7161,plain,
% 86.82/87.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | node14(c_e_h_1, c_h, s5, s6) | node15(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))),
% 86.82/87.01 inference(quant_inst,[status(thm)],[])).
% 86.82/87.01 tff(7162,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6)),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7161, 7160])).
% 86.82/87.02 tff(7163,plain,
% 86.82/87.02 (node16(c_e_h_1, c_h, s5) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7162, 189, 7127])).
% 86.82/87.02 tff(7164,plain,
% 86.82/87.02 (node14(c_e_h_1, c_h, s5, s6)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7163, 7156, 7151])).
% 86.82/87.02 tff(7165,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7166,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7167,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7166, 7165])).
% 86.82/87.02 tff(7168,plain,
% 86.82/87.02 ($false),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7167, 283, 7113, 7164, 7144])).
% 86.82/87.02 tff(7169,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | m_c_h_element_v_out(c_e_h_1, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 86.82/87.02 tff(7170,plain,
% 86.82/87.02 (~m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7169, 7111, 7109])).
% 86.82/87.02 tff(7171,plain,
% 86.82/87.02 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7172,plain,
% 86.82/87.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7173,plain,
% 86.82/87.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7172, 7171])).
% 86.82/87.02 tff(7174,plain,
% 86.82/87.02 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7173, 23, 7170])).
% 86.82/87.02 tff(7175,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s7)), introduced(assumption)).
% 86.82/87.02 tff(7176,plain,
% 86.82/87.02 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[6698, 23, 7111])).
% 86.82/87.02 tff(7177,plain,
% 86.82/87.02 (~node20(c_e_h_1, c_i, s5)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[6706, 7176])).
% 86.82/87.02 tff(7178,plain,
% 86.82/87.02 (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[6727, 7177])).
% 86.82/87.02 tff(7179,assumption,(~node20(c_e_h_1, c_i, s6)), introduced(assumption)).
% 86.82/87.02 tff(7180,assumption,(node21(c_e_h_1, c_i, s6, s7)), introduced(assumption)).
% 86.82/87.02 tff(7181,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | node20(c_e_h_1, c_i, s6) | (~node21(c_e_h_1, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | node20(c_e_h_1, c_i, s6) | (~node21(c_e_h_1, c_i, s6, s7)))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7182,plain,
% 86.82/87.02 ((node20(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node21(c_e_h_1, c_i, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | node20(c_e_h_1, c_i, s6) | (~node21(c_e_h_1, c_i, s6, s7)))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7183,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node21(c_e_h_1, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | node20(c_e_h_1, c_i, s6) | (~node21(c_e_h_1, c_i, s6, s7))))),
% 86.82/87.02 inference(monotonicity,[status(thm)],[7182])).
% 86.82/87.02 tff(7184,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node21(c_e_h_1, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | node20(c_e_h_1, c_i, s6) | (~node21(c_e_h_1, c_i, s6, s7)))),
% 86.82/87.02 inference(transitivity,[status(thm)],[7183, 7181])).
% 86.82/87.02 tff(7185,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node21(c_e_h_1, c_i, s6, s7)))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7186,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | node20(c_e_h_1, c_i, s6) | (~node21(c_e_h_1, c_i, s6, s7))),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7185, 7184])).
% 86.82/87.02 tff(7187,plain,
% 86.82/87.02 ($false),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7186, 51, 7180, 7175, 7179])).
% 86.82/87.02 tff(7188,plain,((~node21(c_e_h_1, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | node20(c_e_h_1, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 86.82/87.02 tff(7189,plain,
% 86.82/87.02 (~node21(c_e_h_1, c_i, s6, s7)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7188, 7175, 7179])).
% 86.82/87.02 tff(7190,assumption,(node22(c_e_h_1, c_i, s6, s7)), introduced(assumption)).
% 86.82/87.02 tff(7191,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7192,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7193,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7192, 7191])).
% 86.82/87.02 tff(7194,plain,
% 86.82/87.02 ($false),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7193, 107, 6730, 7190, 7175])).
% 86.82/87.02 tff(7195,plain,((~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7))), inference(lemma,lemma(discharge,[]))).
% 86.82/87.02 tff(7196,plain,
% 86.82/87.02 (~node22(c_e_h_1, c_i, s6, s7)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7195, 7175, 6730])).
% 86.82/87.02 tff(7197,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7198,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7199,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7)),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7198, 7197])).
% 86.82/87.02 tff(7200,plain,
% 86.82/87.02 (node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7199, 81, 1552])).
% 86.82/87.02 tff(7201,plain,
% 86.82/87.02 ($false),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7200, 7196, 7189])).
% 86.82/87.02 tff(7202,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6) | node20(c_e_h_1, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 86.82/87.02 tff(7203,plain,
% 86.82/87.02 (node20(c_e_h_1, c_i, s6)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7202, 7178, 7175])).
% 86.82/87.02 tff(7204,plain,
% 86.82/87.02 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s6))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7205,plain,
% 86.82/87.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s6))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7206,plain,
% 86.82/87.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s6)),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7205, 7204])).
% 86.82/87.02 tff(7207,plain,
% 86.82/87.02 ($false),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7206, 37, 7203, 7174])).
% 86.82/87.02 tff(7208,plain,(m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 86.82/87.02 tff(7209,plain,
% 86.82/87.02 (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7208, 6603, 7037])).
% 86.82/87.02 tff(7210,plain,
% 86.82/87.02 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7211,plain,
% 86.82/87.02 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7212,plain,
% 86.82/87.02 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7211, 7210])).
% 86.82/87.02 tff(7213,plain,
% 86.82/87.02 (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7212, 365, 7209])).
% 86.82/87.02 tff(7214,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s7)), introduced(assumption)).
% 86.82/87.02 tff(7215,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s8)), introduced(assumption)).
% 86.82/87.02 tff(7216,assumption,(node18(c_e_h_1, c_e, s7, s8)), introduced(assumption)).
% 86.82/87.02 tff(7217,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8)))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7218,plain,
% 86.82/87.02 (((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~node18(c_e_h_1, c_e, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8)))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7219,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~node18(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8))))),
% 86.82/87.02 inference(monotonicity,[status(thm)],[7218])).
% 86.82/87.02 tff(7220,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~node18(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8)))),
% 86.82/87.02 inference(transitivity,[status(thm)],[7219, 7217])).
% 86.82/87.02 tff(7221,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~node18(c_e_h_1, c_e, s7, s8)))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7222,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8))),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7221, 7220])).
% 86.82/87.02 tff(7223,plain,
% 86.82/87.02 ($false),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7222, 124, 7215, 6805, 7216])).
% 86.82/87.02 tff(7224,plain,((~node18(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 86.82/87.02 tff(7225,plain,
% 86.82/87.02 (~node18(c_e_h_1, c_e, s7, s8)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7224, 6805, 7215])).
% 86.82/87.02 tff(7226,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_e, s7, s8))),
% 86.82/87.02 inference(rewrite,[status(thm)],[])).
% 86.82/87.02 tff(7227,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_e, s7, s8))),
% 86.82/87.02 inference(quant_inst,[status(thm)],[])).
% 86.82/87.02 tff(7228,plain,
% 86.82/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_e, s7, s8)),
% 86.82/87.02 inference(modus_ponens,[status(thm)],[7227, 7226])).
% 86.82/87.02 tff(7229,plain,
% 86.82/87.02 (node19(c_e_h_1, c_e, s7, s8)),
% 86.82/87.02 inference(unit_resolution,[status(thm)],[7228, 141, 2152])).
% 86.82/87.02 tff(7230,plain,
% 86.82/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s7) | (~node19(c_e_h_1, c_e, s7, s8)) | node18(c_e_h_1, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s7) | (~node19(c_e_h_1, c_e, s7, s8)) | node18(c_e_h_1, c_e, s7, s8))),
% 86.84/87.02 inference(rewrite,[status(thm)],[])).
% 86.84/87.02 tff(7231,plain,
% 86.84/87.02 ((node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8))) <=> (node17(c_e_h_1, c_e, s7) | (~node19(c_e_h_1, c_e, s7, s8)) | node18(c_e_h_1, c_e, s7, s8))),
% 86.84/87.02 inference(rewrite,[status(thm)],[])).
% 86.84/87.02 tff(7232,plain,
% 86.84/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s7) | (~node19(c_e_h_1, c_e, s7, s8)) | node18(c_e_h_1, c_e, s7, s8)))),
% 86.84/87.02 inference(monotonicity,[status(thm)],[7231])).
% 86.84/87.02 tff(7233,plain,
% 86.84/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s7) | (~node19(c_e_h_1, c_e, s7, s8)) | node18(c_e_h_1, c_e, s7, s8))),
% 86.84/87.02 inference(transitivity,[status(thm)],[7232, 7230])).
% 86.84/87.02 tff(7234,plain,
% 86.84/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))),
% 86.84/87.02 inference(quant_inst,[status(thm)],[])).
% 86.84/87.02 tff(7235,plain,
% 86.84/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s7) | (~node19(c_e_h_1, c_e, s7, s8)) | node18(c_e_h_1, c_e, s7, s8)),
% 86.84/87.02 inference(modus_ponens,[status(thm)],[7234, 7233])).
% 86.84/87.02 tff(7236,plain,
% 86.84/87.02 (node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7235, 156, 7229])).
% 86.84/87.02 tff(7237,plain,
% 86.84/87.02 (node17(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7236, 7225])).
% 86.84/87.02 tff(7238,plain,
% 86.84/87.02 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))),
% 86.84/87.02 inference(rewrite,[status(thm)],[])).
% 86.84/87.02 tff(7239,plain,
% 86.84/87.02 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))),
% 86.84/87.02 inference(rewrite,[status(thm)],[])).
% 86.84/87.02 tff(7240,plain,
% 86.84/87.02 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7))))),
% 86.84/87.02 inference(monotonicity,[status(thm)],[7239])).
% 86.84/87.02 tff(7241,plain,
% 86.84/87.02 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))),
% 86.84/87.02 inference(transitivity,[status(thm)],[7240, 7238])).
% 86.84/87.02 tff(7242,plain,
% 86.84/87.02 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))),
% 86.84/87.02 inference(quant_inst,[status(thm)],[])).
% 86.84/87.02 tff(7243,plain,
% 86.84/87.02 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7))),
% 86.84/87.02 inference(modus_ponens,[status(thm)],[7242, 7241])).
% 86.84/87.02 tff(7244,plain,
% 86.84/87.02 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7))),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7243, 209, 7214])).
% 86.84/87.02 tff(7245,plain,
% 86.84/87.02 (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7244, 7237])).
% 86.84/87.02 tff(7246,assumption,(node15(c_e_h_1, c_e, s7, s8)), introduced(assumption)).
% 86.84/87.02 tff(7247,plain,
% 86.84/87.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 86.84/87.02 inference(rewrite,[status(thm)],[])).
% 86.84/87.02 tff(7248,plain,
% 86.84/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 86.84/87.02 inference(quant_inst,[status(thm)],[])).
% 86.84/87.02 tff(7249,plain,
% 86.84/87.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(modus_ponens,[status(thm)],[7248, 7247])).
% 86.84/87.02 tff(7250,plain,
% 86.84/87.02 ($false),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7249, 173, 7215, 6805, 7246])).
% 86.84/87.02 tff(7251,plain,((~node15(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.02 tff(7252,plain,
% 86.84/87.02 (~node15(c_e_h_1, c_e, s7, s8)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7251, 6805, 7215])).
% 86.84/87.02 tff(7253,assumption,(node17(c_e_h_1, c_e, s7)), introduced(assumption)).
% 86.84/87.02 tff(7254,assumption,(node16(c_e_h_1, c_e, s7)), introduced(assumption)).
% 86.84/87.02 tff(7255,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s7)), introduced(assumption)).
% 86.84/87.02 tff(7256,plain,
% 86.84/87.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))),
% 86.84/87.02 inference(rewrite,[status(thm)],[])).
% 86.84/87.02 tff(7257,plain,
% 86.84/87.02 ((m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))),
% 86.84/87.02 inference(rewrite,[status(thm)],[])).
% 86.84/87.02 tff(7258,plain,
% 86.84/87.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7))))),
% 86.84/87.02 inference(monotonicity,[status(thm)],[7257])).
% 86.84/87.02 tff(7259,plain,
% 86.84/87.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))),
% 86.84/87.02 inference(transitivity,[status(thm)],[7258, 7256])).
% 86.84/87.02 tff(7260,plain,
% 86.84/87.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))),
% 86.84/87.02 inference(quant_inst,[status(thm)],[])).
% 86.84/87.02 tff(7261,plain,
% 86.84/87.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7))),
% 86.84/87.02 inference(modus_ponens,[status(thm)],[7260, 7259])).
% 86.84/87.02 tff(7262,plain,
% 86.84/87.02 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7261, 245, 7253])).
% 86.84/87.02 tff(7263,plain,
% 86.84/87.02 (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7262, 7255])).
% 86.84/87.02 tff(7264,plain,
% 86.84/87.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7))),
% 86.84/87.02 inference(rewrite,[status(thm)],[])).
% 86.84/87.02 tff(7265,plain,
% 86.84/87.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7))),
% 86.84/87.02 inference(quant_inst,[status(thm)],[])).
% 86.84/87.02 tff(7266,plain,
% 86.84/87.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(modus_ponens,[status(thm)],[7265, 7264])).
% 86.84/87.02 tff(7267,plain,
% 86.84/87.02 (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7266, 228, 7254])).
% 86.84/87.02 tff(7268,plain,
% 86.84/87.02 ($false),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7267, 7263, 7255])).
% 86.84/87.02 tff(7269,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node16(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.02 tff(7270,plain,
% 86.84/87.02 (m_c_h_element_v_in1(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7269, 7254, 7253])).
% 86.84/87.02 tff(7271,plain,
% 86.84/87.02 (m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7))),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7243, 209, 7253])).
% 86.84/87.02 tff(7272,plain,
% 86.84/87.02 (m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 86.84/87.02 inference(unit_resolution,[status(thm)],[7271, 7270])).
% 86.84/87.02 tff(7273,plain,
% 86.84/87.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7274,plain,
% 86.84/87.03 (((~node16(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7275,plain,
% 86.84/87.03 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7))))),
% 86.84/87.03 inference(monotonicity,[status(thm)],[7274])).
% 86.84/87.03 tff(7276,plain,
% 86.84/87.03 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7)))),
% 86.84/87.03 inference(transitivity,[status(thm)],[7275, 7273])).
% 86.84/87.03 tff(7277,plain,
% 86.84/87.03 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7278,plain,
% 86.84/87.03 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7))),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7277, 7276])).
% 86.84/87.03 tff(7279,plain,
% 86.84/87.03 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7))),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7278, 263, 7254])).
% 86.84/87.03 tff(7280,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7279, 7272, 7270])).
% 86.84/87.03 tff(7281,plain,((~node16(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7282,plain,
% 86.84/87.03 (~node16(c_e_h_1, c_e, s7)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7281, 7237])).
% 86.84/87.03 tff(7283,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7284,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7285,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8))),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7284, 7283])).
% 86.84/87.03 tff(7286,plain,
% 86.84/87.03 (node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7285, 189, 7229])).
% 86.84/87.03 tff(7287,plain,
% 86.84/87.03 (node14(c_e_h_1, c_e, s7, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7286, 7282, 7252])).
% 86.84/87.03 tff(7288,assumption,(node14(c_e_h_1, c_e, s7, s8)), introduced(assumption)).
% 86.84/87.03 tff(7289,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7290,plain,
% 86.84/87.03 (((~node14(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7291,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8))))),
% 86.84/87.03 inference(monotonicity,[status(thm)],[7290])).
% 86.84/87.03 tff(7292,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))),
% 86.84/87.03 inference(transitivity,[status(thm)],[7291, 7289])).
% 86.84/87.03 tff(7293,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7294,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7293, 7292])).
% 86.84/87.03 tff(7295,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7294, 283, 7215, 7288, 7255])).
% 86.84/87.03 tff(7296,plain,((~node14(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7297,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7296, 7287, 7245, 7215])).
% 86.84/87.03 tff(7298,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7299,plain,
% 86.84/87.03 (~m_c_h_element_v_out(c_e_h_1, c_e, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7298, 6805, 7214])).
% 86.84/87.03 tff(7300,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)), introduced(assumption)).
% 86.84/87.03 tff(7301,plain,
% 86.84/87.03 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[6810, 6805])).
% 86.84/87.03 tff(7302,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)), introduced(assumption)).
% 86.84/87.03 tff(7303,plain,
% 86.84/87.03 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[6815, 1142, 6268])).
% 86.84/87.03 tff(7304,plain,
% 86.84/87.03 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[6848, 6832, 7303, 6819])).
% 86.84/87.03 tff(7305,assumption,(node11(c_e_h_1, c_n, s8, s9)), introduced(assumption)).
% 86.84/87.03 tff(7306,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)), introduced(assumption)).
% 86.84/87.03 tff(7307,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | (~node11(c_e_h_1, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | (~node11(c_e_h_1, c_n, s8, s9)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7308,plain,
% 86.84/87.03 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | (~node11(c_e_h_1, c_n, s8, s9)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7309,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | (~node11(c_e_h_1, c_n, s8, s9))))),
% 86.84/87.03 inference(monotonicity,[status(thm)],[7308])).
% 86.84/87.03 tff(7310,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | (~node11(c_e_h_1, c_n, s8, s9)))),
% 86.84/87.03 inference(transitivity,[status(thm)],[7309, 7307])).
% 86.84/87.03 tff(7311,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7312,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | (~node11(c_e_h_1, c_n, s8, s9))),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7311, 7310])).
% 86.84/87.03 tff(7313,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7312, 1161, 7300, 7306, 7305])).
% 86.84/87.03 tff(7314,plain,((~node11(c_e_h_1, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7315,plain,
% 86.84/87.03 (~node11(c_e_h_1, c_n, s8, s9)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7314, 7304, 7300])).
% 86.84/87.03 tff(7316,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7317,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7318,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9)),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7317, 7316])).
% 86.84/87.03 tff(7319,plain,
% 86.84/87.03 (node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7318, 1092, 2636])).
% 86.84/87.03 tff(7320,plain,
% 86.84/87.03 (node10(c_e_h_1, c_n, s8, s9)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7319, 7315])).
% 86.84/87.03 tff(7321,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)), introduced(assumption)).
% 86.84/87.03 tff(7322,assumption,(node10(c_e_h_1, c_n, s8, s9)), introduced(assumption)).
% 86.84/87.03 tff(7323,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7324,plain,
% 86.84/87.03 (((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7325,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9))))),
% 86.84/87.03 inference(monotonicity,[status(thm)],[7324])).
% 86.84/87.03 tff(7326,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9)))),
% 86.84/87.03 inference(transitivity,[status(thm)],[7325, 7323])).
% 86.84/87.03 tff(7327,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7328,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9))),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7327, 7326])).
% 86.84/87.03 tff(7329,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7328, 1191, 7300, 7322, 7321, 7302])).
% 86.84/87.03 tff(7330,plain,((~node10(c_e_h_1, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7331,plain,
% 86.84/87.03 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7330, 7320, 7302, 7300])).
% 86.84/87.03 tff(7332,plain,
% 86.84/87.03 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7333,plain,
% 86.84/87.03 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7334,plain,
% 86.84/87.03 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7333, 7332])).
% 86.84/87.03 tff(7335,plain,
% 86.84/87.03 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7334, 1142, 7331])).
% 86.84/87.03 tff(7336,plain,
% 86.84/87.03 (~node11(c_e_h_1, c_m, s7, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[6273, 7335, 6268])).
% 86.84/87.03 tff(7337,plain,
% 86.84/87.03 (node10(c_e_h_1, c_m, s7, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[6277, 1092, 2152, 7336])).
% 86.84/87.03 tff(7338,plain,
% 86.84/87.03 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[6262, 1048, 6832])).
% 86.84/87.03 tff(7339,plain,
% 86.84/87.03 (~node9(c_e_h_1, c_m, s7)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[6266, 1062, 7338])).
% 86.84/87.03 tff(7340,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[6282, 1076, 7335, 7339, 7337])).
% 86.84/87.03 tff(7341,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7342,plain,
% 86.84/87.03 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7341, 7301, 6268, 6832, 7300])).
% 86.84/87.03 tff(7343,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)), introduced(assumption)).
% 86.84/87.03 tff(7344,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s8)), introduced(assumption)).
% 86.84/87.03 tff(7345,plain,
% 86.84/87.03 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7346,plain,
% 86.84/87.03 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7347,plain,
% 86.84/87.03 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8)),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7346, 7345])).
% 86.84/87.03 tff(7348,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7347, 976, 7344, 7343])).
% 86.84/87.03 tff(7349,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7350,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7349, 7342, 7299])).
% 86.84/87.03 tff(7351,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7352,plain,
% 86.84/87.03 (m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7351, 5776])).
% 86.84/87.03 tff(7353,plain,
% 86.84/87.03 (m_c_h_element_v_out(c_e_h_1, c_e, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7352, 6259])).
% 86.84/87.03 tff(7354,plain,
% 86.84/87.03 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7353, 6803, 7213])).
% 86.84/87.03 tff(7355,plain,
% 86.84/87.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7356,plain,
% 86.84/87.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7357,plain,
% 86.84/87.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7356, 7355])).
% 86.84/87.03 tff(7358,plain,
% 86.84/87.03 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7357, 1048, 7354])).
% 86.84/87.03 tff(7359,plain,
% 86.84/87.03 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7360,plain,
% 86.84/87.03 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7361,plain,
% 86.84/87.03 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7360, 7359])).
% 86.84/87.03 tff(7362,plain,
% 86.84/87.03 (~node9(c_e_h_1, c_m, s9)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7361, 1062, 7358])).
% 86.84/87.03 tff(7363,assumption,(~node9(c_e_h_1, c_m, s9)), introduced(assumption)).
% 86.84/87.03 tff(7364,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)), introduced(assumption)).
% 86.84/87.03 tff(7365,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)), introduced(assumption)).
% 86.84/87.03 tff(7366,assumption,(node11(c_e_h_1, c_m, s9, s10)), introduced(assumption)).
% 86.84/87.03 tff(7367,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7368,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7369,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7368, 7367])).
% 86.84/87.03 tff(7370,plain,
% 86.84/87.03 ($false),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7369, 1130, 7365, 7364, 7366])).
% 86.84/87.03 tff(7371,plain,((~node11(c_e_h_1, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.03 tff(7372,plain,
% 86.84/87.03 (~node11(c_e_h_1, c_m, s9, s10)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7371, 7365, 7364])).
% 86.84/87.03 tff(7373,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7374,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10))),
% 86.84/87.03 inference(quant_inst,[status(thm)],[])).
% 86.84/87.03 tff(7375,plain,
% 86.84/87.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10)),
% 86.84/87.03 inference(modus_ponens,[status(thm)],[7374, 7373])).
% 86.84/87.03 tff(7376,plain,
% 86.84/87.03 (node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7375, 1092, 3175])).
% 86.84/87.03 tff(7377,plain,
% 86.84/87.03 (node10(c_e_h_1, c_m, s9, s10)),
% 86.84/87.03 inference(unit_resolution,[status(thm)],[7376, 7372])).
% 86.84/87.03 tff(7378,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7379,plain,
% 86.84/87.03 ((node9(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node10(c_e_h_1, c_m, s9, s10))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10)))),
% 86.84/87.03 inference(rewrite,[status(thm)],[])).
% 86.84/87.03 tff(7380,plain,
% 86.84/87.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node10(c_e_h_1, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10))))),
% 86.84/87.04 inference(monotonicity,[status(thm)],[7379])).
% 86.84/87.04 tff(7381,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node10(c_e_h_1, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10)))),
% 86.84/87.04 inference(transitivity,[status(thm)],[7380, 7378])).
% 86.84/87.04 tff(7382,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node10(c_e_h_1, c_m, s9, s10)))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7383,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10))),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7382, 7381])).
% 86.84/87.04 tff(7384,plain,
% 86.84/87.04 ($false),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7383, 1076, 7365, 7377, 7363])).
% 86.84/87.04 tff(7385,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.04 tff(7386,plain,
% 86.84/87.04 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7385, 6887, 7362])).
% 86.84/87.04 tff(7387,plain,
% 86.84/87.04 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7388,plain,
% 86.84/87.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7389,plain,
% 86.84/87.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7388, 7387])).
% 86.84/87.04 tff(7390,plain,
% 86.84/87.04 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7389, 1521])).
% 86.84/87.04 tff(7391,plain,
% 86.84/87.04 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7390, 7386])).
% 86.84/87.04 tff(7392,plain,
% 86.84/87.04 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s10))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7393,plain,
% 86.84/87.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s10))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7394,plain,
% 86.84/87.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s10)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7393, 7392])).
% 86.84/87.04 tff(7395,plain,
% 86.84/87.04 (~node20(c_e_h_1, c_r, s10)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7394, 1535, 7391])).
% 86.84/87.04 tff(7396,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | node20(c_e_h_1, c_r, s10) | (~node21(c_e_h_1, c_r, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | node20(c_e_h_1, c_r, s10) | (~node21(c_e_h_1, c_r, s10, s11)))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7397,plain,
% 86.84/87.04 ((node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node21(c_e_h_1, c_r, s10, s11))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | node20(c_e_h_1, c_r, s10) | (~node21(c_e_h_1, c_r, s10, s11)))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7398,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node21(c_e_h_1, c_r, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | node20(c_e_h_1, c_r, s10) | (~node21(c_e_h_1, c_r, s10, s11))))),
% 86.84/87.04 inference(monotonicity,[status(thm)],[7397])).
% 86.84/87.04 tff(7399,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node21(c_e_h_1, c_r, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | node20(c_e_h_1, c_r, s10) | (~node21(c_e_h_1, c_r, s10, s11)))),
% 86.84/87.04 inference(transitivity,[status(thm)],[7398, 7396])).
% 86.84/87.04 tff(7400,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node21(c_e_h_1, c_r, s10, s11)))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7401,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | node20(c_e_h_1, c_r, s10) | (~node21(c_e_h_1, c_r, s10, s11))),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7400, 7399])).
% 86.84/87.04 tff(7402,plain,
% 86.84/87.04 ($false),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7401, 51, 6907, 7395, 6916])).
% 86.84/87.04 tff(7403,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.04 tff(7404,plain,
% 86.84/87.04 (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7403, 6905])).
% 86.84/87.04 tff(7405,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7406,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7407,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7406, 7405])).
% 86.84/87.04 tff(7408,plain,
% 86.84/87.04 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12))),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7407, 107, 7404])).
% 86.84/87.04 tff(7409,plain,
% 86.84/87.04 (~node22(c_e_h_1, c_r, s11, s12)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7408, 4500])).
% 86.84/87.04 tff(7410,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s6)), introduced(assumption)).
% 86.84/87.04 tff(7411,plain,
% 86.84/87.04 (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7104, 6603, 7037])).
% 86.84/87.04 tff(7412,assumption,(node6(c_e_h_1, c_j, s5, s6)), introduced(assumption)).
% 86.84/87.04 tff(7413,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s5)), introduced(assumption)).
% 86.84/87.04 tff(7414,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6)))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7415,plain,
% 86.84/87.04 (((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6)))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7416,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6))))),
% 86.84/87.04 inference(monotonicity,[status(thm)],[7415])).
% 86.84/87.04 tff(7417,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6)))),
% 86.84/87.04 inference(transitivity,[status(thm)],[7416, 7414])).
% 86.84/87.04 tff(7418,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7419,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6))),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7418, 7417])).
% 86.84/87.04 tff(7420,plain,
% 86.84/87.04 ($false),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7419, 899, 7413, 7410, 7412])).
% 86.84/87.04 tff(7421,plain,((~node6(c_e_h_1, c_j, s5, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.04 tff(7422,plain,
% 86.84/87.04 ((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6))),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7421, 7411])).
% 86.84/87.04 tff(7423,plain,
% 86.84/87.04 (~node6(c_e_h_1, c_j, s5, s6)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7422, 7410])).
% 86.84/87.04 tff(7424,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node5(c_e_h_1, c_j, s5, s6) | node6(c_e_h_1, c_j, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_1, c_j, s5, s6) | node6(c_e_h_1, c_j, s5, s6))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7425,plain,
% 86.84/87.04 ((node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6) | (~trans(s5, s6))) <=> ((~trans(s5, s6)) | node5(c_e_h_1, c_j, s5, s6) | node6(c_e_h_1, c_j, s5, s6))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7426,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node5(c_e_h_1, c_j, s5, s6) | node6(c_e_h_1, c_j, s5, s6)))),
% 86.84/87.04 inference(monotonicity,[status(thm)],[7425])).
% 86.84/87.04 tff(7427,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_1, c_j, s5, s6) | node6(c_e_h_1, c_j, s5, s6))),
% 86.84/87.04 inference(transitivity,[status(thm)],[7426, 7424])).
% 86.84/87.04 tff(7428,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6) | (~trans(s5, s6)))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7429,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_1, c_j, s5, s6) | node6(c_e_h_1, c_j, s5, s6)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7428, 7427])).
% 86.84/87.04 tff(7430,plain,
% 86.84/87.04 (node5(c_e_h_1, c_j, s5, s6) | node6(c_e_h_1, c_j, s5, s6)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7429, 881, 1499])).
% 86.84/87.04 tff(7431,plain,
% 86.84/87.04 (node5(c_e_h_1, c_j, s5, s6)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7430, 7423])).
% 86.84/87.04 tff(7432,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s5)), introduced(assumption)).
% 86.84/87.04 tff(7433,assumption,(node21(c_e_h_3, c_q, s4, s5)), introduced(assumption)).
% 86.84/87.04 tff(7434,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s0)), introduced(assumption)).
% 86.84/87.04 tff(7435,plain,
% 86.84/87.04 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7436,plain,
% 86.84/87.04 ($false),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7435, 94, 7434])).
% 86.84/87.04 tff(7437,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.04 tff(7438,plain,
% 86.84/87.04 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7439,plain,
% 86.84/87.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7440,plain,
% 86.84/87.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7439, 7438])).
% 86.84/87.04 tff(7441,plain,
% 86.84/87.04 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7440, 801, 7437])).
% 86.84/87.04 tff(7442,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s0)), introduced(assumption)).
% 86.84/87.04 tff(7443,plain,
% 86.84/87.04 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7444,plain,
% 86.84/87.04 ($false),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7443, 94, 7442])).
% 86.84/87.04 tff(7445,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.04 tff(7446,plain,
% 86.84/87.04 (m_cell_v_left(c_e_h_2, c_e_h_3) <=> m_cell_v_left(c_e_h_2, c_e_h_3)),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7447,axiom,(m_cell_v_left(c_e_h_2, c_e_h_3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_main_4')).
% 86.84/87.04 tff(7448,plain,
% 86.84/87.04 (m_cell_v_left(c_e_h_2, c_e_h_3)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7447, 7446])).
% 86.84/87.04 tff(7449,plain,
% 86.84/87.04 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s0))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7450,plain,
% 86.84/87.04 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s0))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7451,plain,
% 86.84/87.04 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s0)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7450, 7449])).
% 86.84/87.04 tff(7452,plain,
% 86.84/87.04 (node3(c_e_h_2, c_e_h_3, s0)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7451, 7448, 814])).
% 86.84/87.04 tff(7453,plain,
% 86.84/87.04 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s0)) | (~node3(c_e_h_2, c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s0)) | (~node3(c_e_h_2, c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7454,plain,
% 86.84/87.04 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s0)) | (~node3(c_e_h_2, c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7455,plain,
% 86.84/87.04 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s0)) | (~node3(c_e_h_2, c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7454, 7453])).
% 86.84/87.04 tff(7456,plain,
% 86.84/87.04 ((~m_cell_v_ack(c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7455, 836, 7452])).
% 86.84/87.04 tff(7457,plain,
% 86.84/87.04 (~m_cell_v_ack(c_e_h_3, s0)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7456, 7445])).
% 86.84/87.04 tff(7458,plain,
% 86.84/87.04 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)) | m_cell_v_ack(c_e_h_3, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)) | m_cell_v_ack(c_e_h_3, s0))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7459,plain,
% 86.84/87.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)) | m_cell_v_ack(c_e_h_3, s0))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7460,plain,
% 86.84/87.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)) | m_cell_v_ack(c_e_h_3, s0)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7459, 7458])).
% 86.84/87.04 tff(7461,plain,
% 86.84/87.04 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7460, 848, 7457])).
% 86.84/87.04 tff(7462,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s1)), introduced(assumption)).
% 86.84/87.04 tff(7463,assumption,(node6(c_e_h_3, c_j, s0, s1)), introduced(assumption)).
% 86.84/87.04 tff(7464,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s0)), introduced(assumption)).
% 86.84/87.04 tff(7465,plain,
% 86.84/87.04 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s0))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7466,plain,
% 86.84/87.04 ($false),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7465, 299, 7464])).
% 86.84/87.04 tff(7467,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.04 tff(7468,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~node6(c_e_h_3, c_j, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~node6(c_e_h_3, c_j, s0, s1)))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7469,plain,
% 86.84/87.04 (((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~node6(c_e_h_3, c_j, s0, s1)))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7470,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~node6(c_e_h_3, c_j, s0, s1))))),
% 86.84/87.04 inference(monotonicity,[status(thm)],[7469])).
% 86.84/87.04 tff(7471,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~node6(c_e_h_3, c_j, s0, s1)))),
% 86.84/87.04 inference(transitivity,[status(thm)],[7470, 7468])).
% 86.84/87.04 tff(7472,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7473,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~node6(c_e_h_3, c_j, s0, s1))),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7472, 7471])).
% 86.84/87.04 tff(7474,plain,
% 86.84/87.04 ($false),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7473, 899, 7462, 7467, 7463])).
% 86.84/87.04 tff(7475,plain,((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.04 tff(7476,plain,
% 86.84/87.04 (~node6(c_e_h_3, c_j, s0, s1)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7475, 7462])).
% 86.84/87.04 tff(7477,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_3, c_j, s0, s1) | node6(c_e_h_3, c_j, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_j, s0, s1) | node6(c_e_h_3, c_j, s0, s1))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7478,plain,
% 86.84/87.04 ((node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node5(c_e_h_3, c_j, s0, s1) | node6(c_e_h_3, c_j, s0, s1))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7479,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_3, c_j, s0, s1) | node6(c_e_h_3, c_j, s0, s1)))),
% 86.84/87.04 inference(monotonicity,[status(thm)],[7478])).
% 86.84/87.04 tff(7480,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_j, s0, s1) | node6(c_e_h_3, c_j, s0, s1))),
% 86.84/87.04 inference(transitivity,[status(thm)],[7479, 7477])).
% 86.84/87.04 tff(7481,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1) | (~trans(s0, s1)))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7482,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_j, s0, s1) | node6(c_e_h_3, c_j, s0, s1)),
% 86.84/87.04 inference(modus_ponens,[status(thm)],[7481, 7480])).
% 86.84/87.04 tff(7483,plain,
% 86.84/87.04 (node5(c_e_h_3, c_j, s0, s1) | node6(c_e_h_3, c_j, s0, s1)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7482, 881, 71])).
% 86.84/87.04 tff(7484,plain,
% 86.84/87.04 (node5(c_e_h_3, c_j, s0, s1)),
% 86.84/87.04 inference(unit_resolution,[status(thm)],[7483, 7476])).
% 86.84/87.04 tff(7485,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7486,plain,
% 86.84/87.04 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0))),
% 86.84/87.04 inference(rewrite,[status(thm)],[])).
% 86.84/87.04 tff(7487,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0)))),
% 86.84/87.04 inference(monotonicity,[status(thm)],[7486])).
% 86.84/87.04 tff(7488,plain,
% 86.84/87.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0))),
% 86.84/87.04 inference(transitivity,[status(thm)],[7487, 7485])).
% 86.84/87.04 tff(7489,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)))),
% 86.84/87.04 inference(quant_inst,[status(thm)],[])).
% 86.84/87.04 tff(7490,plain,
% 86.84/87.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7489, 7488])).
% 86.84/87.05 tff(7491,plain,
% 86.84/87.05 ($false),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7490, 862, 7462, 7484, 7461, 7441])).
% 86.84/87.05 tff(7492,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.05 tff(7493,plain,
% 86.84/87.05 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7494,plain,
% 86.84/87.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7495,plain,
% 86.84/87.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7494, 7493])).
% 86.84/87.05 tff(7496,plain,
% 86.84/87.05 (~m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7495, 309, 7492])).
% 86.84/87.05 tff(7497,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s2)), introduced(assumption)).
% 86.84/87.05 tff(7498,assumption,(node18(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 86.84/87.05 tff(7499,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s1)), introduced(assumption)).
% 86.84/87.05 tff(7500,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s0)), introduced(assumption)).
% 86.84/87.05 tff(7501,plain,
% 86.84/87.05 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7502,plain,
% 86.84/87.05 ($false),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7501, 13, 7500])).
% 86.84/87.05 tff(7503,plain,(~m_c_h_element_v_out(c_e_h_3, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.05 tff(7504,assumption,(node18(c_e_h_3, c_h, s0, s1)), introduced(assumption)).
% 86.84/87.05 tff(7505,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node18(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node18(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7506,plain,
% 86.84/87.05 (((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~node18(c_e_h_3, c_h, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node18(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7507,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~node18(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node18(c_e_h_3, c_h, s0, s1))))),
% 86.84/87.05 inference(monotonicity,[status(thm)],[7506])).
% 86.84/87.05 tff(7508,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~node18(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node18(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(transitivity,[status(thm)],[7507, 7505])).
% 86.84/87.05 tff(7509,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~node18(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7510,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node18(c_e_h_3, c_h, s0, s1))),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7509, 7508])).
% 86.84/87.05 tff(7511,plain,
% 86.84/87.05 ($false),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7510, 124, 7504, 7499, 7503])).
% 86.84/87.05 tff(7512,plain,((~node18(c_e_h_3, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.05 tff(7513,plain,
% 86.84/87.05 (~node18(c_e_h_3, c_h, s0, s1)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7512, 7499])).
% 86.84/87.05 tff(7514,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_h, s0, s1))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7515,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_h, s0, s1))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7516,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_h, s0, s1)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7515, 7514])).
% 86.84/87.05 tff(7517,plain,
% 86.84/87.05 (node19(c_e_h_3, c_h, s0, s1)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7516, 141, 71])).
% 86.84/87.05 tff(7518,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7519,plain,
% 86.84/87.05 ((node17(c_e_h_3, c_h, s0) | node18(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1))) <=> ((~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7520,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s0) | node18(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0)))),
% 86.84/87.05 inference(monotonicity,[status(thm)],[7519])).
% 86.84/87.05 tff(7521,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s0) | node18(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(transitivity,[status(thm)],[7520, 7518])).
% 86.84/87.05 tff(7522,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s0) | node18(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7523,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7522, 7521])).
% 86.84/87.05 tff(7524,plain,
% 86.84/87.05 (node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7523, 156, 7517])).
% 86.84/87.05 tff(7525,plain,
% 86.84/87.05 (node17(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7524, 7513])).
% 86.84/87.05 tff(7526,plain,
% 86.84/87.05 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7527,plain,
% 86.84/87.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7528,plain,
% 86.84/87.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7527, 7526])).
% 86.84/87.05 tff(7529,plain,
% 86.84/87.05 (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7528, 309, 7467])).
% 86.84/87.05 tff(7530,plain,
% 86.84/87.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7531,plain,
% 86.84/87.05 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7532,plain,
% 86.84/87.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0))))),
% 86.84/87.05 inference(monotonicity,[status(thm)],[7531])).
% 86.84/87.05 tff(7533,plain,
% 86.84/87.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0)))),
% 86.84/87.05 inference(transitivity,[status(thm)],[7532, 7530])).
% 86.84/87.05 tff(7534,plain,
% 86.84/87.05 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0)))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7535,plain,
% 86.84/87.05 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7534, 7533])).
% 86.84/87.05 tff(7536,plain,
% 86.84/87.05 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7535, 209, 7529])).
% 86.84/87.05 tff(7537,plain,
% 86.84/87.05 (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7536, 7525])).
% 86.84/87.05 tff(7538,plain,
% 86.84/87.05 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | m_c_h_element_v_in2(c_e_h_3, c_h, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | m_c_h_element_v_in2(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7539,plain,
% 86.84/87.05 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | m_c_h_element_v_in2(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7540,plain,
% 86.84/87.05 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | m_c_h_element_v_in2(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7539, 7538])).
% 86.84/87.05 tff(7541,plain,
% 86.84/87.05 ((~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7540, 228, 7529])).
% 86.84/87.05 tff(7542,plain,
% 86.84/87.05 (~node16(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7541, 7537])).
% 86.84/87.05 tff(7543,assumption,(node15(c_e_h_3, c_h, s0, s1)), introduced(assumption)).
% 86.84/87.05 tff(7544,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7545,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7546,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7545, 7544])).
% 86.84/87.05 tff(7547,plain,
% 86.84/87.05 ($false),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7546, 173, 7543, 7499, 7503])).
% 86.84/87.05 tff(7548,plain,((~node15(c_e_h_3, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.05 tff(7549,plain,
% 86.84/87.05 (~node15(c_e_h_3, c_h, s0, s1)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7548, 7499])).
% 86.84/87.05 tff(7550,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node15(c_e_h_3, c_h, s0, s1) | node16(c_e_h_3, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node15(c_e_h_3, c_h, s0, s1) | node16(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7551,plain,
% 86.84/87.05 ((node16(c_e_h_3, c_h, s0) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1))) <=> (node14(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node15(c_e_h_3, c_h, s0, s1) | node16(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7552,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s0) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node15(c_e_h_3, c_h, s0, s1) | node16(c_e_h_3, c_h, s0)))),
% 86.84/87.05 inference(monotonicity,[status(thm)],[7551])).
% 86.84/87.05 tff(7553,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s0) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node15(c_e_h_3, c_h, s0, s1) | node16(c_e_h_3, c_h, s0))),
% 86.84/87.05 inference(transitivity,[status(thm)],[7552, 7550])).
% 86.84/87.05 tff(7554,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s0) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7555,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node15(c_e_h_3, c_h, s0, s1) | node16(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7554, 7553])).
% 86.84/87.05 tff(7556,plain,
% 86.84/87.05 (node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | node16(c_e_h_3, c_h, s0)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7555, 189, 7517])).
% 86.84/87.05 tff(7557,plain,
% 86.84/87.05 (node14(c_e_h_3, c_h, s0, s1)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7556, 7549, 7542])).
% 86.84/87.05 tff(7558,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7559,plain,
% 86.84/87.05 (((~node14(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7560,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1))))),
% 86.84/87.05 inference(monotonicity,[status(thm)],[7559])).
% 86.84/87.05 tff(7561,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1)))),
% 86.84/87.05 inference(transitivity,[status(thm)],[7560, 7558])).
% 86.84/87.05 tff(7562,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7563,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1))),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7562, 7561])).
% 86.84/87.05 tff(7564,plain,
% 86.84/87.05 ($false),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7563, 283, 7557, 7499, 7537])).
% 86.84/87.05 tff(7565,plain,(~m_c_h_element_v_out(c_e_h_3, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.05 tff(7566,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7567,plain,
% 86.84/87.05 (((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7568,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2))))),
% 86.84/87.05 inference(monotonicity,[status(thm)],[7567])).
% 86.84/87.05 tff(7569,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.05 inference(transitivity,[status(thm)],[7568, 7566])).
% 86.84/87.05 tff(7570,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7571,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2))),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7570, 7569])).
% 86.84/87.05 tff(7572,plain,
% 86.84/87.05 ($false),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7571, 124, 7497, 7565, 7498])).
% 86.84/87.05 tff(7573,plain,((~node18(c_e_h_3, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.05 tff(7574,plain,
% 86.84/87.05 (~node18(c_e_h_3, c_h, s1, s2)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7573, 7497])).
% 86.84/87.05 tff(7575,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7576,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7577,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2)),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7576, 7575])).
% 86.84/87.05 tff(7578,plain,
% 86.84/87.05 (node19(c_e_h_3, c_h, s1, s2)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7577, 141, 344])).
% 86.84/87.05 tff(7579,plain,
% 86.84/87.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7580,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.05 inference(quant_inst,[status(thm)],[])).
% 86.84/87.05 tff(7581,plain,
% 86.84/87.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2))),
% 86.84/87.05 inference(modus_ponens,[status(thm)],[7580, 7579])).
% 86.84/87.05 tff(7582,plain,
% 86.84/87.05 (node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7581, 156, 7578])).
% 86.84/87.05 tff(7583,plain,
% 86.84/87.05 (node17(c_e_h_3, c_h, s1)),
% 86.84/87.05 inference(unit_resolution,[status(thm)],[7582, 7574])).
% 86.84/87.05 tff(7584,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s1)), introduced(assumption)).
% 86.84/87.05 tff(7585,plain,
% 86.84/87.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7586,plain,
% 86.84/87.05 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~node17(c_e_h_3, c_h, s1))) <=> ((~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 86.84/87.05 inference(rewrite,[status(thm)],[])).
% 86.84/87.05 tff(7587,plain,
% 86.84/87.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~node17(c_e_h_3, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)))),
% 86.84/87.05 inference(monotonicity,[status(thm)],[7586])).
% 86.84/87.05 tff(7588,plain,
% 86.84/87.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~node17(c_e_h_3, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 86.84/87.06 inference(transitivity,[status(thm)],[7587, 7585])).
% 86.84/87.06 tff(7589,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~node17(c_e_h_3, c_h, s1)))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7590,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7589, 7588])).
% 86.84/87.06 tff(7591,plain,
% 86.84/87.06 ((~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1))),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7590, 209, 7584])).
% 86.84/87.06 tff(7592,plain,
% 86.84/87.06 (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7591, 7583])).
% 86.84/87.06 tff(7593,assumption,(node15(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 86.84/87.06 tff(7594,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7595,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7596,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7595, 7594])).
% 86.84/87.06 tff(7597,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7596, 173, 7497, 7565, 7593])).
% 86.84/87.06 tff(7598,plain,((~node15(c_e_h_3, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7599,plain,
% 86.84/87.06 (~node15(c_e_h_3, c_h, s1, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7598, 7497])).
% 86.84/87.06 tff(7600,plain,
% 86.84/87.06 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7601,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7602,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7601, 7600])).
% 86.84/87.06 tff(7603,plain,
% 86.84/87.06 ((~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7602, 228, 7584])).
% 86.84/87.06 tff(7604,plain,
% 86.84/87.06 (~node16(c_e_h_3, c_h, s1)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7603, 7592])).
% 86.84/87.06 tff(7605,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s1) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7606,plain,
% 86.84/87.06 ((node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2))) <=> (node16(c_e_h_3, c_h, s1) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7607,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.06 inference(monotonicity,[status(thm)],[7606])).
% 86.84/87.06 tff(7608,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s1) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2))),
% 86.84/87.06 inference(transitivity,[status(thm)],[7607, 7605])).
% 86.84/87.06 tff(7609,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7610,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s1) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7609, 7608])).
% 86.84/87.06 tff(7611,plain,
% 86.84/87.06 (node16(c_e_h_3, c_h, s1) | node15(c_e_h_3, c_h, s1, s2) | node14(c_e_h_3, c_h, s1, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7610, 189, 7578])).
% 86.84/87.06 tff(7612,plain,
% 86.84/87.06 (node14(c_e_h_3, c_h, s1, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7611, 7604, 7599])).
% 86.84/87.06 tff(7613,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node14(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node14(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7614,plain,
% 86.84/87.06 (((~node14(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node14(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7615,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node14(c_e_h_3, c_h, s1, s2))))),
% 86.84/87.06 inference(monotonicity,[status(thm)],[7614])).
% 86.84/87.06 tff(7616,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node14(c_e_h_3, c_h, s1, s2)))),
% 86.84/87.06 inference(transitivity,[status(thm)],[7615, 7613])).
% 86.84/87.06 tff(7617,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7618,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node14(c_e_h_3, c_h, s1, s2))),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7617, 7616])).
% 86.84/87.06 tff(7619,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7618, 283, 7497, 7612, 7592])).
% 86.84/87.06 tff(7620,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7621,plain,
% 86.84/87.06 (~m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7620, 7496])).
% 86.84/87.06 tff(7622,plain,
% 86.84/87.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7623,plain,
% 86.84/87.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7624,plain,
% 86.84/87.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7623, 7622])).
% 86.84/87.06 tff(7625,plain,
% 86.84/87.06 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7624, 23, 7621])).
% 86.84/87.06 tff(7626,plain,
% 86.84/87.06 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s2))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7627,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s2))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7628,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s2)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7627, 7626])).
% 86.84/87.06 tff(7629,plain,
% 86.84/87.06 (~node20(c_e_h_3, c_i, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7628, 37, 7625])).
% 86.84/87.06 tff(7630,assumption,(~node20(c_e_h_3, c_i, s2)), introduced(assumption)).
% 86.84/87.06 tff(7631,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s3)), introduced(assumption)).
% 86.84/87.06 tff(7632,assumption,(node22(c_e_h_3, c_i, s2, s3)), introduced(assumption)).
% 86.84/87.06 tff(7633,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s2)), introduced(assumption)).
% 86.84/87.06 tff(7634,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s1)), introduced(assumption)).
% 86.84/87.06 tff(7635,plain,
% 86.84/87.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7636,plain,
% 86.84/87.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7637,plain,
% 86.84/87.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7636, 7635])).
% 86.84/87.06 tff(7638,plain,
% 86.84/87.06 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7637, 23, 7503])).
% 86.84/87.06 tff(7639,plain,
% 86.84/87.06 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7640,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7641,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7640, 7639])).
% 86.84/87.06 tff(7642,plain,
% 86.84/87.06 (~node20(c_e_h_3, c_i, s0)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7641, 37, 7638])).
% 86.84/87.06 tff(7643,assumption,(node21(c_e_h_3, c_i, s0, s1)), introduced(assumption)).
% 86.84/87.06 tff(7644,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1)))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7645,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1)))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7646,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1))),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7645, 7644])).
% 86.84/87.06 tff(7647,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7646, 51, 7634, 7643, 7642])).
% 86.84/87.06 tff(7648,plain,((~node21(c_e_h_3, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7649,plain,
% 86.84/87.06 (~node21(c_e_h_3, c_i, s0, s1)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7648, 7634])).
% 86.84/87.06 tff(7650,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s0)), introduced(assumption)).
% 86.84/87.06 tff(7651,plain,
% 86.84/87.06 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7652,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7651, 94, 7650])).
% 86.84/87.06 tff(7653,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7654,assumption,(node22(c_e_h_3, c_i, s0, s1)), introduced(assumption)).
% 86.84/87.06 tff(7655,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s0)), introduced(assumption)).
% 86.84/87.06 tff(7656,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7657,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7658,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7657, 7656])).
% 86.84/87.06 tff(7659,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7658, 107, 7655, 7634, 7654])).
% 86.84/87.06 tff(7660,plain,((~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7661,plain,
% 86.84/87.06 ((~node22(c_e_h_3, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7660, 7653])).
% 86.84/87.06 tff(7662,plain,
% 86.84/87.06 (~node22(c_e_h_3, c_i, s0, s1)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7661, 7634])).
% 86.84/87.06 tff(7663,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7664,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7665,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7664, 7663])).
% 86.84/87.06 tff(7666,plain,
% 86.84/87.06 (node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7665, 81, 71])).
% 86.84/87.06 tff(7667,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7666, 7662, 7649])).
% 86.84/87.06 tff(7668,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7669,assumption,(node22(c_e_h_3, c_i, s1, s2)), introduced(assumption)).
% 86.84/87.06 tff(7670,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s1)), introduced(assumption)).
% 86.84/87.06 tff(7671,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7672,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7673,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7672, 7671])).
% 86.84/87.06 tff(7674,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7673, 107, 7633, 7670, 7669])).
% 86.84/87.06 tff(7675,plain,((~node22(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7676,plain,
% 86.84/87.06 ((~node22(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7675, 7668])).
% 86.84/87.06 tff(7677,plain,
% 86.84/87.06 (~node22(c_e_h_3, c_i, s1, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7676, 7633])).
% 86.84/87.06 tff(7678,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_i, s1)), introduced(assumption)).
% 86.84/87.06 tff(7679,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s1)), introduced(assumption)).
% 86.84/87.06 tff(7680,plain,
% 86.84/87.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7681,plain,
% 86.84/87.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7682,plain,
% 86.84/87.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7681, 7680])).
% 86.84/87.06 tff(7683,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7682, 23, 7679, 7678])).
% 86.84/87.06 tff(7684,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7685,plain,
% 86.84/87.06 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7684, 7565])).
% 86.84/87.06 tff(7686,plain,
% 86.84/87.06 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s1))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7687,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s1))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7688,plain,
% 86.84/87.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s1)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7687, 7686])).
% 86.84/87.06 tff(7689,plain,
% 86.84/87.06 (~node20(c_e_h_3, c_i, s1)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7688, 37, 7685])).
% 86.84/87.06 tff(7690,assumption,(~node20(c_e_h_3, c_i, s1)), introduced(assumption)).
% 86.84/87.06 tff(7691,assumption,(node21(c_e_h_3, c_i, s1, s2)), introduced(assumption)).
% 86.84/87.06 tff(7692,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s1) | (~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s1) | (~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7693,plain,
% 86.84/87.06 ((node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2))) <=> (node20(c_e_h_3, c_i, s1) | (~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7694,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s1) | (~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2))))),
% 86.84/87.06 inference(monotonicity,[status(thm)],[7693])).
% 86.84/87.06 tff(7695,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s1) | (~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)))),
% 86.84/87.06 inference(transitivity,[status(thm)],[7694, 7692])).
% 86.84/87.06 tff(7696,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2)))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7697,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s1) | (~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7696, 7695])).
% 86.84/87.06 tff(7698,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7697, 51, 7633, 7691, 7690])).
% 86.84/87.06 tff(7699,plain,((~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | node20(c_e_h_3, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7700,plain,
% 86.84/87.06 (~node21(c_e_h_3, c_i, s1, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7699, 7633, 7689])).
% 86.84/87.06 tff(7701,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2))),
% 86.84/87.06 inference(rewrite,[status(thm)],[])).
% 86.84/87.06 tff(7702,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2))),
% 86.84/87.06 inference(quant_inst,[status(thm)],[])).
% 86.84/87.06 tff(7703,plain,
% 86.84/87.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2)),
% 86.84/87.06 inference(modus_ponens,[status(thm)],[7702, 7701])).
% 86.84/87.06 tff(7704,plain,
% 86.84/87.06 (node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2)),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7703, 81, 344])).
% 86.84/87.06 tff(7705,plain,
% 86.84/87.06 ($false),
% 86.84/87.06 inference(unit_resolution,[status(thm)],[7704, 7700, 7677])).
% 86.84/87.06 tff(7706,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.06 tff(7707,plain,
% 86.84/87.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7708,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7709,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7708, 7707])).
% 86.84/87.07 tff(7710,plain,
% 86.84/87.07 ($false),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7709, 107, 7706, 7631, 7632])).
% 86.84/87.07 tff(7711,plain,((~node22(c_e_h_3, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.07 tff(7712,plain,
% 86.84/87.07 (~node22(c_e_h_3, c_i, s2, s3)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7711, 7631])).
% 86.84/87.07 tff(7713,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7714,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7715,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7714, 7713])).
% 86.84/87.07 tff(7716,plain,
% 86.84/87.07 (node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7715, 81, 582])).
% 86.84/87.07 tff(7717,plain,
% 86.84/87.07 (node21(c_e_h_3, c_i, s2, s3)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7716, 7712])).
% 86.84/87.07 tff(7718,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3)))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7719,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3)))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7720,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3))),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7719, 7718])).
% 86.84/87.07 tff(7721,plain,
% 86.84/87.07 ($false),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7720, 51, 7631, 7717, 7630])).
% 86.84/87.07 tff(7722,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | node20(c_e_h_3, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.07 tff(7723,plain,
% 86.84/87.07 (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7722, 7629])).
% 86.84/87.07 tff(7724,plain,
% 86.84/87.07 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7725,plain,
% 86.84/87.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7726,plain,
% 86.84/87.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7725, 7724])).
% 86.84/87.07 tff(7727,plain,
% 86.84/87.07 (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7726, 2218, 7723])).
% 86.84/87.07 tff(7728,plain,
% 86.84/87.07 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7729,plain,
% 86.84/87.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7730,plain,
% 86.84/87.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7729, 7728])).
% 86.84/87.07 tff(7731,plain,
% 86.84/87.07 (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7730, 2218, 7706])).
% 86.84/87.07 tff(7732,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s3)), introduced(assumption)).
% 86.84/87.07 tff(7733,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s1)), introduced(assumption)).
% 86.84/87.07 tff(7734,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s0)), introduced(assumption)).
% 86.84/87.07 tff(7735,plain,
% 86.84/87.07 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7736,plain,
% 86.84/87.07 ($false),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7735, 465, 7734])).
% 86.84/87.07 tff(7737,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s0)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.07 tff(7738,plain,
% 86.84/87.07 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X)) <=> ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X)))),
% 86.84/87.07 inference(bind,[status(th)],[])).
% 86.84/87.07 tff(7739,plain,
% 86.84/87.07 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 86.84/87.07 inference(quant_intro,[status(thm)],[7738])).
% 86.84/87.07 tff(7740,plain,
% 86.84/87.07 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7741,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_16')).
% 86.84/87.07 tff(7742,plain,
% 86.84/87.07 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7741, 7740])).
% 86.84/87.07 tff(7743,plain,(
% 86.84/87.07 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 86.84/87.07 inference(skolemize,[status(sab)],[7742])).
% 86.84/87.07 tff(7744,plain,
% 86.84/87.07 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7743, 7739])).
% 86.84/87.07 tff(7745,plain,
% 86.84/87.07 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7746,plain,
% 86.84/87.07 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7747,plain,
% 86.84/87.07 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7746, 7745])).
% 86.84/87.07 tff(7748,plain,
% 86.84/87.07 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7747, 7744, 7737])).
% 86.84/87.07 tff(7749,plain,
% 86.84/87.07 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s0))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7750,plain,
% 86.84/87.07 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s0))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7751,plain,
% 86.84/87.07 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s0)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7750, 7749])).
% 86.84/87.07 tff(7752,plain,
% 86.84/87.07 (~node20(c_e_h_3, c_d, s0)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7751, 37, 7748])).
% 86.84/87.07 tff(7753,assumption,(node21(c_e_h_3, c_d, s0, s1)), introduced(assumption)).
% 86.84/87.07 tff(7754,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1)))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7755,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1)))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7756,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1))),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7755, 7754])).
% 86.84/87.07 tff(7757,plain,
% 86.84/87.07 ($false),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7756, 51, 7753, 7752, 7733])).
% 86.84/87.07 tff(7758,plain,((~node21(c_e_h_3, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.07 tff(7759,plain,
% 86.84/87.07 (~node21(c_e_h_3, c_d, s0, s1)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7758, 7733])).
% 86.84/87.07 tff(7760,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7761,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7762,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7761, 7760])).
% 86.84/87.07 tff(7763,plain,
% 86.84/87.07 (node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7762, 81, 71])).
% 86.84/87.07 tff(7764,plain,
% 86.84/87.07 (node22(c_e_h_3, c_d, s0, s1)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7763, 7759])).
% 86.84/87.07 tff(7765,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7766,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7767,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7766, 7765])).
% 86.84/87.07 tff(7768,plain,
% 86.84/87.07 ($false),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7767, 107, 7764, 5824, 7733])).
% 86.84/87.07 tff(7769,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.07 tff(7770,plain,
% 86.84/87.07 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7771,plain,
% 86.84/87.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7772,plain,
% 86.84/87.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7771, 7770])).
% 86.84/87.07 tff(7773,plain,
% 86.84/87.07 (~m_c_h_element_v_in1(c_e_h_3, c_f, s1)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7772, 5831, 7769])).
% 86.84/87.07 tff(7774,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s1)), introduced(assumption)).
% 86.84/87.07 tff(7775,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s2)), introduced(assumption)).
% 86.84/87.07 tff(7776,assumption,(node18(c_e_h_3, c_f, s1, s2)), introduced(assumption)).
% 86.84/87.07 tff(7777,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2)))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7778,plain,
% 86.84/87.07 (((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~node18(c_e_h_3, c_f, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2)))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7779,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~node18(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2))))),
% 86.84/87.07 inference(monotonicity,[status(thm)],[7778])).
% 86.84/87.07 tff(7780,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~node18(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2)))),
% 86.84/87.07 inference(transitivity,[status(thm)],[7779, 7777])).
% 86.84/87.07 tff(7781,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~node18(c_e_h_3, c_f, s1, s2)))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7782,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2))),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7781, 7780])).
% 86.84/87.07 tff(7783,plain,
% 86.84/87.07 ($false),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7782, 124, 5914, 7775, 7776])).
% 86.84/87.07 tff(7784,plain,((~node18(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.07 tff(7785,plain,
% 86.84/87.07 (~node18(c_e_h_3, c_f, s1, s2)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7784, 7775])).
% 86.84/87.07 tff(7786,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_f, s1, s2))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7787,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_f, s1, s2))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7788,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_f, s1, s2)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7787, 7786])).
% 86.84/87.07 tff(7789,plain,
% 86.84/87.07 (node19(c_e_h_3, c_f, s1, s2)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7788, 141, 344])).
% 86.84/87.07 tff(7790,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s1, s2)) | node18(c_e_h_3, c_f, s1, s2) | node17(c_e_h_3, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node18(c_e_h_3, c_f, s1, s2) | node17(c_e_h_3, c_f, s1))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7791,plain,
% 86.84/87.07 ((node17(c_e_h_3, c_f, s1) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2))) <=> ((~node19(c_e_h_3, c_f, s1, s2)) | node18(c_e_h_3, c_f, s1, s2) | node17(c_e_h_3, c_f, s1))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7792,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s1) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s1, s2)) | node18(c_e_h_3, c_f, s1, s2) | node17(c_e_h_3, c_f, s1)))),
% 86.84/87.07 inference(monotonicity,[status(thm)],[7791])).
% 86.84/87.07 tff(7793,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s1) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node18(c_e_h_3, c_f, s1, s2) | node17(c_e_h_3, c_f, s1))),
% 86.84/87.07 inference(transitivity,[status(thm)],[7792, 7790])).
% 86.84/87.07 tff(7794,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s1) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7795,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node18(c_e_h_3, c_f, s1, s2) | node17(c_e_h_3, c_f, s1)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7794, 7793])).
% 86.84/87.07 tff(7796,plain,
% 86.84/87.07 (node18(c_e_h_3, c_f, s1, s2) | node17(c_e_h_3, c_f, s1)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7795, 156, 7789])).
% 86.84/87.07 tff(7797,plain,
% 86.84/87.07 (node17(c_e_h_3, c_f, s1)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7796, 7785])).
% 86.84/87.07 tff(7798,plain,
% 86.84/87.07 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7799,plain,
% 86.84/87.07 ((m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)) | (~node17(c_e_h_3, c_f, s1))) <=> ((~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7800,plain,
% 86.84/87.07 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)) | (~node17(c_e_h_3, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1))))),
% 86.84/87.07 inference(monotonicity,[status(thm)],[7799])).
% 86.84/87.07 tff(7801,plain,
% 86.84/87.07 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)) | (~node17(c_e_h_3, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)))),
% 86.84/87.07 inference(transitivity,[status(thm)],[7800, 7798])).
% 86.84/87.07 tff(7802,plain,
% 86.84/87.07 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)) | (~node17(c_e_h_3, c_f, s1)))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7803,plain,
% 86.84/87.07 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1))),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7802, 7801])).
% 86.84/87.07 tff(7804,plain,
% 86.84/87.07 (m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1))),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7803, 245, 7797])).
% 86.84/87.07 tff(7805,plain,
% 86.84/87.07 (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7804, 7774])).
% 86.84/87.07 tff(7806,assumption,(node15(c_e_h_3, c_f, s1, s2)), introduced(assumption)).
% 86.84/87.07 tff(7807,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7808,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 86.84/87.07 inference(quant_inst,[status(thm)],[])).
% 86.84/87.07 tff(7809,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 86.84/87.07 inference(modus_ponens,[status(thm)],[7808, 7807])).
% 86.84/87.07 tff(7810,plain,
% 86.84/87.07 ($false),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7809, 173, 5914, 7775, 7806])).
% 86.84/87.07 tff(7811,plain,((~node15(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.07 tff(7812,plain,
% 86.84/87.07 (~node15(c_e_h_3, c_f, s1, s2)),
% 86.84/87.07 inference(unit_resolution,[status(thm)],[7811, 7775])).
% 86.84/87.07 tff(7813,assumption,(node14(c_e_h_3, c_f, s1, s2)), introduced(assumption)).
% 86.84/87.07 tff(7814,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7815,plain,
% 86.84/87.07 (((~node14(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))),
% 86.84/87.07 inference(rewrite,[status(thm)],[])).
% 86.84/87.07 tff(7816,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))))),
% 86.84/87.07 inference(monotonicity,[status(thm)],[7815])).
% 86.84/87.07 tff(7817,plain,
% 86.84/87.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))),
% 86.84/87.07 inference(transitivity,[status(thm)],[7816, 7814])).
% 86.84/87.07 tff(7818,plain,
% 86.84/87.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7819,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7818, 7817])).
% 86.84/87.08 tff(7820,plain,
% 86.84/87.08 ($false),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7819, 283, 7775, 7813, 7774])).
% 86.84/87.08 tff(7821,plain,((~node14(c_e_h_3, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.08 tff(7822,plain,
% 86.84/87.08 (~node14(c_e_h_3, c_f, s1, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7821, 7774, 7775])).
% 86.84/87.08 tff(7823,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s1, s2)) | node16(c_e_h_3, c_f, s1) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node16(c_e_h_3, c_f, s1) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7824,plain,
% 86.84/87.08 ((node16(c_e_h_3, c_f, s1) | node14(c_e_h_3, c_f, s1, s2) | node15(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2))) <=> ((~node19(c_e_h_3, c_f, s1, s2)) | node16(c_e_h_3, c_f, s1) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7825,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s1) | node14(c_e_h_3, c_f, s1, s2) | node15(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s1, s2)) | node16(c_e_h_3, c_f, s1) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2)))),
% 86.84/87.08 inference(monotonicity,[status(thm)],[7824])).
% 86.84/87.08 tff(7826,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s1) | node14(c_e_h_3, c_f, s1, s2) | node15(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node16(c_e_h_3, c_f, s1) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2))),
% 86.84/87.08 inference(transitivity,[status(thm)],[7825, 7823])).
% 86.84/87.08 tff(7827,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s1) | node14(c_e_h_3, c_f, s1, s2) | node15(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7828,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node16(c_e_h_3, c_f, s1) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2)),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7827, 7826])).
% 86.84/87.08 tff(7829,plain,
% 86.84/87.08 (node16(c_e_h_3, c_f, s1) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7828, 189, 7789])).
% 86.84/87.08 tff(7830,plain,
% 86.84/87.08 (node16(c_e_h_3, c_f, s1)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7829, 7822, 7812])).
% 86.84/87.08 tff(7831,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | m_c_h_element_v_in2(c_e_h_3, c_f, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | m_c_h_element_v_in2(c_e_h_3, c_f, s1))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7832,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | m_c_h_element_v_in2(c_e_h_3, c_f, s1))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7833,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | m_c_h_element_v_in2(c_e_h_3, c_f, s1)),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7832, 7831])).
% 86.84/87.08 tff(7834,plain,
% 86.84/87.08 ($false),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7833, 228, 7830, 7774, 7805])).
% 86.84/87.08 tff(7835,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.08 tff(7836,plain,
% 86.84/87.08 (~m_c_h_element_v_out(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7835, 7773])).
% 86.84/87.08 tff(7837,assumption,(node18(c_e_h_3, c_f, s2, s3)), introduced(assumption)).
% 86.84/87.08 tff(7838,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s2)), introduced(assumption)).
% 86.84/87.08 tff(7839,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node18(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node18(c_e_h_3, c_f, s2, s3)))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7840,plain,
% 86.84/87.08 (((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~node18(c_e_h_3, c_f, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node18(c_e_h_3, c_f, s2, s3)))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7841,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~node18(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node18(c_e_h_3, c_f, s2, s3))))),
% 86.84/87.08 inference(monotonicity,[status(thm)],[7840])).
% 86.84/87.08 tff(7842,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~node18(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node18(c_e_h_3, c_f, s2, s3)))),
% 86.84/87.08 inference(transitivity,[status(thm)],[7841, 7839])).
% 86.84/87.08 tff(7843,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~node18(c_e_h_3, c_f, s2, s3)))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7844,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node18(c_e_h_3, c_f, s2, s3))),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7843, 7842])).
% 86.84/87.08 tff(7845,plain,
% 86.84/87.08 ($false),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7844, 124, 7732, 7838, 7837])).
% 86.84/87.08 tff(7846,plain,((~node18(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.08 tff(7847,plain,
% 86.84/87.08 ((~node18(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7846, 7836])).
% 86.84/87.08 tff(7848,plain,
% 86.84/87.08 (~node18(c_e_h_3, c_f, s2, s3)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7847, 7732])).
% 86.84/87.08 tff(7849,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_f, s2, s3))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7850,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_f, s2, s3))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7851,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_f, s2, s3)),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7850, 7849])).
% 86.84/87.08 tff(7852,plain,
% 86.84/87.08 (node19(c_e_h_3, c_f, s2, s3)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7851, 141, 582])).
% 86.84/87.08 tff(7853,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s2, s3)) | node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7854,plain,
% 86.84/87.08 ((node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3))) <=> ((~node19(c_e_h_3, c_f, s2, s3)) | node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7855,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s2, s3)) | node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3)))),
% 86.84/87.08 inference(monotonicity,[status(thm)],[7854])).
% 86.84/87.08 tff(7856,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3))),
% 86.84/87.08 inference(transitivity,[status(thm)],[7855, 7853])).
% 86.84/87.08 tff(7857,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7858,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3)),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7857, 7856])).
% 86.84/87.08 tff(7859,plain,
% 86.84/87.08 (node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7858, 156, 7852])).
% 86.84/87.08 tff(7860,plain,
% 86.84/87.08 (node17(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7859, 7848])).
% 86.84/87.08 tff(7861,assumption,(node17(c_e_h_3, c_f, s2)), introduced(assumption)).
% 86.84/87.08 tff(7862,assumption,(node16(c_e_h_3, c_f, s2)), introduced(assumption)).
% 86.84/87.08 tff(7863,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s2)), introduced(assumption)).
% 86.84/87.08 tff(7864,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7865,plain,
% 86.84/87.08 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node17(c_e_h_3, c_f, s2))) <=> ((~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7866,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node17(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2))))),
% 86.84/87.08 inference(monotonicity,[status(thm)],[7865])).
% 86.84/87.08 tff(7867,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node17(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(transitivity,[status(thm)],[7866, 7864])).
% 86.84/87.08 tff(7868,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node17(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7869,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7868, 7867])).
% 86.84/87.08 tff(7870,plain,
% 86.84/87.08 (m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7869, 209, 7861])).
% 86.84/87.08 tff(7871,plain,
% 86.84/87.08 (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7870, 7863])).
% 86.84/87.08 tff(7872,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7873,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7874,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7873, 7872])).
% 86.84/87.08 tff(7875,plain,
% 86.84/87.08 (m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7874, 228, 7862])).
% 86.84/87.08 tff(7876,plain,
% 86.84/87.08 ($false),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7875, 7871, 7863])).
% 86.84/87.08 tff(7877,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node16(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.08 tff(7878,plain,
% 86.84/87.08 (m_c_h_element_v_in2(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7877, 7862, 7861])).
% 86.84/87.08 tff(7879,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7880,plain,
% 86.84/87.08 ((m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7881,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(monotonicity,[status(thm)],[7880])).
% 86.84/87.08 tff(7882,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(transitivity,[status(thm)],[7881, 7879])).
% 86.84/87.08 tff(7883,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7884,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7883, 7882])).
% 86.84/87.08 tff(7885,plain,
% 86.84/87.08 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7884, 245, 7861])).
% 86.84/87.08 tff(7886,plain,
% 86.84/87.08 (m_c_h_element_v_in1(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7885, 7878])).
% 86.84/87.08 tff(7887,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7888,plain,
% 86.84/87.08 (((~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7889,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2))))),
% 86.84/87.08 inference(monotonicity,[status(thm)],[7888])).
% 86.84/87.08 tff(7890,plain,
% 86.84/87.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(transitivity,[status(thm)],[7889, 7887])).
% 86.84/87.08 tff(7891,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(quant_inst,[status(thm)],[])).
% 86.84/87.08 tff(7892,plain,
% 86.84/87.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~node16(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(modus_ponens,[status(thm)],[7891, 7890])).
% 86.84/87.08 tff(7893,plain,
% 86.84/87.08 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7892, 263, 7862])).
% 86.84/87.08 tff(7894,plain,
% 86.84/87.08 ($false),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7893, 7886, 7878])).
% 86.84/87.08 tff(7895,plain,((~node16(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.08 tff(7896,plain,
% 86.84/87.08 (~node16(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7895, 7860])).
% 86.84/87.08 tff(7897,plain,
% 86.84/87.08 ((~node17(c_e_h_3, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7869, 209, 7863])).
% 86.84/87.08 tff(7898,plain,
% 86.84/87.08 (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)),
% 86.84/87.08 inference(unit_resolution,[status(thm)],[7897, 7860])).
% 86.84/87.08 tff(7899,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s2)), introduced(assumption)).
% 86.84/87.08 tff(7900,assumption,(node14(c_e_h_3, c_f, s2, s3)), introduced(assumption)).
% 86.84/87.08 tff(7901,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7902,plain,
% 86.84/87.08 (((~node14(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3))) <=> ((~node14(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(rewrite,[status(thm)],[])).
% 86.84/87.08 tff(7903,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2)))),
% 86.84/87.08 inference(monotonicity,[status(thm)],[7902])).
% 86.84/87.08 tff(7904,plain,
% 86.84/87.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2))),
% 86.84/87.08 inference(transitivity,[status(thm)],[7903, 7901])).
% 86.84/87.08 tff(7905,plain,
% 86.84/87.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7906,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7905, 7904])).
% 86.84/87.09 tff(7907,plain,
% 86.84/87.09 ($false),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7906, 283, 7732, 7900, 7899])).
% 86.84/87.09 tff(7908,plain,((~node14(c_e_h_3, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.09 tff(7909,plain,
% 86.84/87.09 (~node14(c_e_h_3, c_f, s2, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7908, 7732, 7898])).
% 86.84/87.09 tff(7910,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s2, s3)) | node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7911,plain,
% 86.84/87.09 ((node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3))) <=> ((~node19(c_e_h_3, c_f, s2, s3)) | node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7912,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s2, s3)) | node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3)))),
% 86.84/87.09 inference(monotonicity,[status(thm)],[7911])).
% 86.84/87.09 tff(7913,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3))),
% 86.84/87.09 inference(transitivity,[status(thm)],[7912, 7910])).
% 86.84/87.09 tff(7914,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7915,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7914, 7913])).
% 86.84/87.09 tff(7916,plain,
% 86.84/87.09 (node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7915, 189, 7852])).
% 86.84/87.09 tff(7917,plain,
% 86.84/87.09 (node15(c_e_h_3, c_f, s2, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7916, 7909, 7896])).
% 86.84/87.09 tff(7918,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7919,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7920,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7919, 7918])).
% 86.84/87.09 tff(7921,plain,
% 86.84/87.09 ($false),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7920, 173, 7732, 7836, 7917])).
% 86.84/87.09 tff(7922,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.09 tff(7923,plain,
% 86.84/87.09 (~m_c_h_element_v_out(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7922, 7731])).
% 86.84/87.09 tff(7924,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s4)), introduced(assumption)).
% 86.84/87.09 tff(7925,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s3)), introduced(assumption)).
% 86.84/87.09 tff(7926,assumption,(node18(c_e_h_3, c_f, s3, s4)), introduced(assumption)).
% 86.84/87.09 tff(7927,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node18(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node18(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7928,plain,
% 86.84/87.09 (((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~node18(c_e_h_3, c_f, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node18(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7929,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~node18(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node18(c_e_h_3, c_f, s3, s4))))),
% 86.84/87.09 inference(monotonicity,[status(thm)],[7928])).
% 86.84/87.09 tff(7930,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~node18(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node18(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(transitivity,[status(thm)],[7929, 7927])).
% 86.84/87.09 tff(7931,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~node18(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7932,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node18(c_e_h_3, c_f, s3, s4))),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7931, 7930])).
% 86.84/87.09 tff(7933,plain,
% 86.84/87.09 ($false),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7932, 124, 7925, 7924, 7926])).
% 86.84/87.09 tff(7934,plain,((~node18(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.09 tff(7935,plain,
% 86.84/87.09 (~node18(c_e_h_3, c_f, s3, s4)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7934, 7925, 7924])).
% 86.84/87.09 tff(7936,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_f, s3, s4))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7937,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_f, s3, s4))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7938,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_f, s3, s4)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7937, 7936])).
% 86.84/87.09 tff(7939,plain,
% 86.84/87.09 (node19(c_e_h_3, c_f, s3, s4)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7938, 141, 679])).
% 86.84/87.09 tff(7940,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node17(c_e_h_3, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node17(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7941,plain,
% 86.84/87.09 ((node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4))) <=> (node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node17(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7942,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node17(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(monotonicity,[status(thm)],[7941])).
% 86.84/87.09 tff(7943,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node17(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(transitivity,[status(thm)],[7942, 7940])).
% 86.84/87.09 tff(7944,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7945,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node17(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7944, 7943])).
% 86.84/87.09 tff(7946,plain,
% 86.84/87.09 (node18(c_e_h_3, c_f, s3, s4) | node17(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7945, 156, 7939])).
% 86.84/87.09 tff(7947,plain,
% 86.84/87.09 (node17(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7946, 7935])).
% 86.84/87.09 tff(7948,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s3)), introduced(assumption)).
% 86.84/87.09 tff(7949,plain,
% 86.84/87.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7950,plain,
% 86.84/87.09 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3))) <=> (m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7951,plain,
% 86.84/87.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3))))),
% 86.84/87.09 inference(monotonicity,[status(thm)],[7950])).
% 86.84/87.09 tff(7952,plain,
% 86.84/87.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(transitivity,[status(thm)],[7951, 7949])).
% 86.84/87.09 tff(7953,plain,
% 86.84/87.09 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7954,plain,
% 86.84/87.09 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7953, 7952])).
% 86.84/87.09 tff(7955,plain,
% 86.84/87.09 ((~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7954, 209, 7948])).
% 86.84/87.09 tff(7956,plain,
% 86.84/87.09 (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7955, 7947])).
% 86.84/87.09 tff(7957,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s3)), introduced(assumption)).
% 86.84/87.09 tff(7958,assumption,(node17(c_e_h_3, c_f, s3)), introduced(assumption)).
% 86.84/87.09 tff(7959,plain,
% 86.84/87.09 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7960,plain,
% 86.84/87.09 ((m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3))) <=> ((~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7961,plain,
% 86.84/87.09 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(monotonicity,[status(thm)],[7960])).
% 86.84/87.09 tff(7962,plain,
% 86.84/87.09 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(transitivity,[status(thm)],[7961, 7959])).
% 86.84/87.09 tff(7963,plain,
% 86.84/87.09 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7964,plain,
% 86.84/87.09 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7963, 7962])).
% 86.84/87.09 tff(7965,plain,
% 86.84/87.09 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7964, 245, 7958])).
% 86.84/87.09 tff(7966,plain,
% 86.84/87.09 (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7965, 7957])).
% 86.84/87.09 tff(7967,assumption,(~node15(c_e_h_3, c_f, s3, s4)), introduced(assumption)).
% 86.84/87.09 tff(7968,assumption,(node14(c_e_h_3, c_f, s3, s4)), introduced(assumption)).
% 86.84/87.09 tff(7969,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~node14(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~node14(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7970,plain,
% 86.84/87.09 (((~node14(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~node14(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7971,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~node14(c_e_h_3, c_f, s3, s4))))),
% 86.84/87.09 inference(monotonicity,[status(thm)],[7970])).
% 86.84/87.09 tff(7972,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~node14(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(transitivity,[status(thm)],[7971, 7969])).
% 86.84/87.09 tff(7973,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7974,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~node14(c_e_h_3, c_f, s3, s4))),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7973, 7972])).
% 86.84/87.09 tff(7975,plain,
% 86.84/87.09 ($false),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7974, 283, 7924, 7968, 7957])).
% 86.84/87.09 tff(7976,plain,((~node14(c_e_h_3, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.09 tff(7977,plain,
% 86.84/87.09 (~node14(c_e_h_3, c_f, s3, s4)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7976, 7957, 7924])).
% 86.84/87.09 tff(7978,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7979,plain,
% 86.84/87.09 ((node16(c_e_h_3, c_f, s3) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4))) <=> (node14(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7980,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s3) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3)))),
% 86.84/87.09 inference(monotonicity,[status(thm)],[7979])).
% 86.84/87.09 tff(7981,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s3) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(transitivity,[status(thm)],[7980, 7978])).
% 86.84/87.09 tff(7982,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s3) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7983,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7982, 7981])).
% 86.84/87.09 tff(7984,plain,
% 86.84/87.09 (node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7983, 189, 7939])).
% 86.84/87.09 tff(7985,plain,
% 86.84/87.09 (node16(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7984, 7977, 7967])).
% 86.84/87.09 tff(7986,plain,
% 86.84/87.09 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7987,plain,
% 86.84/87.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7988,plain,
% 86.84/87.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7987, 7986])).
% 86.84/87.09 tff(7989,plain,
% 86.84/87.09 ($false),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7988, 228, 7985, 7957, 7966])).
% 86.84/87.09 tff(7990,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s3) | node15(c_e_h_3, c_f, s3, s4) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.09 tff(7991,plain,
% 86.84/87.09 (node15(c_e_h_3, c_f, s3, s4)),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7990, 7956, 7924, 7947])).
% 86.84/87.09 tff(7992,plain,
% 86.84/87.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node15(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node15(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(rewrite,[status(thm)],[])).
% 86.84/87.09 tff(7993,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node15(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 86.84/87.09 inference(quant_inst,[status(thm)],[])).
% 86.84/87.09 tff(7994,plain,
% 86.84/87.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node15(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3)),
% 86.84/87.09 inference(modus_ponens,[status(thm)],[7993, 7992])).
% 86.84/87.09 tff(7995,plain,
% 86.84/87.09 ($false),
% 86.84/87.09 inference(unit_resolution,[status(thm)],[7994, 173, 7925, 7924, 7991])).
% 86.84/87.09 tff(7996,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.09 tff(7997,plain,
% 86.84/87.09 ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[7996, 7923])).
% 86.84/87.10 tff(7998,plain,
% 86.84/87.10 (~m_c_h_element_v_out(c_e_h_3, c_f, s4)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[7997, 7727])).
% 86.84/87.10 tff(7999,plain,
% 86.84/87.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8000,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8001,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s4)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8000, 7999])).
% 86.84/87.10 tff(8002,plain,
% 86.84/87.10 (~m_and_h_gate_v_in1(c_e_h_3, c_q, s4)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8001, 1666, 7998])).
% 86.84/87.10 tff(8003,plain,
% 86.84/87.10 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s4))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8004,plain,
% 86.84/87.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s4))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8005,plain,
% 86.84/87.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s4)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8004, 8003])).
% 86.84/87.10 tff(8006,plain,
% 86.84/87.10 (~node20(c_e_h_3, c_q, s4)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8005, 37, 8002])).
% 86.84/87.10 tff(8007,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5)))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8008,plain,
% 86.84/87.10 ((node20(c_e_h_3, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node21(c_e_h_3, c_q, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5)))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8009,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node21(c_e_h_3, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5))))),
% 86.84/87.10 inference(monotonicity,[status(thm)],[8008])).
% 86.84/87.10 tff(8010,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node21(c_e_h_3, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5)))),
% 86.84/87.10 inference(transitivity,[status(thm)],[8009, 8007])).
% 86.84/87.10 tff(8011,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node21(c_e_h_3, c_q, s4, s5)))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8012,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5))),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8011, 8010])).
% 86.84/87.10 tff(8013,plain,
% 86.84/87.10 ($false),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8012, 51, 7432, 8006, 7433])).
% 86.84/87.10 tff(8014,plain,((~node21(c_e_h_3, c_q, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.10 tff(8015,plain,
% 86.84/87.10 (~node21(c_e_h_3, c_q, s4, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8014, 7432])).
% 86.84/87.10 tff(8016,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8017,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8018,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8017, 8016])).
% 86.84/87.10 tff(8019,plain,
% 86.84/87.10 (node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8018, 81, 1432])).
% 86.84/87.10 tff(8020,plain,
% 86.84/87.10 (node22(c_e_h_3, c_q, s4, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8019, 8015])).
% 86.84/87.10 tff(8021,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node22(c_e_h_3, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node22(c_e_h_3, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8022,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node22(c_e_h_3, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8023,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node22(c_e_h_3, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 86.84/87.10 tff(8024,plain,
% 86.84/87.10 ($false),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8023, 107, 7432, 7020, 8020])).
% 86.84/87.10 tff(8025,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.10 tff(8026,plain,
% 86.84/87.10 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s5))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8027,plain,
% 86.84/87.10 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s5))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8028,plain,
% 86.84/87.10 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s5)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 86.84/87.10 tff(8029,plain,
% 86.84/87.10 (node3(c_e_h_3, c_e_h_1, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8028, 3860, 814])).
% 86.84/87.10 tff(8030,plain,
% 86.84/87.10 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s5)) | (~node3(c_e_h_3, c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s5)) | (~node3(c_e_h_3, c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8031,plain,
% 86.84/87.10 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s5)) | (~node3(c_e_h_3, c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8032,plain,
% 86.84/87.10 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s5)) | (~node3(c_e_h_3, c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8031, 8030])).
% 86.84/87.10 tff(8033,plain,
% 86.84/87.10 ((~m_cell_v_ack(c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8032, 836, 8029])).
% 86.84/87.10 tff(8034,plain,
% 86.84/87.10 (~m_cell_v_ack(c_e_h_1, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8033, 8025])).
% 86.84/87.10 tff(8035,plain,
% 86.84/87.10 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)) | m_cell_v_ack(c_e_h_1, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)) | m_cell_v_ack(c_e_h_1, s5))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8036,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)) | m_cell_v_ack(c_e_h_1, s5))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8037,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)) | m_cell_v_ack(c_e_h_1, s5)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8036, 8035])).
% 86.84/87.10 tff(8038,plain,
% 86.84/87.10 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8037, 848, 8034])).
% 86.84/87.10 tff(8039,plain,
% 86.84/87.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8040,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8041,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8040, 8039])).
% 86.84/87.10 tff(8042,plain,
% 86.84/87.10 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8041, 1638, 5004])).
% 86.84/87.10 tff(8043,plain,
% 86.84/87.10 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s4))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8044,plain,
% 86.84/87.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s4))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8045,plain,
% 86.84/87.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s4)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8044, 8043])).
% 86.84/87.10 tff(8046,plain,
% 86.84/87.10 (~node20(c_e_h_1, c_l, s4)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8045, 1535, 8042])).
% 86.84/87.10 tff(8047,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s5)), introduced(assumption)).
% 86.84/87.10 tff(8048,assumption,(~node20(c_e_h_1, c_l, s4)), introduced(assumption)).
% 86.84/87.10 tff(8049,assumption,(node22(c_e_h_1, c_l, s4, s5)), introduced(assumption)).
% 86.84/87.10 tff(8050,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8051,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8052,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8051, 8050])).
% 86.84/87.10 tff(8053,plain,
% 86.84/87.10 ($false),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8052, 107, 8049, 7068, 8047])).
% 86.84/87.10 tff(8054,plain,((~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.10 tff(8055,plain,
% 86.84/87.10 (~node22(c_e_h_1, c_l, s4, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8054, 8047, 7068])).
% 86.84/87.10 tff(8056,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8057,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8058,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8057, 8056])).
% 86.84/87.10 tff(8059,plain,
% 86.84/87.10 (node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8058, 81, 1432])).
% 86.84/87.10 tff(8060,plain,
% 86.84/87.10 (node21(c_e_h_1, c_l, s4, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8059, 8055])).
% 86.84/87.10 tff(8061,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | node20(c_e_h_1, c_l, s4) | (~node21(c_e_h_1, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | node20(c_e_h_1, c_l, s4) | (~node21(c_e_h_1, c_l, s4, s5)))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8062,plain,
% 86.84/87.10 ((node20(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node21(c_e_h_1, c_l, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | node20(c_e_h_1, c_l, s4) | (~node21(c_e_h_1, c_l, s4, s5)))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8063,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node21(c_e_h_1, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | node20(c_e_h_1, c_l, s4) | (~node21(c_e_h_1, c_l, s4, s5))))),
% 86.84/87.10 inference(monotonicity,[status(thm)],[8062])).
% 86.84/87.10 tff(8064,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node21(c_e_h_1, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | node20(c_e_h_1, c_l, s4) | (~node21(c_e_h_1, c_l, s4, s5)))),
% 86.84/87.10 inference(transitivity,[status(thm)],[8063, 8061])).
% 86.84/87.10 tff(8065,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node21(c_e_h_1, c_l, s4, s5)))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8066,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | node20(c_e_h_1, c_l, s4) | (~node21(c_e_h_1, c_l, s4, s5))),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8065, 8064])).
% 86.84/87.10 tff(8067,plain,
% 86.84/87.10 ($false),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8066, 51, 8060, 8048, 8047])).
% 86.84/87.10 tff(8068,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | node20(c_e_h_1, c_l, s4) | m_and_h_gate_v_out(c_e_h_1, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.10 tff(8069,plain,
% 86.84/87.10 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8068, 8046])).
% 86.84/87.10 tff(8070,plain,
% 86.84/87.10 (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8069, 7067])).
% 86.84/87.10 tff(8071,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s5)), introduced(assumption)).
% 86.84/87.10 tff(8072,plain,
% 86.84/87.10 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8073,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8074,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8073, 8072])).
% 86.84/87.10 tff(8075,plain,
% 86.84/87.10 ($false),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8074, 801, 8071, 8070])).
% 86.84/87.10 tff(8076,plain,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.10 tff(8077,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6)))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8078,plain,
% 86.84/87.10 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6))) <=> (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6)))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8079,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6))))),
% 86.84/87.10 inference(monotonicity,[status(thm)],[8078])).
% 86.84/87.10 tff(8080,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6)))),
% 86.84/87.10 inference(transitivity,[status(thm)],[8079, 8077])).
% 86.84/87.10 tff(8081,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8082,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6))),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8081, 8080])).
% 86.84/87.10 tff(8083,plain,
% 86.84/87.10 ($false),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8082, 862, 8076, 8038, 7410, 7431])).
% 86.84/87.10 tff(8084,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.10 tff(8085,plain,
% 86.84/87.10 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8086,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8087,plain,
% 86.84/87.10 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8086, 8085])).
% 86.84/87.10 tff(8088,plain,
% 86.84/87.10 (~m_c_h_element_v_in2(c_e_h_1, c_h, s6)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8087, 309, 8084])).
% 86.84/87.10 tff(8089,plain,
% 86.84/87.10 (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[7108, 309, 7411])).
% 86.84/87.10 tff(8090,plain,
% 86.84/87.10 (~m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[6693, 6608, 6643])).
% 86.84/87.10 tff(8091,plain,
% 86.84/87.10 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[6698, 23, 8090])).
% 86.84/87.10 tff(8092,plain,
% 86.84/87.10 (~node20(c_e_h_1, c_i, s5)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[6706, 8091])).
% 86.84/87.10 tff(8093,plain,
% 86.84/87.10 (~m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[7169, 8090, 7136])).
% 86.84/87.10 tff(8094,plain,
% 86.84/87.10 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[7173, 23, 8093])).
% 86.84/87.10 tff(8095,plain,
% 86.84/87.10 (~node20(c_e_h_1, c_i, s6)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[7206, 37, 8094])).
% 86.84/87.10 tff(8096,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s8)), introduced(assumption)).
% 86.84/87.10 tff(8097,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s6)), introduced(assumption)).
% 86.84/87.10 tff(8098,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s7)), introduced(assumption)).
% 86.84/87.10 tff(8099,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s6)), introduced(assumption)).
% 86.84/87.10 tff(8100,assumption,(node15(c_e_h_1, c_h, s6, s7)), introduced(assumption)).
% 86.84/87.10 tff(8101,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node15(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node15(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8102,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node15(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 86.84/87.10 inference(quant_inst,[status(thm)],[])).
% 86.84/87.10 tff(8103,plain,
% 86.84/87.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node15(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 86.84/87.10 inference(modus_ponens,[status(thm)],[8102, 8101])).
% 86.84/87.10 tff(8104,plain,
% 86.84/87.10 ($false),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8103, 173, 8098, 8099, 8100])).
% 86.84/87.10 tff(8105,plain,((~node15(c_e_h_1, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.10 tff(8106,plain,
% 86.84/87.10 (~node15(c_e_h_1, c_h, s6, s7)),
% 86.84/87.10 inference(unit_resolution,[status(thm)],[8105, 8099, 8098])).
% 86.84/87.10 tff(8107,assumption,(node18(c_e_h_1, c_h, s6, s7)), introduced(assumption)).
% 86.84/87.10 tff(8108,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node18(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node18(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8109,plain,
% 86.84/87.10 (((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~node18(c_e_h_1, c_h, s6, s7))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node18(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.10 inference(rewrite,[status(thm)],[])).
% 86.84/87.10 tff(8110,plain,
% 86.84/87.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~node18(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node18(c_e_h_1, c_h, s6, s7))))),
% 86.84/87.11 inference(monotonicity,[status(thm)],[8109])).
% 86.84/87.11 tff(8111,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~node18(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node18(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.11 inference(transitivity,[status(thm)],[8110, 8108])).
% 86.84/87.11 tff(8112,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~node18(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8113,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node18(c_e_h_1, c_h, s6, s7))),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8112, 8111])).
% 86.84/87.11 tff(8114,plain,
% 86.84/87.11 ($false),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8113, 124, 8098, 8099, 8107])).
% 86.84/87.11 tff(8115,plain,((~node18(c_e_h_1, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.11 tff(8116,plain,
% 86.84/87.11 (~node18(c_e_h_1, c_h, s6, s7)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8115, 8099, 8098])).
% 86.84/87.11 tff(8117,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_h, s6, s7))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8118,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_h, s6, s7))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8119,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_h, s6, s7)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8118, 8117])).
% 86.84/87.11 tff(8120,plain,
% 86.84/87.11 (node19(c_e_h_1, c_h, s6, s7)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8119, 141, 1552])).
% 86.84/87.11 tff(8121,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s6, s7)) | node18(c_e_h_1, c_h, s6, s7) | node17(c_e_h_1, c_h, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s6, s7)) | node18(c_e_h_1, c_h, s6, s7) | node17(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8122,plain,
% 86.84/87.11 ((node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7))) <=> ((~node19(c_e_h_1, c_h, s6, s7)) | node18(c_e_h_1, c_h, s6, s7) | node17(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8123,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s6, s7)) | node18(c_e_h_1, c_h, s6, s7) | node17(c_e_h_1, c_h, s6)))),
% 86.84/87.11 inference(monotonicity,[status(thm)],[8122])).
% 86.84/87.11 tff(8124,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s6, s7)) | node18(c_e_h_1, c_h, s6, s7) | node17(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(transitivity,[status(thm)],[8123, 8121])).
% 86.84/87.11 tff(8125,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8126,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s6, s7)) | node18(c_e_h_1, c_h, s6, s7) | node17(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8125, 8124])).
% 86.84/87.11 tff(8127,plain,
% 86.84/87.11 (node18(c_e_h_1, c_h, s6, s7) | node17(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8126, 156, 8120])).
% 86.84/87.11 tff(8128,plain,
% 86.84/87.11 (node17(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8127, 8116])).
% 86.84/87.11 tff(8129,plain,
% 86.84/87.11 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8130,plain,
% 86.84/87.11 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~node17(c_e_h_1, c_h, s6))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8131,plain,
% 86.84/87.11 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~node17(c_e_h_1, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)))),
% 86.84/87.11 inference(monotonicity,[status(thm)],[8130])).
% 86.84/87.11 tff(8132,plain,
% 86.84/87.11 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~node17(c_e_h_1, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(transitivity,[status(thm)],[8131, 8129])).
% 86.84/87.11 tff(8133,plain,
% 86.84/87.11 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~node17(c_e_h_1, c_h, s6)))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8134,plain,
% 86.84/87.11 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8133, 8132])).
% 86.84/87.11 tff(8135,plain,
% 86.84/87.11 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8134, 209, 8097])).
% 86.84/87.11 tff(8136,plain,
% 86.84/87.11 (~m_c_h_element_v_in1(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8135, 8128])).
% 86.84/87.11 tff(8137,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s6)), introduced(assumption)).
% 86.84/87.11 tff(8138,assumption,(node14(c_e_h_1, c_h, s6, s7)), introduced(assumption)).
% 86.84/87.11 tff(8139,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node14(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node14(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8140,plain,
% 86.84/87.11 (((~node14(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node14(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8141,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node14(c_e_h_1, c_h, s6, s7))))),
% 86.84/87.11 inference(monotonicity,[status(thm)],[8140])).
% 86.84/87.11 tff(8142,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node14(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.11 inference(transitivity,[status(thm)],[8141, 8139])).
% 86.84/87.11 tff(8143,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8144,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node14(c_e_h_1, c_h, s6, s7))),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8143, 8142])).
% 86.84/87.11 tff(8145,plain,
% 86.84/87.11 ($false),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8144, 283, 8098, 8138, 8137])).
% 86.84/87.11 tff(8146,plain,((~node14(c_e_h_1, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.11 tff(8147,plain,
% 86.84/87.11 (~node14(c_e_h_1, c_h, s6, s7)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8146, 8136, 8098])).
% 86.84/87.11 tff(8148,plain,
% 86.84/87.11 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8149,plain,
% 86.84/87.11 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8150,plain,
% 86.84/87.11 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8149, 8148])).
% 86.84/87.11 tff(8151,plain,
% 86.84/87.11 ((~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8150, 228, 8097])).
% 86.84/87.11 tff(8152,plain,
% 86.84/87.11 (~node16(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8151, 8136])).
% 86.84/87.11 tff(8153,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8154,plain,
% 86.84/87.11 ((node16(c_e_h_1, c_h, s6) | node14(c_e_h_1, c_h, s6, s7) | node15(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7))) <=> (node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8155,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | node14(c_e_h_1, c_h, s6, s7) | node15(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.11 inference(monotonicity,[status(thm)],[8154])).
% 86.84/87.11 tff(8156,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | node14(c_e_h_1, c_h, s6, s7) | node15(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7))),
% 86.84/87.11 inference(transitivity,[status(thm)],[8155, 8153])).
% 86.84/87.11 tff(8157,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | node14(c_e_h_1, c_h, s6, s7) | node15(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8158,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8157, 8156])).
% 86.84/87.11 tff(8159,plain,
% 86.84/87.11 (node16(c_e_h_1, c_h, s6) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8158, 189, 8120])).
% 86.84/87.11 tff(8160,plain,
% 86.84/87.11 ($false),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8159, 8152, 8147, 8106])).
% 86.84/87.11 tff(8161,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.11 tff(8162,plain,
% 86.84/87.11 (~m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8161, 8093, 8097])).
% 86.84/87.11 tff(8163,plain,
% 86.84/87.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8164,plain,
% 86.84/87.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8165,plain,
% 86.84/87.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8164, 8163])).
% 86.84/87.11 tff(8166,plain,
% 86.84/87.11 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8165, 23, 8162])).
% 86.84/87.11 tff(8167,plain,
% 86.84/87.11 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s7))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8168,plain,
% 86.84/87.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s7))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8169,plain,
% 86.84/87.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s7)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8168, 8167])).
% 86.84/87.11 tff(8170,plain,
% 86.84/87.11 (~node20(c_e_h_1, c_i, s7)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8169, 37, 8166])).
% 86.84/87.11 tff(8171,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s7)), introduced(assumption)).
% 86.84/87.11 tff(8172,assumption,(node22(c_e_h_1, c_i, s7, s8)), introduced(assumption)).
% 86.84/87.11 tff(8173,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8174,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8175,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8174, 8173])).
% 86.84/87.11 tff(8176,plain,
% 86.84/87.11 ($false),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8175, 107, 8171, 8172, 8096])).
% 86.84/87.11 tff(8177,plain,((~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.11 tff(8178,plain,
% 86.84/87.11 (~node22(c_e_h_1, c_i, s7, s8)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8177, 8096, 8171])).
% 86.84/87.11 tff(8179,assumption,(~node20(c_e_h_1, c_i, s7)), introduced(assumption)).
% 86.84/87.11 tff(8180,assumption,(node21(c_e_h_1, c_i, s7, s8)), introduced(assumption)).
% 86.84/87.11 tff(8181,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node21(c_e_h_1, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node21(c_e_h_1, c_i, s7, s8)))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8182,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node21(c_e_h_1, c_i, s7, s8)))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8183,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node21(c_e_h_1, c_i, s7, s8))),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8182, 8181])).
% 86.84/87.11 tff(8184,plain,
% 86.84/87.11 ($false),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8183, 51, 8179, 8180, 8096])).
% 86.84/87.11 tff(8185,plain,((~node21(c_e_h_1, c_i, s7, s8)) | node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.11 tff(8186,plain,
% 86.84/87.11 (~node21(c_e_h_1, c_i, s7, s8)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8185, 8096, 8179])).
% 86.84/87.11 tff(8187,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8188,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8189,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8188, 8187])).
% 86.84/87.11 tff(8190,plain,
% 86.84/87.11 (node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8189, 81, 2152])).
% 86.84/87.11 tff(8191,plain,
% 86.84/87.11 ($false),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8190, 8186, 8178])).
% 86.84/87.11 tff(8192,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | node20(c_e_h_1, c_i, s7) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.11 tff(8193,plain,
% 86.84/87.11 (m_and_h_gate_v_out(c_e_h_1, c_i, s7)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8192, 8170, 8096])).
% 86.84/87.11 tff(8194,plain,
% 86.84/87.11 (m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[7202, 8193, 8095])).
% 86.84/87.11 tff(8195,plain,
% 86.84/87.11 (m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[6726, 8194, 8092])).
% 86.84/87.11 tff(8196,plain,
% 86.84/87.11 (node20(c_e_h_1, c_i, s4)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[6105, 8195])).
% 86.84/87.11 tff(8197,plain,
% 86.84/87.11 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[6079, 23, 6608])).
% 86.84/87.11 tff(8198,plain,
% 86.84/87.11 ($false),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[6083, 37, 8197, 8196])).
% 86.84/87.11 tff(8199,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.11 tff(8200,plain,
% 86.84/87.11 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8199, 6076])).
% 86.84/87.11 tff(8201,plain,
% 86.84/87.11 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8200, 8089, 6607])).
% 86.84/87.11 tff(8202,plain,
% 86.84/87.11 (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8201, 8088])).
% 86.84/87.11 tff(8203,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s8)), introduced(assumption)).
% 86.84/87.11 tff(8204,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s8)), introduced(assumption)).
% 86.84/87.11 tff(8205,plain,
% 86.84/87.11 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8206,plain,
% 86.84/87.11 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8207,plain,
% 86.84/87.11 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)),
% 86.84/87.11 inference(modus_ponens,[status(thm)],[8206, 8205])).
% 86.84/87.11 tff(8208,plain,
% 86.84/87.11 ($false),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8207, 365, 8204, 8203])).
% 86.84/87.11 tff(8209,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 86.84/87.11 tff(8210,plain,
% 86.84/87.11 (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[8209, 8202])).
% 86.84/87.11 tff(8211,plain,
% 86.84/87.11 (~m_c_h_element_v_out(c_e_h_1, c_e, s8)),
% 86.84/87.11 inference(unit_resolution,[status(thm)],[7298, 6803, 7213])).
% 86.84/87.11 tff(8212,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s9)), introduced(assumption)).
% 86.84/87.11 tff(8213,assumption,(node18(c_e_h_1, c_e, s8, s9)), introduced(assumption)).
% 86.84/87.11 tff(8214,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9)))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8215,plain,
% 86.84/87.11 (((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~node18(c_e_h_1, c_e, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9)))),
% 86.84/87.11 inference(rewrite,[status(thm)],[])).
% 86.84/87.11 tff(8216,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~node18(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9))))),
% 86.84/87.11 inference(monotonicity,[status(thm)],[8215])).
% 86.84/87.11 tff(8217,plain,
% 86.84/87.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~node18(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9)))),
% 86.84/87.11 inference(transitivity,[status(thm)],[8216, 8214])).
% 86.84/87.11 tff(8218,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~node18(c_e_h_1, c_e, s8, s9)))),
% 86.84/87.11 inference(quant_inst,[status(thm)],[])).
% 86.84/87.11 tff(8219,plain,
% 86.84/87.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9))),
% 86.84/87.12 inference(modus_ponens,[status(thm)],[8218, 8217])).
% 86.84/87.12 tff(8220,plain,
% 86.84/87.12 ($false),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8219, 124, 7344, 8212, 8213])).
% 86.84/87.12 tff(8221,plain,((~node18(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.12 tff(8222,plain,
% 86.84/87.12 (~node18(c_e_h_1, c_e, s8, s9)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8221, 7344, 8212])).
% 86.84/87.12 tff(8223,plain,
% 86.84/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_e, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_e, s8, s9))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8224,plain,
% 86.84/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_e, s8, s9))),
% 86.84/87.12 inference(quant_inst,[status(thm)],[])).
% 86.84/87.12 tff(8225,plain,
% 86.84/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_e, s8, s9)),
% 86.84/87.12 inference(modus_ponens,[status(thm)],[8224, 8223])).
% 86.84/87.12 tff(8226,plain,
% 86.84/87.12 (node19(c_e_h_1, c_e, s8, s9)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8225, 141, 2636])).
% 86.84/87.12 tff(8227,plain,
% 86.84/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node17(c_e_h_1, c_e, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node17(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8228,plain,
% 86.84/87.12 ((node17(c_e_h_1, c_e, s8) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9))) <=> (node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node17(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8229,plain,
% 86.84/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s8) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node17(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(monotonicity,[status(thm)],[8228])).
% 86.84/87.12 tff(8230,plain,
% 86.84/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s8) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node17(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(transitivity,[status(thm)],[8229, 8227])).
% 86.84/87.12 tff(8231,plain,
% 86.84/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s8) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 86.84/87.12 inference(quant_inst,[status(thm)],[])).
% 86.84/87.12 tff(8232,plain,
% 86.84/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node17(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(modus_ponens,[status(thm)],[8231, 8230])).
% 86.84/87.12 tff(8233,plain,
% 86.84/87.12 (node18(c_e_h_1, c_e, s8, s9) | node17(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8232, 156, 8226])).
% 86.84/87.12 tff(8234,plain,
% 86.84/87.12 (node17(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8233, 8222])).
% 86.84/87.12 tff(8235,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s8)), introduced(assumption)).
% 86.84/87.12 tff(8236,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8237,plain,
% 86.84/87.12 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8238,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(monotonicity,[status(thm)],[8237])).
% 86.84/87.12 tff(8239,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(transitivity,[status(thm)],[8238, 8236])).
% 86.84/87.12 tff(8240,plain,
% 86.84/87.12 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(quant_inst,[status(thm)],[])).
% 86.84/87.12 tff(8241,plain,
% 86.84/87.12 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(modus_ponens,[status(thm)],[8240, 8239])).
% 86.84/87.12 tff(8242,plain,
% 86.84/87.12 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8241, 209, 8235])).
% 86.84/87.12 tff(8243,plain,
% 86.84/87.12 (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8242, 8234])).
% 86.84/87.12 tff(8244,assumption,(node15(c_e_h_1, c_e, s8, s9)), introduced(assumption)).
% 86.84/87.12 tff(8245,plain,
% 86.84/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8246,plain,
% 86.84/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(quant_inst,[status(thm)],[])).
% 86.84/87.12 tff(8247,plain,
% 86.84/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(modus_ponens,[status(thm)],[8246, 8245])).
% 86.84/87.12 tff(8248,plain,
% 86.84/87.12 ($false),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8247, 173, 7344, 8212, 8244])).
% 86.84/87.12 tff(8249,plain,((~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.12 tff(8250,plain,
% 86.84/87.12 (~node15(c_e_h_1, c_e, s8, s9)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8249, 7344, 8212])).
% 86.84/87.12 tff(8251,assumption,(node17(c_e_h_1, c_e, s8)), introduced(assumption)).
% 86.84/87.12 tff(8252,assumption,(node16(c_e_h_1, c_e, s8)), introduced(assumption)).
% 86.84/87.12 tff(8253,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s8)), introduced(assumption)).
% 86.84/87.12 tff(8254,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8255,plain,
% 86.84/87.12 ((m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8256,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))))),
% 86.84/87.12 inference(monotonicity,[status(thm)],[8255])).
% 86.84/87.12 tff(8257,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(transitivity,[status(thm)],[8256, 8254])).
% 86.84/87.12 tff(8258,plain,
% 86.84/87.12 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(quant_inst,[status(thm)],[])).
% 86.84/87.12 tff(8259,plain,
% 86.84/87.12 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(modus_ponens,[status(thm)],[8258, 8257])).
% 86.84/87.12 tff(8260,plain,
% 86.84/87.12 (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8259, 245, 8251])).
% 86.84/87.12 tff(8261,plain,
% 86.84/87.12 (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8260, 8253])).
% 86.84/87.12 tff(8262,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8263,plain,
% 86.84/87.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(quant_inst,[status(thm)],[])).
% 86.84/87.12 tff(8264,plain,
% 86.84/87.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(modus_ponens,[status(thm)],[8263, 8262])).
% 86.84/87.12 tff(8265,plain,
% 86.84/87.12 (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8264, 228, 8252])).
% 86.84/87.12 tff(8266,plain,
% 86.84/87.12 ($false),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8265, 8261, 8253])).
% 86.84/87.12 tff(8267,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node16(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 86.84/87.12 tff(8268,plain,
% 86.84/87.12 (m_c_h_element_v_in1(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8267, 8252, 8251])).
% 86.84/87.12 tff(8269,plain,
% 86.84/87.12 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8241, 209, 8251])).
% 86.84/87.12 tff(8270,plain,
% 86.84/87.12 (m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8269, 8268])).
% 86.84/87.12 tff(8271,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8272,plain,
% 86.84/87.12 (((~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(rewrite,[status(thm)],[])).
% 86.84/87.12 tff(8273,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))))),
% 86.84/87.12 inference(monotonicity,[status(thm)],[8272])).
% 86.84/87.12 tff(8274,plain,
% 86.84/87.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(transitivity,[status(thm)],[8273, 8271])).
% 86.84/87.12 tff(8275,plain,
% 86.84/87.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 86.84/87.12 inference(quant_inst,[status(thm)],[])).
% 86.84/87.12 tff(8276,plain,
% 86.84/87.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(modus_ponens,[status(thm)],[8275, 8274])).
% 86.84/87.12 tff(8277,plain,
% 86.84/87.12 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 86.84/87.12 inference(unit_resolution,[status(thm)],[8276, 263, 8252])).
% 86.93/87.12 tff(8278,plain,
% 86.93/87.12 ($false),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8277, 8270, 8268])).
% 86.93/87.12 tff(8279,plain,((~node16(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.12 tff(8280,plain,
% 86.93/87.12 (~node16(c_e_h_1, c_e, s8)),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8279, 8234])).
% 86.93/87.12 tff(8281,plain,
% 86.93/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node14(c_e_h_1, c_e, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node14(c_e_h_1, c_e, s8, s9))),
% 86.93/87.12 inference(rewrite,[status(thm)],[])).
% 86.93/87.12 tff(8282,plain,
% 86.93/87.12 ((node16(c_e_h_1, c_e, s8) | node14(c_e_h_1, c_e, s8, s9) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9))) <=> (node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node14(c_e_h_1, c_e, s8, s9))),
% 86.93/87.12 inference(rewrite,[status(thm)],[])).
% 86.93/87.12 tff(8283,plain,
% 86.93/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node14(c_e_h_1, c_e, s8, s9) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node14(c_e_h_1, c_e, s8, s9)))),
% 86.93/87.12 inference(monotonicity,[status(thm)],[8282])).
% 86.93/87.12 tff(8284,plain,
% 86.93/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node14(c_e_h_1, c_e, s8, s9) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node14(c_e_h_1, c_e, s8, s9))),
% 86.93/87.12 inference(transitivity,[status(thm)],[8283, 8281])).
% 86.93/87.12 tff(8285,plain,
% 86.93/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node14(c_e_h_1, c_e, s8, s9) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 86.93/87.12 inference(quant_inst,[status(thm)],[])).
% 86.93/87.12 tff(8286,plain,
% 86.93/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)) | node14(c_e_h_1, c_e, s8, s9)),
% 86.93/87.12 inference(modus_ponens,[status(thm)],[8285, 8284])).
% 86.93/87.12 tff(8287,plain,
% 86.93/87.12 (node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | node14(c_e_h_1, c_e, s8, s9)),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8286, 189, 8226])).
% 86.93/87.12 tff(8288,plain,
% 86.93/87.12 (node14(c_e_h_1, c_e, s8, s9)),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8287, 8280, 8250])).
% 86.93/87.12 tff(8289,assumption,(node14(c_e_h_1, c_e, s8, s9)), introduced(assumption)).
% 86.93/87.12 tff(8290,plain,
% 86.93/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node14(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node14(c_e_h_1, c_e, s8, s9)))),
% 86.93/87.12 inference(rewrite,[status(thm)],[])).
% 86.93/87.12 tff(8291,plain,
% 86.93/87.12 (((~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node14(c_e_h_1, c_e, s8, s9)))),
% 86.93/87.12 inference(rewrite,[status(thm)],[])).
% 86.93/87.12 tff(8292,plain,
% 86.93/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node14(c_e_h_1, c_e, s8, s9))))),
% 86.93/87.12 inference(monotonicity,[status(thm)],[8291])).
% 86.93/87.12 tff(8293,plain,
% 86.93/87.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node14(c_e_h_1, c_e, s8, s9)))),
% 86.93/87.12 inference(transitivity,[status(thm)],[8292, 8290])).
% 86.93/87.12 tff(8294,plain,
% 86.93/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)))),
% 86.93/87.12 inference(quant_inst,[status(thm)],[])).
% 86.93/87.12 tff(8295,plain,
% 86.93/87.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node14(c_e_h_1, c_e, s8, s9))),
% 86.93/87.12 inference(modus_ponens,[status(thm)],[8294, 8293])).
% 86.93/87.12 tff(8296,plain,
% 86.93/87.12 ($false),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8295, 283, 8212, 8289, 8253])).
% 86.93/87.12 tff(8297,plain,((~node14(c_e_h_1, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.12 tff(8298,plain,
% 86.93/87.12 ($false),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8297, 8288, 8243, 8212])).
% 86.93/87.12 tff(8299,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.12 tff(8300,plain,
% 86.93/87.12 ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8299, 8211])).
% 86.93/87.12 tff(8301,plain,
% 86.93/87.12 (~m_c_h_element_v_out(c_e_h_1, c_e, s9)),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8300, 8210])).
% 86.93/87.12 tff(8302,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)), introduced(assumption)).
% 86.93/87.12 tff(8303,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s9)), introduced(assumption)).
% 86.93/87.12 tff(8304,plain,
% 86.93/87.12 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9))),
% 86.93/87.12 inference(rewrite,[status(thm)],[])).
% 86.93/87.12 tff(8305,plain,
% 86.93/87.12 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9))),
% 86.93/87.12 inference(quant_inst,[status(thm)],[])).
% 86.93/87.12 tff(8306,plain,
% 86.93/87.12 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)),
% 86.93/87.12 inference(modus_ponens,[status(thm)],[8305, 8304])).
% 86.93/87.12 tff(8307,plain,
% 86.93/87.12 ($false),
% 86.93/87.12 inference(unit_resolution,[status(thm)],[8306, 976, 8303, 8302])).
% 86.93/87.13 tff(8308,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.13 tff(8309,plain,
% 86.93/87.13 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8308, 8301])).
% 86.93/87.13 tff(8310,plain,
% 86.93/87.13 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8311,plain,
% 86.93/87.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8312,plain,
% 86.93/87.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8311, 8310])).
% 86.93/87.13 tff(8313,plain,
% 86.93/87.13 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8312, 1142, 6887])).
% 86.93/87.13 tff(8314,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)), introduced(assumption)).
% 86.93/87.13 tff(8315,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)), introduced(assumption)).
% 86.93/87.13 tff(8316,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)), introduced(assumption)).
% 86.93/87.13 tff(8317,assumption,(node10(c_e_h_1, c_n, s9, s10)), introduced(assumption)).
% 86.93/87.13 tff(8318,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8319,plain,
% 86.93/87.13 (((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8320,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10))))),
% 86.93/87.13 inference(monotonicity,[status(thm)],[8319])).
% 86.93/87.13 tff(8321,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10)))),
% 86.93/87.13 inference(transitivity,[status(thm)],[8320, 8318])).
% 86.93/87.13 tff(8322,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8323,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8322, 8321])).
% 86.93/87.13 tff(8324,plain,
% 86.93/87.13 ($false),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8323, 1191, 8316, 8317, 8315, 8314])).
% 86.93/87.13 tff(8325,plain,((~node10(c_e_h_1, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.13 tff(8326,plain,
% 86.93/87.13 (~node10(c_e_h_1, c_n, s9, s10)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8325, 8316, 8315, 8314])).
% 86.93/87.13 tff(8327,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)), introduced(assumption)).
% 86.93/87.13 tff(8328,assumption,(node11(c_e_h_1, c_n, s9, s10)), introduced(assumption)).
% 86.93/87.13 tff(8329,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8330,plain,
% 86.93/87.13 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~node11(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8331,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~node11(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10))))),
% 86.93/87.13 inference(monotonicity,[status(thm)],[8330])).
% 86.93/87.13 tff(8332,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~node11(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10)))),
% 86.93/87.13 inference(transitivity,[status(thm)],[8331, 8329])).
% 86.93/87.13 tff(8333,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~node11(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8334,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8333, 8332])).
% 86.93/87.13 tff(8335,plain,
% 86.93/87.13 ($false),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8334, 1161, 8316, 8327, 8328])).
% 86.93/87.13 tff(8336,plain,((~node11(c_e_h_1, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.13 tff(8337,plain,
% 86.93/87.13 (~node11(c_e_h_1, c_n, s9, s10)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8336, 8316, 8327])).
% 86.93/87.13 tff(8338,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8339,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8340,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8339, 8338])).
% 86.93/87.13 tff(8341,plain,
% 86.93/87.13 (node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8340, 1092, 3175])).
% 86.93/87.13 tff(8342,plain,
% 86.93/87.13 ($false),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8341, 8337, 8326])).
% 86.93/87.13 tff(8343,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.13 tff(8344,plain,
% 86.93/87.13 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9))),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8343, 7354, 8313])).
% 86.93/87.13 tff(8345,plain,
% 86.93/87.13 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8344, 8309])).
% 86.93/87.13 tff(8346,plain,
% 86.93/87.13 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8347,plain,
% 86.93/87.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8348,plain,
% 86.93/87.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8347, 8346])).
% 86.93/87.13 tff(8349,plain,
% 86.93/87.13 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8348, 1048, 8345])).
% 86.93/87.13 tff(8350,plain,
% 86.93/87.13 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8351,plain,
% 86.93/87.13 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8352,plain,
% 86.93/87.13 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8351, 8350])).
% 86.93/87.13 tff(8353,plain,
% 86.93/87.13 (~node9(c_e_h_1, c_m, s10)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8352, 1062, 8349])).
% 86.93/87.13 tff(8354,assumption,(~node9(c_e_h_1, c_m, s10)), introduced(assumption)).
% 86.93/87.13 tff(8355,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)), introduced(assumption)).
% 86.93/87.13 tff(8356,assumption,(node10(c_e_h_1, c_m, s10, s11)), introduced(assumption)).
% 86.93/87.13 tff(8357,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s10) | (~node10(c_e_h_1, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s10) | (~node10(c_e_h_1, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8358,plain,
% 86.93/87.13 ((node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node10(c_e_h_1, c_m, s10, s11))) <=> (node9(c_e_h_1, c_m, s10) | (~node10(c_e_h_1, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8359,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node10(c_e_h_1, c_m, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s10) | (~node10(c_e_h_1, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))))),
% 86.93/87.13 inference(monotonicity,[status(thm)],[8358])).
% 86.93/87.13 tff(8360,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node10(c_e_h_1, c_m, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s10) | (~node10(c_e_h_1, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)))),
% 86.93/87.13 inference(transitivity,[status(thm)],[8359, 8357])).
% 86.93/87.13 tff(8361,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node10(c_e_h_1, c_m, s10, s11)))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8362,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s10) | (~node10(c_e_h_1, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8361, 8360])).
% 86.93/87.13 tff(8363,plain,
% 86.93/87.13 ($false),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8362, 1076, 8355, 8356, 8354])).
% 86.93/87.13 tff(8364,plain,((~node10(c_e_h_1, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | node9(c_e_h_1, c_m, s10)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.13 tff(8365,plain,
% 86.93/87.13 (~node10(c_e_h_1, c_m, s10, s11)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8364, 8355, 8354])).
% 86.93/87.13 tff(8366,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8367,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8368,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8367, 8366])).
% 86.93/87.13 tff(8369,plain,
% 86.93/87.13 (node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8368, 1092, 3778])).
% 86.93/87.13 tff(8370,plain,
% 86.93/87.13 (node11(c_e_h_1, c_m, s10, s11)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8369, 8365])).
% 86.93/87.13 tff(8371,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)), introduced(assumption)).
% 86.93/87.13 tff(8372,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8373,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8374,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8373, 8372])).
% 86.93/87.13 tff(8375,plain,
% 86.93/87.13 ($false),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8374, 1130, 8371, 8355, 8370])).
% 86.93/87.13 tff(8376,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10) | node9(c_e_h_1, c_m, s10)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.13 tff(8377,plain,
% 86.93/87.13 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | node9(c_e_h_1, c_m, s10)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8376, 7386])).
% 86.93/87.13 tff(8378,plain,
% 86.93/87.13 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8377, 8353])).
% 86.93/87.13 tff(8379,plain,
% 86.93/87.13 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8380,plain,
% 86.93/87.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8381,plain,
% 86.93/87.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8380, 8379])).
% 86.93/87.13 tff(8382,plain,
% 86.93/87.13 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8381, 1521, 8378])).
% 86.93/87.13 tff(8383,plain,
% 86.93/87.13 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s11))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8384,plain,
% 86.93/87.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s11))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8385,plain,
% 86.93/87.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s11)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8384, 8383])).
% 86.93/87.13 tff(8386,plain,
% 86.93/87.13 (~node20(c_e_h_1, c_r, s11)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8385, 1535, 8382])).
% 86.93/87.13 tff(8387,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8388,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12)))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8389,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8388, 8387])).
% 86.93/87.13 tff(8390,plain,
% 86.93/87.13 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12))),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8389, 51, 8386])).
% 86.93/87.13 tff(8391,plain,
% 86.93/87.13 (~node21(c_e_h_1, c_r, s11, s12)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8390, 4500])).
% 86.93/87.13 tff(8392,plain,
% 86.93/87.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8393,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8394,plain,
% 86.93/87.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8393, 8392])).
% 86.93/87.13 tff(8395,plain,
% 86.93/87.13 ($false),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8394, 81, 4461, 8391, 7409])).
% 86.93/87.13 tff(8396,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s12)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.13 tff(8397,plain,
% 86.93/87.13 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8398,plain,
% 86.93/87.13 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8399,plain,
% 86.93/87.13 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8398, 8397])).
% 86.93/87.13 tff(8400,plain,
% 86.93/87.13 (~m_user_v_ack(c_e_h_1, c_u, s12)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8399, 4481, 8396])).
% 86.93/87.13 tff(8401,plain,
% 86.93/87.13 (^[X: $i] : refl((m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))))),
% 86.93/87.13 inference(bind,[status(th)],[])).
% 86.93/87.13 tff(8402,plain,
% 86.93/87.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 86.93/87.13 inference(quant_intro,[status(thm)],[8401])).
% 86.93/87.13 tff(8403,plain,
% 86.93/87.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8404,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty3')).
% 86.93/87.13 tff(8405,plain,
% 86.93/87.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8404, 8403])).
% 86.93/87.13 tff(8406,plain,(
% 86.93/87.13 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 86.93/87.13 inference(skolemize,[status(sab)],[8405])).
% 86.93/87.13 tff(8407,plain,
% 86.93/87.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8406, 8402])).
% 86.93/87.13 tff(8408,plain,
% 86.93/87.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s12) | (~node24(s12)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s12) | (~node24(s12)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8409,plain,
% 86.93/87.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s12) | (~node24(s12)))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8410,plain,
% 86.93/87.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s12) | (~node24(s12))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8409, 8408])).
% 86.93/87.13 tff(8411,plain,
% 86.93/87.13 (~node24(s12)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8410, 8407, 8400])).
% 86.93/87.13 tff(8412,plain,
% 86.93/87.13 (^[X: $i] : refl((m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X))) <=> (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X))))),
% 86.93/87.13 inference(bind,[status(th)],[])).
% 86.93/87.13 tff(8413,plain,
% 86.93/87.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 86.93/87.13 inference(quant_intro,[status(thm)],[8412])).
% 86.93/87.13 tff(8414,plain,
% 86.93/87.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8415,axiom,(![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty1')).
% 86.93/87.13 tff(8416,plain,
% 86.93/87.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8415, 8414])).
% 86.93/87.13 tff(8417,plain,(
% 86.93/87.13 ![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 86.93/87.13 inference(skolemize,[status(sab)],[8416])).
% 86.93/87.13 tff(8418,plain,
% 86.93/87.13 (![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8417, 8413])).
% 86.93/87.13 tff(8419,plain,
% 86.93/87.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s12)) | m_user_v_ack(c_e_h_1, c_u, s12))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s12)) | m_user_v_ack(c_e_h_1, c_u, s12))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8420,plain,
% 86.93/87.13 ((m_user_v_ack(c_e_h_1, c_u, s12) | (~node23(s12))) <=> ((~node23(s12)) | m_user_v_ack(c_e_h_1, c_u, s12))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8421,plain,
% 86.93/87.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s12) | (~node23(s12)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s12)) | m_user_v_ack(c_e_h_1, c_u, s12)))),
% 86.93/87.13 inference(monotonicity,[status(thm)],[8420])).
% 86.93/87.13 tff(8422,plain,
% 86.93/87.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s12) | (~node23(s12)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s12)) | m_user_v_ack(c_e_h_1, c_u, s12))),
% 86.93/87.13 inference(transitivity,[status(thm)],[8421, 8419])).
% 86.93/87.13 tff(8423,plain,
% 86.93/87.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s12) | (~node23(s12)))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8424,plain,
% 86.93/87.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s12)) | m_user_v_ack(c_e_h_1, c_u, s12)),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8423, 8422])).
% 86.93/87.13 tff(8425,plain,
% 86.93/87.13 (~node23(s12)),
% 86.93/87.13 inference(unit_resolution,[status(thm)],[8424, 8418, 8400])).
% 86.93/87.13 tff(8426,plain,
% 86.93/87.13 (^[X: $i] : refl((node23(X) | node24(X) | node25(X) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X))))),
% 86.93/87.13 inference(bind,[status(th)],[])).
% 86.93/87.13 tff(8427,plain,
% 86.93/87.13 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 86.93/87.13 inference(quant_intro,[status(thm)],[8426])).
% 86.93/87.13 tff(8428,plain,
% 86.93/87.13 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8429,plain,
% 86.93/87.13 (^[X: $i] : trans(monotonicity(rewrite(((node23(X) | node24(X)) | node25(X)) <=> (node23(X) | node24(X) | node25(X))), ((((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> ((node23(X) | node24(X) | node25(X)) | (~node26(X))))), rewrite(((node23(X) | node24(X) | node25(X)) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X)))), ((((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> (node23(X) | node24(X) | node25(X) | (~node26(X)))))),
% 86.93/87.13 inference(bind,[status(th)],[])).
% 86.93/87.13 tff(8430,plain,
% 86.93/87.13 (![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X))) <=> ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 86.93/87.13 inference(quant_intro,[status(thm)],[8429])).
% 86.93/87.13 tff(8431,axiom,(![X: $i] : (((node23(X) | node24(X)) | node25(X)) | (~node26(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty7')).
% 86.93/87.13 tff(8432,plain,
% 86.93/87.13 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8431, 8430])).
% 86.93/87.13 tff(8433,plain,
% 86.93/87.13 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8432, 8428])).
% 86.93/87.13 tff(8434,plain,(
% 86.93/87.13 ![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 86.93/87.13 inference(skolemize,[status(sab)],[8433])).
% 86.93/87.13 tff(8435,plain,
% 86.93/87.13 (![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))),
% 86.93/87.13 inference(modus_ponens,[status(thm)],[8434, 8427])).
% 86.93/87.13 tff(8436,plain,
% 86.93/87.13 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s12) | node24(s12) | node25(s12) | (~node26(s12)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s12) | node24(s12) | node25(s12) | (~node26(s12)))),
% 86.93/87.13 inference(rewrite,[status(thm)],[])).
% 86.93/87.13 tff(8437,plain,
% 86.93/87.13 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s12) | node24(s12) | node25(s12) | (~node26(s12)))),
% 86.93/87.13 inference(quant_inst,[status(thm)],[])).
% 86.93/87.13 tff(8438,plain,
% 86.93/87.13 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s12) | node24(s12) | node25(s12) | (~node26(s12))),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8437, 8436])).
% 86.93/87.14 tff(8439,plain,
% 86.93/87.14 (node25(s12) | (~node26(s12))),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8438, 8435, 8425, 8411])).
% 86.93/87.14 tff(8440,plain,
% 86.93/87.14 (~node26(s12)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8439, 4499])).
% 86.93/87.14 tff(8441,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s9)), introduced(assumption)).
% 86.93/87.14 tff(8442,plain,
% 86.93/87.14 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)) <=> ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)))),
% 86.93/87.14 inference(bind,[status(th)],[])).
% 86.93/87.14 tff(8443,plain,
% 86.93/87.14 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 86.93/87.14 inference(quant_intro,[status(thm)],[8442])).
% 86.93/87.14 tff(8444,plain,
% 86.93/87.14 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8445,plain,
% 86.93/87.14 (^[I0: $i, X: $i] : rewrite((m_or_h_gate_v_in1(I0, c_j, X) | (~m_and_h_gate_v_out(I0, c_l, X))) <=> ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)))),
% 86.93/87.14 inference(bind,[status(th)],[])).
% 86.93/87.14 tff(8446,plain,
% 86.93/87.14 (![I0: $i, X: $i] : (m_or_h_gate_v_in1(I0, c_j, X) | (~m_and_h_gate_v_out(I0, c_l, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 86.93/87.14 inference(quant_intro,[status(thm)],[8445])).
% 86.93/87.14 tff(8447,axiom,(![I0: $i, X: $i] : (m_or_h_gate_v_in1(I0, c_j, X) | (~m_and_h_gate_v_out(I0, c_l, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_39')).
% 86.93/87.14 tff(8448,plain,
% 86.93/87.14 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8447, 8446])).
% 86.93/87.14 tff(8449,plain,
% 86.93/87.14 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8448, 8444])).
% 86.93/87.14 tff(8450,plain,(
% 86.93/87.14 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 86.93/87.14 inference(skolemize,[status(sab)],[8449])).
% 86.93/87.14 tff(8451,plain,
% 86.93/87.14 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8450, 8443])).
% 86.93/87.14 tff(8452,plain,
% 86.93/87.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8453,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8454,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8453, 8452])).
% 86.93/87.14 tff(8455,plain,
% 86.93/87.14 ($false),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8454, 8451, 3787, 3820])).
% 86.93/87.14 tff(8456,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.14 tff(8457,plain,
% 86.93/87.14 (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8456, 3820])).
% 86.93/87.14 tff(8458,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s5)), introduced(assumption)).
% 86.93/87.14 tff(8459,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s6)), introduced(assumption)).
% 86.93/87.14 tff(8460,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8461,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8462,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8461, 8460])).
% 86.93/87.14 tff(8463,plain,
% 86.93/87.14 ((~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8462, 107])).
% 86.93/87.14 tff(8464,plain,
% 86.93/87.14 (~node22(c_e_h_2, c_l, s5, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8463, 8459, 8458])).
% 86.93/87.14 tff(8465,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_l, s5)), introduced(assumption)).
% 86.93/87.14 tff(8466,plain,
% 86.93/87.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8467,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8468,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8467, 8466])).
% 86.93/87.14 tff(8469,plain,
% 86.93/87.14 ($false),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8468, 1638, 1482, 8465])).
% 86.93/87.14 tff(8470,plain,(~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.14 tff(8471,plain,
% 86.93/87.14 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s5))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8472,plain,
% 86.93/87.14 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s5))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8473,plain,
% 86.93/87.14 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s5)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8472, 8471])).
% 86.93/87.14 tff(8474,plain,
% 86.93/87.14 (~node20(c_e_h_2, c_l, s5)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8473, 1535, 8470])).
% 86.93/87.14 tff(8475,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6)))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8476,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6)))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8477,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6))),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8476, 8475])).
% 86.93/87.14 tff(8478,plain,
% 86.93/87.14 (node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6))),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8477, 51])).
% 86.93/87.14 tff(8479,plain,
% 86.93/87.14 ((~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6))),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8478, 8474])).
% 86.93/87.14 tff(8480,plain,
% 86.93/87.14 (~node21(c_e_h_2, c_l, s5, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8479, 8459])).
% 86.93/87.14 tff(8481,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8482,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8483,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8482, 8481])).
% 86.93/87.14 tff(8484,plain,
% 86.93/87.14 ($false),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8483, 81, 1499, 8480, 8464])).
% 86.93/87.14 tff(8485,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.14 tff(8486,plain,
% 86.93/87.14 (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8485, 8457])).
% 86.93/87.14 tff(8487,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s7)), introduced(assumption)).
% 86.93/87.14 tff(8488,assumption,(node21(c_e_h_2, c_l, s6, s7)), introduced(assumption)).
% 86.93/87.14 tff(8489,plain,
% 86.93/87.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8490,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8491,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8490, 8489])).
% 86.93/87.14 tff(8492,plain,
% 86.93/87.14 ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8491, 1638])).
% 86.93/87.14 tff(8493,plain,
% 86.93/87.14 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8492, 1514])).
% 86.93/87.14 tff(8494,plain,
% 86.93/87.14 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s6))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8495,plain,
% 86.93/87.14 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s6))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8496,plain,
% 86.93/87.14 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s6)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8495, 8494])).
% 86.93/87.14 tff(8497,plain,
% 86.93/87.14 (~node20(c_e_h_2, c_l, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8496, 1535, 8493])).
% 86.93/87.14 tff(8498,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node21(c_e_h_2, c_l, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node21(c_e_h_2, c_l, s6, s7)))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8499,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node21(c_e_h_2, c_l, s6, s7)))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8500,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node21(c_e_h_2, c_l, s6, s7))),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8499, 8498])).
% 86.93/87.14 tff(8501,plain,
% 86.93/87.14 ($false),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8500, 51, 8487, 8497, 8488])).
% 86.93/87.14 tff(8502,plain,((~node21(c_e_h_2, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.14 tff(8503,plain,
% 86.93/87.14 (~node21(c_e_h_2, c_l, s6, s7)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8502, 8487])).
% 86.93/87.14 tff(8504,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8505,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8506,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8505, 8504])).
% 86.93/87.14 tff(8507,plain,
% 86.93/87.14 (node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8506, 81, 1552])).
% 86.93/87.14 tff(8508,plain,
% 86.93/87.14 (node22(c_e_h_2, c_l, s6, s7)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8507, 8503])).
% 86.93/87.14 tff(8509,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s6)), introduced(assumption)).
% 86.93/87.14 tff(8510,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node22(c_e_h_2, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node22(c_e_h_2, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8511,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node22(c_e_h_2, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8512,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node22(c_e_h_2, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8511, 8510])).
% 86.93/87.14 tff(8513,plain,
% 86.93/87.14 ($false),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8512, 107, 8509, 8487, 8508])).
% 86.93/87.14 tff(8514,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.14 tff(8515,plain,
% 86.93/87.14 (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8514, 8486])).
% 86.93/87.14 tff(8516,plain,
% 86.93/87.14 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8517,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8518,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8517, 8516])).
% 86.93/87.14 tff(8519,plain,
% 86.93/87.14 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8518, 801, 8515])).
% 86.93/87.14 tff(8520,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s7)), introduced(assumption)).
% 86.93/87.14 tff(8521,plain,
% 86.93/87.14 (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8485, 8458])).
% 86.93/87.14 tff(8522,plain,
% 86.93/87.14 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8523,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8524,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8523, 8522])).
% 86.93/87.14 tff(8525,plain,
% 86.93/87.14 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8524, 801, 8521])).
% 86.93/87.14 tff(8526,plain,
% 86.93/87.14 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[3817, 801, 8458])).
% 86.93/87.14 tff(8527,plain,
% 86.93/87.14 (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[4150, 8526, 3821])).
% 86.93/87.14 tff(8528,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s6)), introduced(assumption)).
% 86.93/87.14 tff(8529,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s5)), introduced(assumption)).
% 86.93/87.14 tff(8530,assumption,(node18(c_e_h_1, c_f, s4, s5)), introduced(assumption)).
% 86.93/87.14 tff(8531,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5)))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8532,plain,
% 86.93/87.14 (((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~node18(c_e_h_1, c_f, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5)))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8533,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~node18(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5))))),
% 86.93/87.14 inference(monotonicity,[status(thm)],[8532])).
% 86.93/87.14 tff(8534,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~node18(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5)))),
% 86.93/87.14 inference(transitivity,[status(thm)],[8533, 8531])).
% 86.93/87.14 tff(8535,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~node18(c_e_h_1, c_f, s4, s5)))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8536,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5))),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8535, 8534])).
% 86.93/87.14 tff(8537,plain,
% 86.93/87.14 ($false),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8536, 124, 4077, 8530, 8529])).
% 86.93/87.14 tff(8538,plain,((~node18(c_e_h_1, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.14 tff(8539,plain,
% 86.93/87.14 (~node18(c_e_h_1, c_f, s4, s5)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8538, 8529])).
% 86.93/87.14 tff(8540,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_f, s4, s5))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8541,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_f, s4, s5))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8542,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_f, s4, s5)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8541, 8540])).
% 86.93/87.14 tff(8543,plain,
% 86.93/87.14 (node19(c_e_h_1, c_f, s4, s5)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8542, 141, 1432])).
% 86.93/87.14 tff(8544,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)) | node17(c_e_h_1, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)) | node17(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8545,plain,
% 86.93/87.14 ((node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5))) <=> (node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)) | node17(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8546,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)) | node17(c_e_h_1, c_f, s4)))),
% 86.93/87.14 inference(monotonicity,[status(thm)],[8545])).
% 86.93/87.14 tff(8547,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)) | node17(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(transitivity,[status(thm)],[8546, 8544])).
% 86.93/87.14 tff(8548,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8549,plain,
% 86.93/87.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)) | node17(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8548, 8547])).
% 86.93/87.14 tff(8550,plain,
% 86.93/87.14 (node18(c_e_h_1, c_f, s4, s5) | node17(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8549, 156, 8543])).
% 86.93/87.14 tff(8551,plain,
% 86.93/87.14 (node17(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8550, 8539])).
% 86.93/87.14 tff(8552,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s4)), introduced(assumption)).
% 86.93/87.14 tff(8553,plain,
% 86.93/87.14 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8554,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8555,plain,
% 86.93/87.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8554, 8553])).
% 86.93/87.14 tff(8556,plain,
% 86.93/87.14 ($false),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8555, 2218, 6086, 8552])).
% 86.93/87.14 tff(8557,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.14 tff(8558,plain,
% 86.93/87.14 (~m_c_h_element_v_in2(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8557, 5613])).
% 86.93/87.14 tff(8559,plain,
% 86.93/87.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8560,plain,
% 86.93/87.14 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4))) <=> ((~node17(c_e_h_1, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8561,plain,
% 86.93/87.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4)))),
% 86.93/87.14 inference(monotonicity,[status(thm)],[8560])).
% 86.93/87.14 tff(8562,plain,
% 86.93/87.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(transitivity,[status(thm)],[8561, 8559])).
% 86.93/87.14 tff(8563,plain,
% 86.93/87.14 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4)))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8564,plain,
% 86.93/87.14 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8563, 8562])).
% 86.93/87.14 tff(8565,plain,
% 86.93/87.14 ((~node17(c_e_h_1, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8564, 209, 8558])).
% 86.93/87.14 tff(8566,plain,
% 86.93/87.14 (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8565, 8551])).
% 86.93/87.14 tff(8567,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s4)), introduced(assumption)).
% 86.93/87.14 tff(8568,assumption,(~node15(c_e_h_1, c_f, s4, s5)), introduced(assumption)).
% 86.93/87.14 tff(8569,plain,
% 86.93/87.14 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8570,plain,
% 86.93/87.14 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(quant_inst,[status(thm)],[])).
% 86.93/87.14 tff(8571,plain,
% 86.93/87.14 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(modus_ponens,[status(thm)],[8570, 8569])).
% 86.93/87.14 tff(8572,plain,
% 86.93/87.14 ((~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8571, 228, 8558])).
% 86.93/87.14 tff(8573,plain,
% 86.93/87.14 (~node16(c_e_h_1, c_f, s4)),
% 86.93/87.14 inference(unit_resolution,[status(thm)],[8572, 8567])).
% 86.93/87.14 tff(8574,plain,
% 86.93/87.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s4, s5)) | node15(c_e_h_1, c_f, s4, s5) | node14(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s4, s5)) | node15(c_e_h_1, c_f, s4, s5) | node14(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4))),
% 86.93/87.14 inference(rewrite,[status(thm)],[])).
% 86.93/87.14 tff(8575,plain,
% 86.93/87.15 ((node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5) | node15(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5))) <=> ((~node19(c_e_h_1, c_f, s4, s5)) | node15(c_e_h_1, c_f, s4, s5) | node14(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8576,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5) | node15(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s4, s5)) | node15(c_e_h_1, c_f, s4, s5) | node14(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4)))),
% 86.93/87.15 inference(monotonicity,[status(thm)],[8575])).
% 86.93/87.15 tff(8577,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5) | node15(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s4, s5)) | node15(c_e_h_1, c_f, s4, s5) | node14(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4))),
% 86.93/87.15 inference(transitivity,[status(thm)],[8576, 8574])).
% 86.93/87.15 tff(8578,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5) | node15(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8579,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s4, s5)) | node15(c_e_h_1, c_f, s4, s5) | node14(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8578, 8577])).
% 86.93/87.15 tff(8580,plain,
% 86.93/87.15 (node15(c_e_h_1, c_f, s4, s5) | node14(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8579, 189, 8543])).
% 86.93/87.15 tff(8581,plain,
% 86.93/87.15 (node14(c_e_h_1, c_f, s4, s5)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8580, 8573, 8568])).
% 86.93/87.15 tff(8582,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8583,plain,
% 86.93/87.15 (((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8584,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4)))),
% 86.93/87.15 inference(monotonicity,[status(thm)],[8583])).
% 86.93/87.15 tff(8585,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4))),
% 86.93/87.15 inference(transitivity,[status(thm)],[8584, 8582])).
% 86.93/87.15 tff(8586,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8587,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8586, 8585])).
% 86.93/87.15 tff(8588,plain,
% 86.93/87.15 ($false),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8587, 283, 8581, 8529, 8567])).
% 86.93/87.15 tff(8589,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | node15(c_e_h_1, c_f, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.15 tff(8590,plain,
% 86.93/87.15 (node15(c_e_h_1, c_f, s4, s5)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8589, 8566, 8529])).
% 86.93/87.15 tff(8591,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node15(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node15(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8592,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node15(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8593,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node15(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8592, 8591])).
% 86.93/87.15 tff(8594,plain,
% 86.93/87.15 ($false),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8593, 173, 4077, 8590, 8529])).
% 86.93/87.15 tff(8595,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.15 tff(8596,plain,
% 86.93/87.15 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8597,plain,
% 86.93/87.15 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8598,plain,
% 86.93/87.15 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8597, 8596])).
% 86.93/87.15 tff(8599,plain,
% 86.93/87.15 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8598, 1666, 8595])).
% 86.93/87.15 tff(8600,plain,
% 86.93/87.15 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s5))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8601,plain,
% 86.93/87.15 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s5))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8602,plain,
% 86.93/87.15 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s5)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8601, 8600])).
% 86.93/87.15 tff(8603,plain,
% 86.93/87.15 (~node20(c_e_h_1, c_q, s5)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8602, 37, 8599])).
% 86.93/87.15 tff(8604,assumption,(node21(c_e_h_1, c_q, s5, s6)), introduced(assumption)).
% 86.93/87.15 tff(8605,assumption,(~node20(c_e_h_1, c_q, s5)), introduced(assumption)).
% 86.93/87.15 tff(8606,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | node20(c_e_h_1, c_q, s5) | (~node21(c_e_h_1, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | node20(c_e_h_1, c_q, s5) | (~node21(c_e_h_1, c_q, s5, s6)))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8607,plain,
% 86.93/87.15 ((node20(c_e_h_1, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node21(c_e_h_1, c_q, s5, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | node20(c_e_h_1, c_q, s5) | (~node21(c_e_h_1, c_q, s5, s6)))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8608,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node21(c_e_h_1, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | node20(c_e_h_1, c_q, s5) | (~node21(c_e_h_1, c_q, s5, s6))))),
% 86.93/87.15 inference(monotonicity,[status(thm)],[8607])).
% 86.93/87.15 tff(8609,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node21(c_e_h_1, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | node20(c_e_h_1, c_q, s5) | (~node21(c_e_h_1, c_q, s5, s6)))),
% 86.93/87.15 inference(transitivity,[status(thm)],[8608, 8606])).
% 86.93/87.15 tff(8610,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node21(c_e_h_1, c_q, s5, s6)))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8611,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | node20(c_e_h_1, c_q, s5) | (~node21(c_e_h_1, c_q, s5, s6))),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8610, 8609])).
% 86.93/87.15 tff(8612,plain,
% 86.93/87.15 ($false),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8611, 51, 8528, 8605, 8604])).
% 86.93/87.15 tff(8613,plain,((~node21(c_e_h_1, c_q, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | node20(c_e_h_1, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.15 tff(8614,plain,
% 86.93/87.15 ((~node21(c_e_h_1, c_q, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8613, 8603])).
% 86.93/87.15 tff(8615,plain,
% 86.93/87.15 (~node21(c_e_h_1, c_q, s5, s6)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8614, 8528])).
% 86.93/87.15 tff(8616,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s5)), introduced(assumption)).
% 86.93/87.15 tff(8617,assumption,(node22(c_e_h_1, c_q, s5, s6)), introduced(assumption)).
% 86.93/87.15 tff(8618,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node22(c_e_h_1, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node22(c_e_h_1, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8619,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node22(c_e_h_1, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8620,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node22(c_e_h_1, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8619, 8618])).
% 86.93/87.15 tff(8621,plain,
% 86.93/87.15 ($false),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8620, 107, 8528, 8616, 8617])).
% 86.93/87.15 tff(8622,plain,((~node22(c_e_h_1, c_q, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.15 tff(8623,plain,
% 86.93/87.15 (~node22(c_e_h_1, c_q, s5, s6)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8622, 8528, 8616])).
% 86.93/87.15 tff(8624,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8625,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8626,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8625, 8624])).
% 86.93/87.15 tff(8627,plain,
% 86.93/87.15 (node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8626, 81, 1499])).
% 86.93/87.15 tff(8628,plain,
% 86.93/87.15 ($false),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8627, 8623, 8615])).
% 86.93/87.15 tff(8629,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.15 tff(8630,plain,
% 86.93/87.15 (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8629, 4108])).
% 86.93/87.15 tff(8631,plain,
% 86.93/87.15 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s6))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8632,plain,
% 86.93/87.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s6))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8633,plain,
% 86.93/87.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s6)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8632, 8631])).
% 86.93/87.15 tff(8634,plain,
% 86.93/87.15 (node3(c_e_h_1, c_e_h_2, s6)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8633, 817, 814])).
% 86.93/87.15 tff(8635,plain,
% 86.93/87.15 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s6)) | (~node3(c_e_h_1, c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s6)) | (~node3(c_e_h_1, c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8636,plain,
% 86.93/87.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s6)) | (~node3(c_e_h_1, c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8637,plain,
% 86.93/87.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s6)) | (~node3(c_e_h_1, c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8636, 8635])).
% 86.93/87.15 tff(8638,plain,
% 86.93/87.15 ((~m_cell_v_ack(c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8637, 836, 8634])).
% 86.93/87.15 tff(8639,plain,
% 86.93/87.15 (~m_cell_v_ack(c_e_h_2, s6)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8638, 8630])).
% 86.93/87.15 tff(8640,plain,
% 86.93/87.15 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)) | m_cell_v_ack(c_e_h_2, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)) | m_cell_v_ack(c_e_h_2, s6))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8641,plain,
% 86.93/87.15 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)) | m_cell_v_ack(c_e_h_2, s6))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8642,plain,
% 86.93/87.15 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)) | m_cell_v_ack(c_e_h_2, s6)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8641, 8640])).
% 86.93/87.15 tff(8643,plain,
% 86.93/87.15 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8642, 848, 8639])).
% 86.93/87.15 tff(8644,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)), introduced(assumption)).
% 86.93/87.15 tff(8645,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)), introduced(assumption)).
% 86.93/87.15 tff(8646,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s6)), introduced(assumption)).
% 86.93/87.15 tff(8647,assumption,(node6(c_e_h_2, c_j, s6, s7)), introduced(assumption)).
% 86.93/87.15 tff(8648,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | (~node6(c_e_h_2, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | (~node6(c_e_h_2, c_j, s6, s7)))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8649,plain,
% 86.93/87.15 (((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | (~node6(c_e_h_2, c_j, s6, s7)))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8650,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | (~node6(c_e_h_2, c_j, s6, s7))))),
% 86.93/87.15 inference(monotonicity,[status(thm)],[8649])).
% 86.93/87.15 tff(8651,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | (~node6(c_e_h_2, c_j, s6, s7)))),
% 86.93/87.15 inference(transitivity,[status(thm)],[8650, 8648])).
% 86.93/87.15 tff(8652,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8653,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | (~node6(c_e_h_2, c_j, s6, s7))),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8652, 8651])).
% 86.93/87.15 tff(8654,plain,
% 86.93/87.15 ($false),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8653, 899, 8646, 8647, 8520])).
% 86.93/87.15 tff(8655,plain,((~node6(c_e_h_2, c_j, s6, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.15 tff(8656,plain,
% 86.93/87.15 (~node6(c_e_h_2, c_j, s6, s7)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8655, 8520, 8646])).
% 86.93/87.15 tff(8657,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8658,plain,
% 86.93/87.15 ((node6(c_e_h_2, c_j, s6, s7) | node5(c_e_h_2, c_j, s6, s7) | (~trans(s6, s7))) <=> ((~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7))),
% 86.93/87.15 inference(rewrite,[status(thm)],[])).
% 86.93/87.15 tff(8659,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s6, s7) | node5(c_e_h_2, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7)))),
% 86.93/87.15 inference(monotonicity,[status(thm)],[8658])).
% 86.93/87.15 tff(8660,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s6, s7) | node5(c_e_h_2, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7))),
% 86.93/87.15 inference(transitivity,[status(thm)],[8659, 8657])).
% 86.93/87.15 tff(8661,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s6, s7) | node5(c_e_h_2, c_j, s6, s7) | (~trans(s6, s7)))),
% 86.93/87.15 inference(quant_inst,[status(thm)],[])).
% 86.93/87.15 tff(8662,plain,
% 86.93/87.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7)),
% 86.93/87.15 inference(modus_ponens,[status(thm)],[8661, 8660])).
% 86.93/87.15 tff(8663,plain,
% 86.93/87.15 (node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8662, 881, 1552])).
% 86.93/87.15 tff(8664,plain,
% 86.93/87.15 (node5(c_e_h_2, c_j, s6, s7)),
% 86.93/87.15 inference(unit_resolution,[status(thm)],[8663, 8656])).
% 86.93/87.15 tff(8665,plain,
% 86.93/87.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8666,plain,
% 86.93/87.16 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8667,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7))))),
% 86.93/87.16 inference(monotonicity,[status(thm)],[8666])).
% 86.93/87.16 tff(8668,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)))),
% 86.93/87.16 inference(transitivity,[status(thm)],[8667, 8665])).
% 86.93/87.16 tff(8669,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8670,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7))),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8669, 8668])).
% 86.93/87.16 tff(8671,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8670, 862, 8664, 8520, 8645, 8644])).
% 86.93/87.16 tff(8672,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | m_or_h_gate_v_out(c_e_h_2, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8673,plain,
% 86.93/87.16 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_out(c_e_h_2, c_j, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8672, 8643])).
% 86.93/87.16 tff(8674,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8673, 8527, 8525, 8520])).
% 86.93/87.16 tff(8675,plain,(m_and_h_gate_v_out(c_e_h_2, c_l, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8676,plain,
% 86.93/87.16 (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8675, 3821, 8457])).
% 86.93/87.16 tff(8677,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s7)), introduced(assumption)).
% 86.93/87.16 tff(8678,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s6)), introduced(assumption)).
% 86.93/87.16 tff(8679,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s5)), introduced(assumption)).
% 86.93/87.16 tff(8680,plain,
% 86.93/87.16 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8681,plain,
% 86.93/87.16 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8682,plain,
% 86.93/87.16 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8681, 8680])).
% 86.93/87.16 tff(8683,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8682, 2218, 6106, 8679])).
% 86.93/87.16 tff(8684,plain,(~m_c_h_element_v_in2(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8685,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s5)), introduced(assumption)).
% 86.93/87.16 tff(8686,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s6)), introduced(assumption)).
% 86.93/87.16 tff(8687,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s5)), introduced(assumption)).
% 86.93/87.16 tff(8688,assumption,(node15(c_e_h_1, c_f, s5, s6)), introduced(assumption)).
% 86.93/87.16 tff(8689,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8690,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8691,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5)),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8690, 8689])).
% 86.93/87.16 tff(8692,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8691, 173, 8687, 8686, 8688])).
% 86.93/87.16 tff(8693,plain,((~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8694,plain,
% 86.93/87.16 (~node15(c_e_h_1, c_f, s5, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8693, 8687, 8686])).
% 86.93/87.16 tff(8695,assumption,(~node15(c_e_h_1, c_f, s5, s6)), introduced(assumption)).
% 86.93/87.16 tff(8696,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s5)), introduced(assumption)).
% 86.93/87.16 tff(8697,plain,
% 86.93/87.16 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8698,plain,
% 86.93/87.16 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8699,plain,
% 86.93/87.16 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5)),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8698, 8697])).
% 86.93/87.16 tff(8700,plain,
% 86.93/87.16 ((~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8699, 228, 8685])).
% 86.93/87.16 tff(8701,plain,
% 86.93/87.16 (~node16(c_e_h_1, c_f, s5)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8700, 8696])).
% 86.93/87.16 tff(8702,assumption,(node14(c_e_h_1, c_f, s5, s6)), introduced(assumption)).
% 86.93/87.16 tff(8703,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8704,plain,
% 86.93/87.16 (((~node14(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8705,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6))))),
% 86.93/87.16 inference(monotonicity,[status(thm)],[8704])).
% 86.93/87.16 tff(8706,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(transitivity,[status(thm)],[8705, 8703])).
% 86.93/87.16 tff(8707,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8708,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6))),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8707, 8706])).
% 86.93/87.16 tff(8709,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8708, 283, 8686, 8702, 8696])).
% 86.93/87.16 tff(8710,plain,((~node14(c_e_h_1, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8711,plain,
% 86.93/87.16 (~node14(c_e_h_1, c_f, s5, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8710, 8696, 8686])).
% 86.93/87.16 tff(8712,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_f, s5, s6))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8713,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_f, s5, s6))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8714,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_f, s5, s6)),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8713, 8712])).
% 86.93/87.16 tff(8715,plain,
% 86.93/87.16 (node19(c_e_h_1, c_f, s5, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8714, 141, 1499])).
% 86.93/87.16 tff(8716,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | node15(c_e_h_1, c_f, s5, s6) | node14(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s5) | node15(c_e_h_1, c_f, s5, s6) | node14(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8717,plain,
% 86.93/87.16 ((node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6))) <=> (node16(c_e_h_1, c_f, s5) | node15(c_e_h_1, c_f, s5, s6) | node14(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8718,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | node15(c_e_h_1, c_f, s5, s6) | node14(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6))))),
% 86.93/87.16 inference(monotonicity,[status(thm)],[8717])).
% 86.93/87.16 tff(8719,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s5) | node15(c_e_h_1, c_f, s5, s6) | node14(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(transitivity,[status(thm)],[8718, 8716])).
% 86.93/87.16 tff(8720,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8721,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s5) | node15(c_e_h_1, c_f, s5, s6) | node14(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6))),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8720, 8719])).
% 86.93/87.16 tff(8722,plain,
% 86.93/87.16 (node16(c_e_h_1, c_f, s5) | node15(c_e_h_1, c_f, s5, s6) | node14(c_e_h_1, c_f, s5, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8721, 189, 8715])).
% 86.93/87.16 tff(8723,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8722, 8711, 8701, 8695])).
% 86.93/87.16 tff(8724,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s5) | node15(c_e_h_1, c_f, s5, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8725,plain,
% 86.93/87.16 (m_c_h_element_v_in1(c_e_h_1, c_f, s5)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8724, 8694, 8686, 8685])).
% 86.93/87.16 tff(8726,plain,
% 86.93/87.16 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8727,plain,
% 86.93/87.16 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8728,plain,
% 86.93/87.16 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5))),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8727, 8726])).
% 86.93/87.16 tff(8729,plain,
% 86.93/87.16 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | (~node17(c_e_h_1, c_f, s5))),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8728, 209, 8685])).
% 86.93/87.16 tff(8730,plain,
% 86.93/87.16 (~node17(c_e_h_1, c_f, s5)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8729, 8725])).
% 86.93/87.16 tff(8731,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8732,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8733,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6))),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8732, 8731])).
% 86.93/87.16 tff(8734,plain,
% 86.93/87.16 (node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8733, 156, 8715])).
% 86.93/87.16 tff(8735,plain,
% 86.93/87.16 (node18(c_e_h_1, c_f, s5, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8734, 8730])).
% 86.93/87.16 tff(8736,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8737,plain,
% 86.93/87.16 (((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~node18(c_e_h_1, c_f, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8738,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~node18(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6))))),
% 86.93/87.16 inference(monotonicity,[status(thm)],[8737])).
% 86.93/87.16 tff(8739,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~node18(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(transitivity,[status(thm)],[8738, 8736])).
% 86.93/87.16 tff(8740,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~node18(c_e_h_1, c_f, s5, s6)))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8741,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6))),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8740, 8739])).
% 86.93/87.16 tff(8742,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8741, 124, 8687, 8686, 8735])).
% 86.93/87.16 tff(8743,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8744,plain,
% 86.93/87.16 (m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8743, 8684])).
% 86.93/87.16 tff(8745,plain,
% 86.93/87.16 (~m_c_h_element_v_out(c_e_h_1, c_f, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8744, 8595])).
% 86.93/87.16 tff(8746,plain,
% 86.93/87.16 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8747,plain,
% 86.93/87.16 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8748,plain,
% 86.93/87.16 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s6)),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8747, 8746])).
% 86.93/87.16 tff(8749,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8748, 1666, 8745, 8678])).
% 86.93/87.16 tff(8750,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8751,plain,
% 86.93/87.16 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s6))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8752,plain,
% 86.93/87.16 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s6))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8753,plain,
% 86.93/87.16 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s6)),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8752, 8751])).
% 86.93/87.16 tff(8754,plain,
% 86.93/87.16 (~node20(c_e_h_1, c_q, s6)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8753, 37, 8750])).
% 86.93/87.16 tff(8755,assumption,(~node20(c_e_h_1, c_q, s6)), introduced(assumption)).
% 86.93/87.16 tff(8756,assumption,(node21(c_e_h_1, c_q, s6, s7)), introduced(assumption)).
% 86.93/87.16 tff(8757,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8758,plain,
% 86.93/87.16 ((node20(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node21(c_e_h_1, c_q, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7)))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8759,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node21(c_e_h_1, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7))))),
% 86.93/87.16 inference(monotonicity,[status(thm)],[8758])).
% 86.93/87.16 tff(8760,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node21(c_e_h_1, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7)))),
% 86.93/87.16 inference(transitivity,[status(thm)],[8759, 8757])).
% 86.93/87.16 tff(8761,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node21(c_e_h_1, c_q, s6, s7)))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8762,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7))),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8761, 8760])).
% 86.93/87.16 tff(8763,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8762, 51, 8677, 8756, 8755])).
% 86.93/87.16 tff(8764,plain,((~node21(c_e_h_1, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.16 tff(8765,plain,
% 86.93/87.16 ((~node21(c_e_h_1, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8764, 8754])).
% 86.93/87.16 tff(8766,plain,
% 86.93/87.16 (~node21(c_e_h_1, c_q, s6, s7)),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8765, 8677])).
% 86.93/87.16 tff(8767,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s6)), introduced(assumption)).
% 86.93/87.16 tff(8768,assumption,(node22(c_e_h_1, c_q, s6, s7)), introduced(assumption)).
% 86.93/87.16 tff(8769,plain,
% 86.93/87.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 86.93/87.16 inference(rewrite,[status(thm)],[])).
% 86.93/87.16 tff(8770,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 86.93/87.16 inference(quant_inst,[status(thm)],[])).
% 86.93/87.16 tff(8771,plain,
% 86.93/87.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6)),
% 86.93/87.16 inference(modus_ponens,[status(thm)],[8770, 8769])).
% 86.93/87.16 tff(8772,plain,
% 86.93/87.16 ($false),
% 86.93/87.16 inference(unit_resolution,[status(thm)],[8771, 107, 8767, 8677, 8768])).
% 86.93/87.16 tff(8773,plain,((~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8774,plain,
% 86.93/87.17 (~node22(c_e_h_1, c_q, s6, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8773, 8677, 8767])).
% 86.93/87.17 tff(8775,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8776,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8777,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8776, 8775])).
% 86.93/87.17 tff(8778,plain,
% 86.93/87.17 (node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8777, 81, 1552])).
% 86.93/87.17 tff(8779,plain,
% 86.93/87.17 ($false),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8778, 8774, 8766])).
% 86.93/87.17 tff(8780,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8781,plain,
% 86.93/87.17 (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8780, 8630])).
% 86.93/87.17 tff(8782,plain,
% 86.93/87.17 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s7))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8783,plain,
% 86.93/87.17 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s7))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8784,plain,
% 86.93/87.17 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s7)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8783, 8782])).
% 86.93/87.17 tff(8785,plain,
% 86.93/87.17 (node3(c_e_h_1, c_e_h_2, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8784, 817, 814])).
% 86.93/87.17 tff(8786,plain,
% 86.93/87.17 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s7)) | (~node3(c_e_h_1, c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s7)) | (~node3(c_e_h_1, c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8787,plain,
% 86.93/87.17 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s7)) | (~node3(c_e_h_1, c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8788,plain,
% 86.93/87.17 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s7)) | (~node3(c_e_h_1, c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8787, 8786])).
% 86.93/87.17 tff(8789,plain,
% 86.93/87.17 ((~m_cell_v_ack(c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8788, 836, 8785])).
% 86.93/87.17 tff(8790,plain,
% 86.93/87.17 (~m_cell_v_ack(c_e_h_2, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8789, 8781])).
% 86.93/87.17 tff(8791,plain,
% 86.93/87.17 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)) | m_cell_v_ack(c_e_h_2, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)) | m_cell_v_ack(c_e_h_2, s7))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8792,plain,
% 86.93/87.17 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)) | m_cell_v_ack(c_e_h_2, s7))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8793,plain,
% 86.93/87.17 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)) | m_cell_v_ack(c_e_h_2, s7)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8792, 8791])).
% 86.93/87.17 tff(8794,plain,
% 86.93/87.17 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8793, 848, 8790])).
% 86.93/87.17 tff(8795,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s7)), introduced(assumption)).
% 86.93/87.17 tff(8796,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s8)), introduced(assumption)).
% 86.93/87.17 tff(8797,assumption,(node6(c_e_h_2, c_j, s7, s8)), introduced(assumption)).
% 86.93/87.17 tff(8798,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~node6(c_e_h_2, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~node6(c_e_h_2, c_j, s7, s8)))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8799,plain,
% 86.93/87.17 (((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7)) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~node6(c_e_h_2, c_j, s7, s8)))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8800,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~node6(c_e_h_2, c_j, s7, s8))))),
% 86.93/87.17 inference(monotonicity,[status(thm)],[8799])).
% 86.93/87.17 tff(8801,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~node6(c_e_h_2, c_j, s7, s8)))),
% 86.93/87.17 inference(transitivity,[status(thm)],[8800, 8798])).
% 86.93/87.17 tff(8802,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8803,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~node6(c_e_h_2, c_j, s7, s8))),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8802, 8801])).
% 86.93/87.17 tff(8804,plain,
% 86.93/87.17 ($false),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8803, 899, 8797, 8796, 8795])).
% 86.93/87.17 tff(8805,plain,((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8806,plain,
% 86.93/87.17 (~node6(c_e_h_2, c_j, s7, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8805, 8796, 8795])).
% 86.93/87.17 tff(8807,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)), introduced(assumption)).
% 86.93/87.17 tff(8808,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)), introduced(assumption)).
% 86.93/87.17 tff(8809,assumption,(node5(c_e_h_2, c_j, s7, s8)), introduced(assumption)).
% 86.93/87.17 tff(8810,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8811,plain,
% 86.93/87.17 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8812,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8))))),
% 86.93/87.17 inference(monotonicity,[status(thm)],[8811])).
% 86.93/87.17 tff(8813,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)))),
% 86.93/87.17 inference(transitivity,[status(thm)],[8812, 8810])).
% 86.93/87.17 tff(8814,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8815,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8))),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8814, 8813])).
% 86.93/87.17 tff(8816,plain,
% 86.93/87.17 ($false),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8815, 862, 8809, 8796, 8808, 8807])).
% 86.93/87.17 tff(8817,plain,((~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8818,plain,
% 86.93/87.17 (~node5(c_e_h_2, c_j, s7, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8817, 8796, 8808, 8807])).
% 86.93/87.17 tff(8819,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8820,plain,
% 86.93/87.17 ((node6(c_e_h_2, c_j, s7, s8) | node5(c_e_h_2, c_j, s7, s8) | (~trans(s7, s8))) <=> ((~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8821,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s7, s8) | node5(c_e_h_2, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8)))),
% 86.93/87.17 inference(monotonicity,[status(thm)],[8820])).
% 86.93/87.17 tff(8822,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s7, s8) | node5(c_e_h_2, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8))),
% 86.93/87.17 inference(transitivity,[status(thm)],[8821, 8819])).
% 86.93/87.17 tff(8823,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s7, s8) | node5(c_e_h_2, c_j, s7, s8) | (~trans(s7, s8)))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8824,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8823, 8822])).
% 86.93/87.17 tff(8825,plain,
% 86.93/87.17 (node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8824, 881, 2152])).
% 86.93/87.17 tff(8826,plain,
% 86.93/87.17 ($false),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8825, 8818, 8806])).
% 86.93/87.17 tff(8827,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_out(c_e_h_2, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8828,plain,
% 86.93/87.17 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_out(c_e_h_2, c_j, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8827, 8794])).
% 86.93/87.17 tff(8829,plain,
% 86.93/87.17 (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8828, 8676, 8519])).
% 86.93/87.17 tff(8830,plain,
% 86.93/87.17 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8831,plain,
% 86.93/87.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8832,plain,
% 86.93/87.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8831, 8830])).
% 86.93/87.17 tff(8833,plain,
% 86.93/87.17 (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8832, 309, 8829])).
% 86.93/87.17 tff(8834,plain,
% 86.93/87.17 (~node18(c_e_h_2, c_h, s6, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[4195, 4187, 4158])).
% 86.93/87.17 tff(8835,plain,
% 86.93/87.17 (m_c_h_element_v_in1(c_e_h_2, c_h, s6)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[4246, 4187, 4158])).
% 86.93/87.17 tff(8836,plain,
% 86.93/87.17 (~node17(c_e_h_2, c_h, s6)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[4255, 8835])).
% 86.93/87.17 tff(8837,plain,
% 86.93/87.17 ($false),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[4243, 8836, 8834])).
% 86.93/87.17 tff(8838,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | m_c_h_element_v_out(c_e_h_2, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8839,plain,
% 86.93/87.17 ($false),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8838, 4157, 4155, 4187])).
% 86.93/87.17 tff(8840,plain,(m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8841,plain,
% 86.93/87.17 (~m_c_h_element_v_out(c_e_h_2, c_h, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8840, 3821, 3820])).
% 86.93/87.17 tff(8842,plain,
% 86.93/87.17 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8843,plain,
% 86.93/87.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8844,plain,
% 86.93/87.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8843, 8842])).
% 86.93/87.17 tff(8845,plain,
% 86.93/87.17 (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8844, 309, 8676])).
% 86.93/87.17 tff(8846,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s7)), introduced(assumption)).
% 86.93/87.17 tff(8847,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s8)), introduced(assumption)).
% 86.93/87.17 tff(8848,assumption,(node18(c_e_h_2, c_h, s7, s8)), introduced(assumption)).
% 86.93/87.17 tff(8849,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8850,plain,
% 86.93/87.17 (((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~node18(c_e_h_2, c_h, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8851,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~node18(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8))))),
% 86.93/87.17 inference(monotonicity,[status(thm)],[8850])).
% 86.93/87.17 tff(8852,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~node18(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.17 inference(transitivity,[status(thm)],[8851, 8849])).
% 86.93/87.17 tff(8853,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~node18(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8854,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8))),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8853, 8852])).
% 86.93/87.17 tff(8855,plain,
% 86.93/87.17 ($false),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8854, 124, 8846, 8847, 8848])).
% 86.93/87.17 tff(8856,plain,((~node18(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8857,plain,
% 86.93/87.17 (~node18(c_e_h_2, c_h, s7, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8856, 8847, 8846])).
% 86.93/87.17 tff(8858,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s7)), introduced(assumption)).
% 86.93/87.17 tff(8859,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_2, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_2, c_h, s7, s8))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8860,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_2, c_h, s7, s8))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8861,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_2, c_h, s7, s8)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8860, 8859])).
% 86.93/87.17 tff(8862,plain,
% 86.93/87.17 (node19(c_e_h_2, c_h, s7, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8861, 141, 2152])).
% 86.93/87.17 tff(8863,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8864,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8865,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8))),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8864, 8863])).
% 86.93/87.17 tff(8866,plain,
% 86.93/87.17 (node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8865, 156, 8862])).
% 86.93/87.17 tff(8867,plain,
% 86.93/87.17 (node17(c_e_h_2, c_h, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8866, 8857])).
% 86.93/87.17 tff(8868,plain,
% 86.93/87.17 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8869,plain,
% 86.93/87.17 ((m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8870,plain,
% 86.93/87.17 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7)))),
% 86.93/87.17 inference(monotonicity,[status(thm)],[8869])).
% 86.93/87.17 tff(8871,plain,
% 86.93/87.17 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7))),
% 86.93/87.17 inference(transitivity,[status(thm)],[8870, 8868])).
% 86.93/87.17 tff(8872,plain,
% 86.93/87.17 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8873,plain,
% 86.93/87.17 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8872, 8871])).
% 86.93/87.17 tff(8874,plain,
% 86.93/87.17 ((~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8873, 245, 8867])).
% 86.93/87.17 tff(8875,plain,
% 86.93/87.17 (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8874, 8858])).
% 86.93/87.17 tff(8876,assumption,(~node16(c_e_h_2, c_h, s7)), introduced(assumption)).
% 86.93/87.17 tff(8877,assumption,(node15(c_e_h_2, c_h, s7, s8)), introduced(assumption)).
% 86.93/87.17 tff(8878,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))),
% 86.93/87.17 inference(rewrite,[status(thm)],[])).
% 86.93/87.17 tff(8879,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))),
% 86.93/87.17 inference(quant_inst,[status(thm)],[])).
% 86.93/87.17 tff(8880,plain,
% 86.93/87.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7)),
% 86.93/87.17 inference(modus_ponens,[status(thm)],[8879, 8878])).
% 86.93/87.17 tff(8881,plain,
% 86.93/87.17 ($false),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8880, 173, 8846, 8847, 8877])).
% 86.93/87.17 tff(8882,plain,((~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.17 tff(8883,plain,
% 86.93/87.17 (~node15(c_e_h_2, c_h, s7, s8)),
% 86.93/87.17 inference(unit_resolution,[status(thm)],[8882, 8847, 8846])).
% 86.93/87.17 tff(8884,assumption,(node14(c_e_h_2, c_h, s7, s8)), introduced(assumption)).
% 86.93/87.17 tff(8885,plain,
% 86.93/87.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node14(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node14(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8886,plain,
% 86.93/87.18 (((~node14(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node14(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8887,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node14(c_e_h_2, c_h, s7, s8))))),
% 86.93/87.18 inference(monotonicity,[status(thm)],[8886])).
% 86.93/87.18 tff(8888,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node14(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.18 inference(transitivity,[status(thm)],[8887, 8885])).
% 86.93/87.18 tff(8889,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8890,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node14(c_e_h_2, c_h, s7, s8))),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8889, 8888])).
% 86.93/87.18 tff(8891,plain,
% 86.93/87.18 ($false),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8890, 283, 8847, 8858, 8884])).
% 86.93/87.18 tff(8892,plain,((~node14(c_e_h_2, c_h, s7, s8)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.18 tff(8893,plain,
% 86.93/87.18 (~node14(c_e_h_2, c_h, s7, s8)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8892, 8847, 8858])).
% 86.93/87.18 tff(8894,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8895,plain,
% 86.93/87.18 ((node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8))) <=> (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8896,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.18 inference(monotonicity,[status(thm)],[8895])).
% 86.93/87.18 tff(8897,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8))),
% 86.93/87.18 inference(transitivity,[status(thm)],[8896, 8894])).
% 86.93/87.18 tff(8898,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8899,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8)),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8898, 8897])).
% 86.93/87.18 tff(8900,plain,
% 86.93/87.18 (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8899, 189, 8862])).
% 86.93/87.18 tff(8901,plain,
% 86.93/87.18 ($false),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8900, 8893, 8883, 8876])).
% 86.93/87.18 tff(8902,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | node16(c_e_h_2, c_h, s7) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_out(c_e_h_2, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.18 tff(8903,plain,
% 86.93/87.18 (node16(c_e_h_2, c_h, s7)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8902, 8858, 8846, 8847])).
% 86.93/87.18 tff(8904,plain,
% 86.93/87.18 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8905,plain,
% 86.93/87.18 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8906,plain,
% 86.93/87.18 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8905, 8904])).
% 86.93/87.18 tff(8907,plain,
% 86.93/87.18 ($false),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8906, 228, 8858, 8903, 8875])).
% 86.93/87.18 tff(8908,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.18 tff(8909,plain,
% 86.93/87.18 (m_c_h_element_v_in1(c_e_h_2, c_h, s7)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8908, 8847, 8846])).
% 86.93/87.18 tff(8910,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s7)), introduced(assumption)).
% 86.93/87.18 tff(8911,plain,
% 86.93/87.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8912,plain,
% 86.93/87.18 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7))) <=> (m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8913,plain,
% 86.93/87.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7))))),
% 86.93/87.18 inference(monotonicity,[status(thm)],[8912])).
% 86.93/87.18 tff(8914,plain,
% 86.93/87.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))),
% 86.93/87.18 inference(transitivity,[status(thm)],[8913, 8911])).
% 86.93/87.18 tff(8915,plain,
% 86.93/87.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8916,plain,
% 86.93/87.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7))),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8915, 8914])).
% 86.93/87.18 tff(8917,plain,
% 86.93/87.18 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7))),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8916, 209, 8910])).
% 86.93/87.18 tff(8918,plain,
% 86.93/87.18 (~node17(c_e_h_2, c_h, s7)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8917, 8909])).
% 86.93/87.18 tff(8919,plain,
% 86.93/87.18 ($false),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8866, 8918, 8857])).
% 86.93/87.18 tff(8920,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | m_c_h_element_v_out(c_e_h_2, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.18 tff(8921,plain,
% 86.93/87.18 (~m_c_h_element_v_out(c_e_h_2, c_h, s8)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8920, 8845, 8841])).
% 86.93/87.18 tff(8922,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s8)), introduced(assumption)).
% 86.93/87.18 tff(8923,assumption,(node18(c_e_h_2, c_h, s8, s9)), introduced(assumption)).
% 86.93/87.18 tff(8924,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8925,plain,
% 86.93/87.18 (((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~node18(c_e_h_2, c_h, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8926,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~node18(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9))))),
% 86.93/87.18 inference(monotonicity,[status(thm)],[8925])).
% 86.93/87.18 tff(8927,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~node18(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(transitivity,[status(thm)],[8926, 8924])).
% 86.93/87.18 tff(8928,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~node18(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8929,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8928, 8927])).
% 86.93/87.18 tff(8930,plain,
% 86.93/87.18 ($false),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8929, 124, 8922, 8441, 8923])).
% 86.93/87.18 tff(8931,plain,((~node18(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.18 tff(8932,plain,
% 86.93/87.18 (~node18(c_e_h_2, c_h, s8, s9)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8931, 8922, 8441])).
% 86.93/87.18 tff(8933,plain,
% 86.93/87.18 (~node18(c_e_h_2, c_h, s8, s9)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8931, 8441, 8922])).
% 86.93/87.18 tff(8934,assumption,(node15(c_e_h_2, c_h, s8, s9)), introduced(assumption)).
% 86.93/87.18 tff(8935,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8936,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8937,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8)),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8936, 8935])).
% 86.93/87.18 tff(8938,plain,
% 86.93/87.18 ($false),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8937, 173, 8922, 8441, 8934])).
% 86.93/87.18 tff(8939,plain,((~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.18 tff(8940,plain,
% 86.93/87.18 (~node15(c_e_h_2, c_h, s8, s9)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8939, 8441, 8922])).
% 86.93/87.18 tff(8941,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s8)), introduced(assumption)).
% 86.93/87.18 tff(8942,assumption,(node17(c_e_h_2, c_h, s8)), introduced(assumption)).
% 86.93/87.18 tff(8943,plain,
% 86.93/87.18 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8944,plain,
% 86.93/87.18 ((m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8945,plain,
% 86.93/87.18 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8))))),
% 86.93/87.18 inference(monotonicity,[status(thm)],[8944])).
% 86.93/87.18 tff(8946,plain,
% 86.93/87.18 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))),
% 86.93/87.18 inference(transitivity,[status(thm)],[8945, 8943])).
% 86.93/87.18 tff(8947,plain,
% 86.93/87.18 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8948,plain,
% 86.93/87.18 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8))),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8947, 8946])).
% 86.93/87.18 tff(8949,plain,
% 86.93/87.18 ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8948, 245, 8942])).
% 86.93/87.18 tff(8950,plain,
% 86.93/87.18 (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8949, 8941])).
% 86.93/87.18 tff(8951,assumption,(~node15(c_e_h_2, c_h, s8, s9)), introduced(assumption)).
% 86.93/87.18 tff(8952,assumption,(node14(c_e_h_2, c_h, s8, s9)), introduced(assumption)).
% 86.93/87.18 tff(8953,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node14(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node14(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8954,plain,
% 86.93/87.18 (((~node14(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node14(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8955,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node14(c_e_h_2, c_h, s8, s9))))),
% 86.93/87.18 inference(monotonicity,[status(thm)],[8954])).
% 86.93/87.18 tff(8956,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node14(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(transitivity,[status(thm)],[8955, 8953])).
% 86.93/87.18 tff(8957,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8958,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~node14(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8957, 8956])).
% 86.93/87.18 tff(8959,plain,
% 86.93/87.18 ($false),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8958, 283, 8441, 8941, 8952])).
% 86.93/87.18 tff(8960,plain,((~node14(c_e_h_2, c_h, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.18 tff(8961,plain,
% 86.93/87.18 (~node14(c_e_h_2, c_h, s8, s9)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8960, 8941, 8441])).
% 86.93/87.18 tff(8962,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_2, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8963,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8964,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_2, c_h, s8, s9)),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8963, 8962])).
% 86.93/87.18 tff(8965,plain,
% 86.93/87.18 (node19(c_e_h_2, c_h, s8, s9)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8964, 141, 2636])).
% 86.93/87.18 tff(8966,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8967,plain,
% 86.93/87.18 ((node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9))) <=> (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8968,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(monotonicity,[status(thm)],[8967])).
% 86.93/87.18 tff(8969,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(transitivity,[status(thm)],[8968, 8966])).
% 86.93/87.18 tff(8970,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8971,plain,
% 86.93/87.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9)),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8970, 8969])).
% 86.93/87.18 tff(8972,plain,
% 86.93/87.18 (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8971, 189, 8965])).
% 86.93/87.18 tff(8973,plain,
% 86.93/87.18 (node16(c_e_h_2, c_h, s8)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8972, 8961, 8951])).
% 86.93/87.18 tff(8974,plain,
% 86.93/87.18 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8975,plain,
% 86.93/87.18 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8))),
% 86.93/87.18 inference(quant_inst,[status(thm)],[])).
% 86.93/87.18 tff(8976,plain,
% 86.93/87.18 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8)),
% 86.93/87.18 inference(modus_ponens,[status(thm)],[8975, 8974])).
% 86.93/87.18 tff(8977,plain,
% 86.93/87.18 ($false),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8976, 228, 8941, 8973, 8950])).
% 86.93/87.18 tff(8978,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s8) | node15(c_e_h_2, c_h, s8, s9) | (~node17(c_e_h_2, c_h, s8)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.18 tff(8979,plain,
% 86.93/87.18 (~node17(c_e_h_2, c_h, s8)),
% 86.93/87.18 inference(unit_resolution,[status(thm)],[8978, 8441, 8941, 8940])).
% 86.93/87.18 tff(8980,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s8) | (~node19(c_e_h_2, c_h, s8, s9)) | node18(c_e_h_2, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s8) | (~node19(c_e_h_2, c_h, s8, s9)) | node18(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8981,plain,
% 86.93/87.18 ((node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9))) <=> (node17(c_e_h_2, c_h, s8) | (~node19(c_e_h_2, c_h, s8, s9)) | node18(c_e_h_2, c_h, s8, s9))),
% 86.93/87.18 inference(rewrite,[status(thm)],[])).
% 86.93/87.18 tff(8982,plain,
% 86.93/87.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s8) | (~node19(c_e_h_2, c_h, s8, s9)) | node18(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.19 inference(monotonicity,[status(thm)],[8981])).
% 86.93/87.19 tff(8983,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s8) | (~node19(c_e_h_2, c_h, s8, s9)) | node18(c_e_h_2, c_h, s8, s9))),
% 86.93/87.19 inference(transitivity,[status(thm)],[8982, 8980])).
% 86.93/87.19 tff(8984,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(8985,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s8) | (~node19(c_e_h_2, c_h, s8, s9)) | node18(c_e_h_2, c_h, s8, s9)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[8984, 8983])).
% 86.93/87.19 tff(8986,plain,
% 86.93/87.19 (node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8985, 156, 8965])).
% 86.93/87.19 tff(8987,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8986, 8979, 8933])).
% 86.93/87.19 tff(8988,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_out(c_e_h_2, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(8989,plain,
% 86.93/87.19 (m_c_h_element_v_in1(c_e_h_2, c_h, s8)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8988, 8922, 8441])).
% 86.93/87.19 tff(8990,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s8)), introduced(assumption)).
% 86.93/87.19 tff(8991,plain,
% 86.93/87.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(8992,plain,
% 86.93/87.19 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8))) <=> (m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(8993,plain,
% 86.93/87.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8))))),
% 86.93/87.19 inference(monotonicity,[status(thm)],[8992])).
% 86.93/87.19 tff(8994,plain,
% 86.93/87.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))),
% 86.93/87.19 inference(transitivity,[status(thm)],[8993, 8991])).
% 86.93/87.19 tff(8995,plain,
% 86.93/87.19 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(8996,plain,
% 86.93/87.19 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8))),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[8995, 8994])).
% 86.93/87.19 tff(8997,plain,
% 86.93/87.19 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8))),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8996, 209, 8990])).
% 86.93/87.19 tff(8998,plain,
% 86.93/87.19 (~node17(c_e_h_2, c_h, s8)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8997, 8989])).
% 86.93/87.19 tff(8999,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8986, 8998, 8932])).
% 86.93/87.19 tff(9000,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9001,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9000, 8921, 8833, 8441])).
% 86.93/87.19 tff(9002,plain,(m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9003,plain,
% 86.93/87.19 (~m_c_h_element_v_out(c_e_h_2, c_h, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9002, 3818, 3459])).
% 86.93/87.19 tff(9004,plain,
% 86.93/87.19 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9005,plain,
% 86.93/87.19 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9006,plain,
% 86.93/87.19 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s9)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9005, 9004])).
% 86.93/87.19 tff(9007,plain,
% 86.93/87.19 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9006, 23, 9003])).
% 86.93/87.19 tff(9008,plain,
% 86.93/87.19 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s9))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9009,plain,
% 86.93/87.19 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s9))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9010,plain,
% 86.93/87.19 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s9)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9009, 9008])).
% 86.93/87.19 tff(9011,plain,
% 86.93/87.19 (~node20(c_e_h_2, c_i, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9010, 37, 9007])).
% 86.93/87.19 tff(9012,plain,
% 86.93/87.19 (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8675, 3459, 3814])).
% 86.93/87.19 tff(9013,plain,
% 86.93/87.19 (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8844, 309, 9012])).
% 86.93/87.19 tff(9014,plain,
% 86.93/87.19 (~m_c_h_element_v_out(c_e_h_2, c_h, s7)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8840, 3818, 3459])).
% 86.93/87.19 tff(9015,plain,
% 86.93/87.19 (~m_c_h_element_v_out(c_e_h_2, c_h, s8)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[8920, 9014, 9013])).
% 86.93/87.19 tff(9016,plain,
% 86.93/87.19 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9017,plain,
% 86.93/87.19 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9018,plain,
% 86.93/87.19 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s8)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9017, 9016])).
% 86.93/87.19 tff(9019,plain,
% 86.93/87.19 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9018, 23, 9015])).
% 86.93/87.19 tff(9020,plain,
% 86.93/87.19 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s8))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9021,plain,
% 86.93/87.19 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s8))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9022,plain,
% 86.93/87.19 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s8)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9021, 9020])).
% 86.93/87.19 tff(9023,plain,
% 86.93/87.19 (~node20(c_e_h_2, c_i, s8)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9022, 37, 9019])).
% 86.93/87.19 tff(9024,assumption,(~node20(c_e_h_2, c_i, s8)), introduced(assumption)).
% 86.93/87.19 tff(9025,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s9)), introduced(assumption)).
% 86.93/87.19 tff(9026,assumption,(node21(c_e_h_2, c_i, s8, s9)), introduced(assumption)).
% 86.93/87.19 tff(9027,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node21(c_e_h_2, c_i, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node21(c_e_h_2, c_i, s8, s9)))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9028,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node21(c_e_h_2, c_i, s8, s9)))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9029,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node21(c_e_h_2, c_i, s8, s9))),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9028, 9027])).
% 86.93/87.19 tff(9030,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9029, 51, 9025, 9026, 9024])).
% 86.93/87.19 tff(9031,plain,((~node21(c_e_h_2, c_i, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | node20(c_e_h_2, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9032,plain,
% 86.93/87.19 (~node21(c_e_h_2, c_i, s8, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9031, 9025, 9024])).
% 86.93/87.19 tff(9033,assumption,(node22(c_e_h_2, c_i, s8, s9)), introduced(assumption)).
% 86.93/87.19 tff(9034,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9035,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9036,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9035, 9034])).
% 86.93/87.19 tff(9037,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9036, 107, 4264, 9025, 9033])).
% 86.93/87.19 tff(9038,plain,((~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9))), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9039,plain,
% 86.93/87.19 (~node22(c_e_h_2, c_i, s8, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9038, 9025, 4264])).
% 86.93/87.19 tff(9040,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9041,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9042,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9041, 9040])).
% 86.93/87.19 tff(9043,plain,
% 86.93/87.19 (node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9042, 81, 2636])).
% 86.93/87.19 tff(9044,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9043, 9039, 9032])).
% 86.93/87.19 tff(9045,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8) | node20(c_e_h_2, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9046,plain,
% 86.93/87.19 (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9045, 9023, 4262])).
% 86.93/87.19 tff(9047,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s9)), introduced(assumption)).
% 86.93/87.19 tff(9048,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s10)), introduced(assumption)).
% 86.93/87.19 tff(9049,assumption,(node22(c_e_h_2, c_i, s9, s10)), introduced(assumption)).
% 86.93/87.19 tff(9050,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node22(c_e_h_2, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node22(c_e_h_2, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9051,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node22(c_e_h_2, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9052,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node22(c_e_h_2, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9051, 9050])).
% 86.93/87.19 tff(9053,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9052, 107, 9048, 9047, 9049])).
% 86.93/87.19 tff(9054,plain,((~node22(c_e_h_2, c_i, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9055,plain,
% 86.93/87.19 (~node22(c_e_h_2, c_i, s9, s10)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9054, 9048, 9047])).
% 86.93/87.19 tff(9056,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9057,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9058,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9057, 9056])).
% 86.93/87.19 tff(9059,plain,
% 86.93/87.19 (node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9058, 81, 3175])).
% 86.93/87.19 tff(9060,plain,
% 86.93/87.19 (node21(c_e_h_2, c_i, s9, s10)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9059, 9055])).
% 86.93/87.19 tff(9061,assumption,(~node20(c_e_h_2, c_i, s9)), introduced(assumption)).
% 86.93/87.19 tff(9062,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node21(c_e_h_2, c_i, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node21(c_e_h_2, c_i, s9, s10)))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9063,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node21(c_e_h_2, c_i, s9, s10)))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9064,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node21(c_e_h_2, c_i, s9, s10))),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9063, 9062])).
% 86.93/87.19 tff(9065,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9064, 51, 9048, 9061, 9060])).
% 86.93/87.19 tff(9066,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | node20(c_e_h_2, c_i, s9) | m_and_h_gate_v_out(c_e_h_2, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9067,plain,
% 86.93/87.19 (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9066, 9046, 9011])).
% 86.93/87.19 tff(9068,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s10)), introduced(assumption)).
% 86.93/87.19 tff(9069,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s10)), introduced(assumption)).
% 86.93/87.19 tff(9070,plain,
% 86.93/87.19 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9071,plain,
% 86.93/87.19 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9072,plain,
% 86.93/87.19 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9071, 9070])).
% 86.93/87.19 tff(9073,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9072, 365, 9069, 9068])).
% 86.93/87.19 tff(9074,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9075,plain,
% 86.93/87.19 (~m_c_h_element_v_in2(c_e_h_2, c_e, s10)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9074, 9067])).
% 86.93/87.19 tff(9076,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s9)), introduced(assumption)).
% 86.93/87.19 tff(9077,plain,
% 86.93/87.19 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9078,plain,
% 86.93/87.19 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9079,plain,
% 86.93/87.19 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9078, 9077])).
% 86.93/87.19 tff(9080,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9079, 365, 9047, 9076])).
% 86.93/87.19 tff(9081,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9082,plain,
% 86.93/87.19 (~m_c_h_element_v_in2(c_e_h_2, c_e, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9081, 9046])).
% 86.93/87.19 tff(9083,plain,
% 86.93/87.19 (~m_c_h_element_v_out(c_e_h_2, c_e, s9)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[4331, 3668, 4270])).
% 86.93/87.19 tff(9084,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s10)), introduced(assumption)).
% 86.93/87.19 tff(9085,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s9)), introduced(assumption)).
% 86.93/87.19 tff(9086,assumption,(~node16(c_e_h_2, c_e, s9)), introduced(assumption)).
% 86.93/87.19 tff(9087,assumption,(node14(c_e_h_2, c_e, s9, s10)), introduced(assumption)).
% 86.93/87.19 tff(9088,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~node14(c_e_h_2, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~node14(c_e_h_2, c_e, s9, s10)))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9089,plain,
% 86.93/87.19 (((~node14(c_e_h_2, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~node14(c_e_h_2, c_e, s9, s10)))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9090,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~node14(c_e_h_2, c_e, s9, s10))))),
% 86.93/87.19 inference(monotonicity,[status(thm)],[9089])).
% 86.93/87.19 tff(9091,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~node14(c_e_h_2, c_e, s9, s10)))),
% 86.93/87.19 inference(transitivity,[status(thm)],[9090, 9088])).
% 86.93/87.19 tff(9092,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9093,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~node14(c_e_h_2, c_e, s9, s10))),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9092, 9091])).
% 86.93/87.19 tff(9094,plain,
% 86.93/87.19 ($false),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9093, 283, 9084, 9087, 9085])).
% 86.93/87.19 tff(9095,plain,((~node14(c_e_h_2, c_e, s9, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 86.93/87.19 tff(9096,plain,
% 86.93/87.19 (~node14(c_e_h_2, c_e, s9, s10)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9095, 9084, 9085])).
% 86.93/87.19 tff(9097,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_2, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_2, c_e, s9, s10))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9098,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_2, c_e, s9, s10))),
% 86.93/87.19 inference(quant_inst,[status(thm)],[])).
% 86.93/87.19 tff(9099,plain,
% 86.93/87.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_2, c_e, s9, s10)),
% 86.93/87.19 inference(modus_ponens,[status(thm)],[9098, 9097])).
% 86.93/87.19 tff(9100,plain,
% 86.93/87.19 (node19(c_e_h_2, c_e, s9, s10)),
% 86.93/87.19 inference(unit_resolution,[status(thm)],[9099, 141, 3175])).
% 86.93/87.19 tff(9101,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s9, s10)) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | node16(c_e_h_2, c_e, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s9, s10)) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | node16(c_e_h_2, c_e, s9))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9102,plain,
% 86.93/87.19 ((node16(c_e_h_2, c_e, s9) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | (~node19(c_e_h_2, c_e, s9, s10))) <=> ((~node19(c_e_h_2, c_e, s9, s10)) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | node16(c_e_h_2, c_e, s9))),
% 86.93/87.19 inference(rewrite,[status(thm)],[])).
% 86.93/87.19 tff(9103,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s9) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | (~node19(c_e_h_2, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s9, s10)) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | node16(c_e_h_2, c_e, s9)))),
% 86.93/87.19 inference(monotonicity,[status(thm)],[9102])).
% 86.93/87.19 tff(9104,plain,
% 86.93/87.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s9) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | (~node19(c_e_h_2, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s9, s10)) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | node16(c_e_h_2, c_e, s9))),
% 87.01/87.20 inference(transitivity,[status(thm)],[9103, 9101])).
% 87.01/87.20 tff(9105,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s9) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | (~node19(c_e_h_2, c_e, s9, s10)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9106,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s9, s10)) | node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | node16(c_e_h_2, c_e, s9)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9105, 9104])).
% 87.01/87.20 tff(9107,plain,
% 87.01/87.20 (node14(c_e_h_2, c_e, s9, s10) | node15(c_e_h_2, c_e, s9, s10) | node16(c_e_h_2, c_e, s9)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9106, 189, 9100])).
% 87.01/87.20 tff(9108,plain,
% 87.01/87.20 (node15(c_e_h_2, c_e, s9, s10)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9107, 9096, 9086])).
% 87.01/87.20 tff(9109,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | (~node15(c_e_h_2, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | (~node15(c_e_h_2, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9110,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | (~node15(c_e_h_2, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9111,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | (~node15(c_e_h_2, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9110, 9109])).
% 87.01/87.20 tff(9112,plain,
% 87.01/87.20 ($false),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9111, 173, 9084, 4386, 9108])).
% 87.01/87.20 tff(9113,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9) | node16(c_e_h_2, c_e, s9) | m_c_h_element_v_in1(c_e_h_2, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.20 tff(9114,plain,
% 87.01/87.20 (node16(c_e_h_2, c_e, s9)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9113, 9085, 4386, 9084])).
% 87.01/87.20 tff(9115,assumption,(node18(c_e_h_2, c_e, s9, s10)), introduced(assumption)).
% 87.01/87.20 tff(9116,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9) | (~node18(c_e_h_2, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9) | (~node18(c_e_h_2, c_e, s9, s10)))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9117,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9) | (~node18(c_e_h_2, c_e, s9, s10)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9118,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9) | (~node18(c_e_h_2, c_e, s9, s10))),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9117, 9116])).
% 87.01/87.20 tff(9119,plain,
% 87.01/87.20 ($false),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9118, 124, 9084, 4386, 9115])).
% 87.01/87.20 tff(9120,plain,((~node18(c_e_h_2, c_e, s9, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.20 tff(9121,plain,
% 87.01/87.20 (~node18(c_e_h_2, c_e, s9, s10)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9120, 9084, 4386])).
% 87.01/87.20 tff(9122,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s9, s10)) | node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s9, s10)) | node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9123,plain,
% 87.01/87.20 ((node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10) | (~node19(c_e_h_2, c_e, s9, s10))) <=> ((~node19(c_e_h_2, c_e, s9, s10)) | node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9124,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10) | (~node19(c_e_h_2, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s9, s10)) | node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10)))),
% 87.01/87.20 inference(monotonicity,[status(thm)],[9123])).
% 87.01/87.20 tff(9125,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10) | (~node19(c_e_h_2, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s9, s10)) | node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10))),
% 87.01/87.20 inference(transitivity,[status(thm)],[9124, 9122])).
% 87.01/87.20 tff(9126,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10) | (~node19(c_e_h_2, c_e, s9, s10)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9127,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s9, s10)) | node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9126, 9125])).
% 87.01/87.20 tff(9128,plain,
% 87.01/87.20 (node17(c_e_h_2, c_e, s9) | node18(c_e_h_2, c_e, s9, s10)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9127, 156, 9100])).
% 87.01/87.20 tff(9129,plain,
% 87.01/87.20 (node17(c_e_h_2, c_e, s9)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9128, 9121])).
% 87.01/87.20 tff(9130,plain,
% 87.01/87.20 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | (~node17(c_e_h_2, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | (~node17(c_e_h_2, c_e, s9)))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9131,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | (~node17(c_e_h_2, c_e, s9)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9132,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s9)) | (~node17(c_e_h_2, c_e, s9))),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9131, 9130])).
% 87.01/87.20 tff(9133,plain,
% 87.01/87.20 (m_c_h_element_v_in1(c_e_h_2, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s9))),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9132, 245, 9129])).
% 87.01/87.20 tff(9134,plain,
% 87.01/87.20 (~m_c_h_element_v_in2(c_e_h_2, c_e, s9)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9133, 9085])).
% 87.01/87.20 tff(9135,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s9)), introduced(assumption)).
% 87.01/87.20 tff(9136,assumption,(node16(c_e_h_2, c_e, s9)), introduced(assumption)).
% 87.01/87.20 tff(9137,plain,
% 87.01/87.20 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s9)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | m_c_h_element_v_in2(c_e_h_2, c_e, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s9)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | m_c_h_element_v_in2(c_e_h_2, c_e, s9))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9138,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s9)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | m_c_h_element_v_in2(c_e_h_2, c_e, s9))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9139,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s9)) | m_c_h_element_v_in1(c_e_h_2, c_e, s9) | m_c_h_element_v_in2(c_e_h_2, c_e, s9)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9138, 9137])).
% 87.01/87.20 tff(9140,plain,
% 87.01/87.20 ($false),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9139, 228, 9136, 9135, 9085])).
% 87.01/87.20 tff(9141,plain,((~node16(c_e_h_2, c_e, s9)) | m_c_h_element_v_in2(c_e_h_2, c_e, s9) | m_c_h_element_v_in1(c_e_h_2, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.20 tff(9142,plain,
% 87.01/87.20 ($false),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9141, 9134, 9114, 9085])).
% 87.01/87.20 tff(9143,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s9) | m_c_h_element_v_out(c_e_h_2, c_e, s9) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.20 tff(9144,plain,
% 87.01/87.20 (m_c_h_element_v_in1(c_e_h_2, c_e, s9)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9143, 9084, 4386])).
% 87.01/87.20 tff(9145,plain,
% 87.01/87.20 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s9)) | m_c_h_element_v_in2(c_e_h_2, c_e, s9) | (~node17(c_e_h_2, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s9)) | m_c_h_element_v_in2(c_e_h_2, c_e, s9) | (~node17(c_e_h_2, c_e, s9)))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9146,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s9)) | m_c_h_element_v_in2(c_e_h_2, c_e, s9) | (~node17(c_e_h_2, c_e, s9)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9147,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s9)) | m_c_h_element_v_in2(c_e_h_2, c_e, s9) | (~node17(c_e_h_2, c_e, s9))),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9146, 9145])).
% 87.01/87.20 tff(9148,plain,
% 87.01/87.20 ($false),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9147, 209, 9129, 9135, 9144])).
% 87.01/87.20 tff(9149,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s9) | m_c_h_element_v_out(c_e_h_2, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.20 tff(9150,plain,
% 87.01/87.20 (~m_c_h_element_v_out(c_e_h_2, c_e, s10)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9149, 9083, 9082])).
% 87.01/87.20 tff(9151,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s11)), introduced(assumption)).
% 87.01/87.20 tff(9152,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s10)), introduced(assumption)).
% 87.01/87.20 tff(9153,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s10)), introduced(assumption)).
% 87.01/87.20 tff(9154,assumption,(node15(c_e_h_2, c_e, s10, s11)), introduced(assumption)).
% 87.01/87.20 tff(9155,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | (~node15(c_e_h_2, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | (~node15(c_e_h_2, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9156,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | (~node15(c_e_h_2, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9157,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | (~node15(c_e_h_2, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9156, 9155])).
% 87.01/87.20 tff(9158,plain,
% 87.01/87.20 ($false),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9157, 173, 9151, 9153, 9154])).
% 87.01/87.20 tff(9159,plain,((~node15(c_e_h_2, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.20 tff(9160,plain,
% 87.01/87.20 (~node15(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9159, 9151, 9153])).
% 87.01/87.20 tff(9161,assumption,(node18(c_e_h_2, c_e, s10, s11)), introduced(assumption)).
% 87.01/87.20 tff(9162,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10) | (~node18(c_e_h_2, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10) | (~node18(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9163,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10) | (~node18(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9164,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10) | (~node18(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9163, 9162])).
% 87.01/87.20 tff(9165,plain,
% 87.01/87.20 ($false),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9164, 124, 9151, 9153, 9161])).
% 87.01/87.20 tff(9166,plain,((~node18(c_e_h_2, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_out(c_e_h_2, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.20 tff(9167,plain,
% 87.01/87.20 (~node18(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9166, 9151, 9153])).
% 87.01/87.20 tff(9168,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_2, c_e, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9169,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9170,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9169, 9168])).
% 87.01/87.20 tff(9171,plain,
% 87.01/87.20 (node19(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9170, 141, 3778])).
% 87.01/87.20 tff(9172,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s10) | (~node19(c_e_h_2, c_e, s10, s11)) | node18(c_e_h_2, c_e, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s10) | (~node19(c_e_h_2, c_e, s10, s11)) | node18(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9173,plain,
% 87.01/87.20 ((node17(c_e_h_2, c_e, s10) | node18(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11))) <=> (node17(c_e_h_2, c_e, s10) | (~node19(c_e_h_2, c_e, s10, s11)) | node18(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9174,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s10) | node18(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s10) | (~node19(c_e_h_2, c_e, s10, s11)) | node18(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(monotonicity,[status(thm)],[9173])).
% 87.01/87.20 tff(9175,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s10) | node18(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s10) | (~node19(c_e_h_2, c_e, s10, s11)) | node18(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(transitivity,[status(thm)],[9174, 9172])).
% 87.01/87.20 tff(9176,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s10) | node18(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9177,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s10) | (~node19(c_e_h_2, c_e, s10, s11)) | node18(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9176, 9175])).
% 87.01/87.20 tff(9178,plain,
% 87.01/87.20 (node17(c_e_h_2, c_e, s10) | node18(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9177, 156, 9171])).
% 87.01/87.20 tff(9179,plain,
% 87.01/87.20 (node17(c_e_h_2, c_e, s10)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9178, 9167])).
% 87.01/87.20 tff(9180,assumption,(node17(c_e_h_2, c_e, s10)), introduced(assumption)).
% 87.01/87.20 tff(9181,plain,
% 87.01/87.20 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | (~node17(c_e_h_2, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | (~node17(c_e_h_2, c_e, s10)))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9182,plain,
% 87.01/87.20 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~node17(c_e_h_2, c_e, s10))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | (~node17(c_e_h_2, c_e, s10)))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9183,plain,
% 87.01/87.20 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~node17(c_e_h_2, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | (~node17(c_e_h_2, c_e, s10))))),
% 87.01/87.20 inference(monotonicity,[status(thm)],[9182])).
% 87.01/87.20 tff(9184,plain,
% 87.01/87.20 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~node17(c_e_h_2, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | (~node17(c_e_h_2, c_e, s10)))),
% 87.01/87.20 inference(transitivity,[status(thm)],[9183, 9181])).
% 87.01/87.20 tff(9185,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~node17(c_e_h_2, c_e, s10)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9186,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s10)) | (~node17(c_e_h_2, c_e, s10))),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9185, 9184])).
% 87.01/87.20 tff(9187,plain,
% 87.01/87.20 (m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s10))),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9186, 209, 9180])).
% 87.01/87.20 tff(9188,plain,
% 87.01/87.20 (~m_c_h_element_v_in1(c_e_h_2, c_e, s10)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9187, 9152])).
% 87.01/87.20 tff(9189,assumption,(~node15(c_e_h_2, c_e, s10, s11)), introduced(assumption)).
% 87.01/87.20 tff(9190,plain,
% 87.01/87.20 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | m_c_h_element_v_in2(c_e_h_2, c_e, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | m_c_h_element_v_in2(c_e_h_2, c_e, s10))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9191,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | m_c_h_element_v_in2(c_e_h_2, c_e, s10))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9192,plain,
% 87.01/87.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s10)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | m_c_h_element_v_in2(c_e_h_2, c_e, s10)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9191, 9190])).
% 87.01/87.20 tff(9193,plain,
% 87.01/87.20 (~node16(c_e_h_2, c_e, s10)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9192, 228, 9152, 9188])).
% 87.01/87.20 tff(9194,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)) | node15(c_e_h_2, c_e, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)) | node15(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9195,plain,
% 87.01/87.20 ((node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | node15(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11))) <=> (node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)) | node15(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9196,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | node15(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)) | node15(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(monotonicity,[status(thm)],[9195])).
% 87.01/87.20 tff(9197,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | node15(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)) | node15(c_e_h_2, c_e, s10, s11))),
% 87.01/87.20 inference(transitivity,[status(thm)],[9196, 9194])).
% 87.01/87.20 tff(9198,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | node15(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(quant_inst,[status(thm)],[])).
% 87.01/87.20 tff(9199,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | (~node19(c_e_h_2, c_e, s10, s11)) | node15(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(modus_ponens,[status(thm)],[9198, 9197])).
% 87.01/87.20 tff(9200,plain,
% 87.01/87.20 (node16(c_e_h_2, c_e, s10) | node14(c_e_h_2, c_e, s10, s11) | node15(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9199, 189, 9171])).
% 87.01/87.20 tff(9201,plain,
% 87.01/87.20 (node14(c_e_h_2, c_e, s10, s11)),
% 87.01/87.20 inference(unit_resolution,[status(thm)],[9200, 9193, 9189])).
% 87.01/87.20 tff(9202,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~node14(c_e_h_2, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~node14(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9203,plain,
% 87.01/87.20 (((~node14(c_e_h_2, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~node14(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(rewrite,[status(thm)],[])).
% 87.01/87.20 tff(9204,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~node14(c_e_h_2, c_e, s10, s11))))),
% 87.01/87.20 inference(monotonicity,[status(thm)],[9203])).
% 87.01/87.20 tff(9205,plain,
% 87.01/87.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~node14(c_e_h_2, c_e, s10, s11)))),
% 87.01/87.20 inference(transitivity,[status(thm)],[9204, 9202])).
% 87.01/87.20 tff(9206,plain,
% 87.01/87.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9207,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s10) | (~node14(c_e_h_2, c_e, s10, s11))),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9206, 9205])).
% 87.01/87.21 tff(9208,plain,
% 87.01/87.21 ($false),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9207, 283, 9151, 9201, 9188])).
% 87.01/87.21 tff(9209,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | node15(c_e_h_2, c_e, s10, s11) | (~node17(c_e_h_2, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.21 tff(9210,plain,
% 87.01/87.21 ($false),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9209, 9179, 9160, 9152, 9151])).
% 87.01/87.21 tff(9211,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | m_c_h_element_v_out(c_e_h_2, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.21 tff(9212,plain,
% 87.01/87.21 (~m_c_h_element_v_out(c_e_h_2, c_e, s11)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9211, 9150, 9075])).
% 87.01/87.21 tff(9213,plain,
% 87.01/87.21 (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[8485, 3814])).
% 87.01/87.21 tff(9214,plain,
% 87.01/87.21 (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[8514, 9213])).
% 87.01/87.21 tff(9215,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s8)), introduced(assumption)).
% 87.01/87.21 tff(9216,plain,
% 87.01/87.21 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9217,plain,
% 87.01/87.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9218,plain,
% 87.01/87.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9217, 9216])).
% 87.01/87.21 tff(9219,plain,
% 87.01/87.21 ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9218, 1638])).
% 87.01/87.21 tff(9220,plain,
% 87.01/87.21 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9219, 2131])).
% 87.01/87.21 tff(9221,plain,
% 87.01/87.21 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s7))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9222,plain,
% 87.01/87.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s7))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9223,plain,
% 87.01/87.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s7)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9222, 9221])).
% 87.01/87.21 tff(9224,plain,
% 87.01/87.21 (~node20(c_e_h_2, c_l, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9223, 1535, 9220])).
% 87.01/87.21 tff(9225,assumption,(node21(c_e_h_2, c_l, s7, s8)), introduced(assumption)).
% 87.01/87.21 tff(9226,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | (~node21(c_e_h_2, c_l, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | (~node21(c_e_h_2, c_l, s7, s8)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9227,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | (~node21(c_e_h_2, c_l, s7, s8)))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9228,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | (~node21(c_e_h_2, c_l, s7, s8))),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9227, 9226])).
% 87.01/87.21 tff(9229,plain,
% 87.01/87.21 ($false),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9228, 51, 9225, 9224, 9215])).
% 87.01/87.21 tff(9230,plain,((~node21(c_e_h_2, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s8))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.21 tff(9231,plain,
% 87.01/87.21 (~node21(c_e_h_2, c_l, s7, s8)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9230, 9215])).
% 87.01/87.21 tff(9232,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_l, s7, s8) | node22(c_e_h_2, c_l, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_l, s7, s8) | node22(c_e_h_2, c_l, s7, s8))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9233,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_l, s7, s8) | node22(c_e_h_2, c_l, s7, s8))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9234,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_l, s7, s8) | node22(c_e_h_2, c_l, s7, s8)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9233, 9232])).
% 87.01/87.21 tff(9235,plain,
% 87.01/87.21 (node21(c_e_h_2, c_l, s7, s8) | node22(c_e_h_2, c_l, s7, s8)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9234, 81, 2152])).
% 87.01/87.21 tff(9236,plain,
% 87.01/87.21 (node22(c_e_h_2, c_l, s7, s8)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9235, 9231])).
% 87.01/87.21 tff(9237,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s7)), introduced(assumption)).
% 87.01/87.21 tff(9238,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | (~node22(c_e_h_2, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | (~node22(c_e_h_2, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9239,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | (~node22(c_e_h_2, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9240,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | (~node22(c_e_h_2, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9239, 9238])).
% 87.01/87.21 tff(9241,plain,
% 87.01/87.21 ($false),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9240, 107, 9237, 9236, 9215])).
% 87.01/87.21 tff(9242,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.21 tff(9243,plain,
% 87.01/87.21 (~m_and_h_gate_v_out(c_e_h_2, c_l, s8)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9242, 9214])).
% 87.01/87.21 tff(9244,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s8)), introduced(assumption)).
% 87.01/87.21 tff(9245,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s8)), introduced(assumption)).
% 87.01/87.21 tff(9246,plain,
% 87.01/87.21 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9247,plain,
% 87.01/87.21 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9248,plain,
% 87.01/87.21 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9247, 9246])).
% 87.01/87.21 tff(9249,plain,
% 87.01/87.21 ($false),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9248, 801, 9245, 9244])).
% 87.01/87.21 tff(9250,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.21 tff(9251,plain,
% 87.01/87.21 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9250, 9243])).
% 87.01/87.21 tff(9252,plain,
% 87.01/87.21 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[8518, 801, 9214])).
% 87.01/87.21 tff(9253,plain,
% 87.01/87.21 (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[8828, 9252, 9012])).
% 87.01/87.21 tff(9254,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s8)), introduced(assumption)).
% 87.01/87.21 tff(9255,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s7)), introduced(assumption)).
% 87.01/87.21 tff(9256,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s6)), introduced(assumption)).
% 87.01/87.21 tff(9257,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s7)), introduced(assumption)).
% 87.01/87.21 tff(9258,assumption,(node15(c_e_h_1, c_f, s6, s7)), introduced(assumption)).
% 87.01/87.21 tff(9259,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node15(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node15(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9260,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node15(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9261,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node15(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9260, 9259])).
% 87.01/87.21 tff(9262,plain,
% 87.01/87.21 ($false),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9261, 173, 9258, 9257, 9256])).
% 87.01/87.21 tff(9263,plain,((~node15(c_e_h_1, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.21 tff(9264,plain,
% 87.01/87.21 (~node15(c_e_h_1, c_f, s6, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9263, 9256, 9257])).
% 87.01/87.21 tff(9265,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s6)), introduced(assumption)).
% 87.01/87.21 tff(9266,assumption,(~node15(c_e_h_1, c_f, s6, s7)), introduced(assumption)).
% 87.01/87.21 tff(9267,plain,
% 87.01/87.21 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9268,plain,
% 87.01/87.21 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9269,plain,
% 87.01/87.21 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9268, 9267])).
% 87.01/87.21 tff(9270,plain,
% 87.01/87.21 (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9269, 2218, 6728])).
% 87.01/87.21 tff(9271,plain,
% 87.01/87.21 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | m_c_h_element_v_in2(c_e_h_1, c_f, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | m_c_h_element_v_in2(c_e_h_1, c_f, s6))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9272,plain,
% 87.01/87.21 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | m_c_h_element_v_in2(c_e_h_1, c_f, s6))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9273,plain,
% 87.01/87.21 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | m_c_h_element_v_in2(c_e_h_1, c_f, s6)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9272, 9271])).
% 87.01/87.21 tff(9274,plain,
% 87.01/87.21 ((~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9273, 228, 9270])).
% 87.01/87.21 tff(9275,plain,
% 87.01/87.21 (~node16(c_e_h_1, c_f, s6)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9274, 9265])).
% 87.01/87.21 tff(9276,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_f, s6, s7))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9277,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_f, s6, s7))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9278,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_f, s6, s7)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9277, 9276])).
% 87.01/87.21 tff(9279,plain,
% 87.01/87.21 (node19(c_e_h_1, c_f, s6, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9278, 141, 1552])).
% 87.01/87.21 tff(9280,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9281,plain,
% 87.01/87.21 ((node16(c_e_h_1, c_f, s6) | node14(c_e_h_1, c_f, s6, s7) | node15(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7))) <=> (node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9282,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s6) | node14(c_e_h_1, c_f, s6, s7) | node15(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7)))),
% 87.01/87.21 inference(monotonicity,[status(thm)],[9281])).
% 87.01/87.21 tff(9283,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s6) | node14(c_e_h_1, c_f, s6, s7) | node15(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7))),
% 87.01/87.21 inference(transitivity,[status(thm)],[9282, 9280])).
% 87.01/87.21 tff(9284,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s6) | node14(c_e_h_1, c_f, s6, s7) | node15(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9285,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7)),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9284, 9283])).
% 87.01/87.21 tff(9286,plain,
% 87.01/87.21 (node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6) | node15(c_e_h_1, c_f, s6, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9285, 189, 9279])).
% 87.01/87.21 tff(9287,plain,
% 87.01/87.21 (node14(c_e_h_1, c_f, s6, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9286, 9275, 9266])).
% 87.01/87.21 tff(9288,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9289,plain,
% 87.01/87.21 (((~node14(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9290,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7))))),
% 87.01/87.21 inference(monotonicity,[status(thm)],[9289])).
% 87.01/87.21 tff(9291,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 87.01/87.21 inference(transitivity,[status(thm)],[9290, 9288])).
% 87.01/87.21 tff(9292,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9293,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9292, 9291])).
% 87.01/87.21 tff(9294,plain,
% 87.01/87.21 ($false),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9293, 283, 9287, 9265, 9257])).
% 87.01/87.21 tff(9295,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | node15(c_e_h_1, c_f, s6, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.21 tff(9296,plain,
% 87.01/87.21 (m_c_h_element_v_in1(c_e_h_1, c_f, s6)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9295, 9264, 9257])).
% 87.01/87.21 tff(9297,plain,
% 87.01/87.21 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9298,plain,
% 87.01/87.21 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~node17(c_e_h_1, c_f, s6))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9299,plain,
% 87.01/87.21 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~node17(c_e_h_1, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6))))),
% 87.01/87.21 inference(monotonicity,[status(thm)],[9298])).
% 87.01/87.21 tff(9300,plain,
% 87.01/87.21 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~node17(c_e_h_1, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6)))),
% 87.01/87.21 inference(transitivity,[status(thm)],[9299, 9297])).
% 87.01/87.21 tff(9301,plain,
% 87.01/87.21 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~node17(c_e_h_1, c_f, s6)))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9302,plain,
% 87.01/87.21 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6))),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9301, 9300])).
% 87.01/87.21 tff(9303,plain,
% 87.01/87.21 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6))),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9302, 209, 9270])).
% 87.01/87.21 tff(9304,plain,
% 87.01/87.21 (~node17(c_e_h_1, c_f, s6)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9303, 9296])).
% 87.01/87.21 tff(9305,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s6, s7) | node17(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s6, s7) | node17(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9306,plain,
% 87.01/87.21 ((node17(c_e_h_1, c_f, s6) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7))) <=> (node18(c_e_h_1, c_f, s6, s7) | node17(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9307,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s6) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s6, s7) | node17(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7))))),
% 87.01/87.21 inference(monotonicity,[status(thm)],[9306])).
% 87.01/87.21 tff(9308,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s6) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s6, s7) | node17(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7)))),
% 87.01/87.21 inference(transitivity,[status(thm)],[9307, 9305])).
% 87.01/87.21 tff(9309,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s6) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))),
% 87.01/87.21 inference(quant_inst,[status(thm)],[])).
% 87.01/87.21 tff(9310,plain,
% 87.01/87.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s6, s7) | node17(c_e_h_1, c_f, s6) | (~node19(c_e_h_1, c_f, s6, s7))),
% 87.01/87.21 inference(modus_ponens,[status(thm)],[9309, 9308])).
% 87.01/87.21 tff(9311,plain,
% 87.01/87.21 (node18(c_e_h_1, c_f, s6, s7) | node17(c_e_h_1, c_f, s6)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9310, 156, 9279])).
% 87.01/87.21 tff(9312,plain,
% 87.01/87.21 (node18(c_e_h_1, c_f, s6, s7)),
% 87.01/87.21 inference(unit_resolution,[status(thm)],[9311, 9304])).
% 87.01/87.21 tff(9313,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9314,plain,
% 87.01/87.21 (((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~node18(c_e_h_1, c_f, s6, s7))) <=> ((~node18(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 87.01/87.21 inference(rewrite,[status(thm)],[])).
% 87.01/87.21 tff(9315,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~node18(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7))))),
% 87.01/87.21 inference(monotonicity,[status(thm)],[9314])).
% 87.01/87.21 tff(9316,plain,
% 87.01/87.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~node18(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 87.01/87.22 inference(transitivity,[status(thm)],[9315, 9313])).
% 87.01/87.22 tff(9317,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~node18(c_e_h_1, c_f, s6, s7)))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9318,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9317, 9316])).
% 87.01/87.22 tff(9319,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9318, 124, 9312, 9257, 9256])).
% 87.01/87.22 tff(9320,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9321,plain,
% 87.01/87.22 (~m_c_h_element_v_out(c_e_h_1, c_f, s7)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9320, 8745])).
% 87.01/87.22 tff(9322,plain,
% 87.01/87.22 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9323,plain,
% 87.01/87.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9324,plain,
% 87.01/87.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9323, 9322])).
% 87.01/87.22 tff(9325,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9324, 1666, 9321, 9255])).
% 87.01/87.22 tff(9326,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9327,plain,
% 87.01/87.22 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s7))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9328,plain,
% 87.01/87.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s7))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9329,plain,
% 87.01/87.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s7)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9328, 9327])).
% 87.01/87.22 tff(9330,plain,
% 87.01/87.22 (~node20(c_e_h_1, c_q, s7)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9329, 37, 9326])).
% 87.01/87.22 tff(9331,assumption,(~node20(c_e_h_1, c_q, s7)), introduced(assumption)).
% 87.01/87.22 tff(9332,assumption,(node21(c_e_h_1, c_q, s7, s8)), introduced(assumption)).
% 87.01/87.22 tff(9333,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7) | (~node21(c_e_h_1, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7) | (~node21(c_e_h_1, c_q, s7, s8)))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9334,plain,
% 87.01/87.22 ((node20(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node21(c_e_h_1, c_q, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7) | (~node21(c_e_h_1, c_q, s7, s8)))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9335,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node21(c_e_h_1, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7) | (~node21(c_e_h_1, c_q, s7, s8))))),
% 87.01/87.22 inference(monotonicity,[status(thm)],[9334])).
% 87.01/87.22 tff(9336,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node21(c_e_h_1, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7) | (~node21(c_e_h_1, c_q, s7, s8)))),
% 87.01/87.22 inference(transitivity,[status(thm)],[9335, 9333])).
% 87.01/87.22 tff(9337,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node21(c_e_h_1, c_q, s7, s8)))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9338,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7) | (~node21(c_e_h_1, c_q, s7, s8))),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9337, 9336])).
% 87.01/87.22 tff(9339,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9338, 51, 9254, 9332, 9331])).
% 87.01/87.22 tff(9340,plain,((~node21(c_e_h_1, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9341,plain,
% 87.01/87.22 ((~node21(c_e_h_1, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9340, 9330])).
% 87.01/87.22 tff(9342,plain,
% 87.01/87.22 (~node21(c_e_h_1, c_q, s7, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9341, 9254])).
% 87.01/87.22 tff(9343,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s7)), introduced(assumption)).
% 87.01/87.22 tff(9344,assumption,(node22(c_e_h_1, c_q, s7, s8)), introduced(assumption)).
% 87.01/87.22 tff(9345,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node22(c_e_h_1, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node22(c_e_h_1, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9346,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node22(c_e_h_1, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9347,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node22(c_e_h_1, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9346, 9345])).
% 87.01/87.22 tff(9348,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9347, 107, 9254, 9343, 9344])).
% 87.01/87.22 tff(9349,plain,((~node22(c_e_h_1, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9350,plain,
% 87.01/87.22 (~node22(c_e_h_1, c_q, s7, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9349, 9254, 9343])).
% 87.01/87.22 tff(9351,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9352,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9353,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9352, 9351])).
% 87.01/87.22 tff(9354,plain,
% 87.01/87.22 (node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9353, 81, 2152])).
% 87.01/87.22 tff(9355,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9354, 9350, 9342])).
% 87.01/87.22 tff(9356,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9357,plain,
% 87.01/87.22 (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9356, 8781])).
% 87.01/87.22 tff(9358,plain,
% 87.01/87.22 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s8))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9359,plain,
% 87.01/87.22 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s8))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9360,plain,
% 87.01/87.22 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s8)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9359, 9358])).
% 87.01/87.22 tff(9361,plain,
% 87.01/87.22 (node3(c_e_h_1, c_e_h_2, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9360, 817, 814])).
% 87.01/87.22 tff(9362,plain,
% 87.01/87.22 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s8)) | (~node3(c_e_h_1, c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s8)) | (~node3(c_e_h_1, c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9363,plain,
% 87.01/87.22 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s8)) | (~node3(c_e_h_1, c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9364,plain,
% 87.01/87.22 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s8)) | (~node3(c_e_h_1, c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9363, 9362])).
% 87.01/87.22 tff(9365,plain,
% 87.01/87.22 ((~m_cell_v_ack(c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9364, 836, 9361])).
% 87.01/87.22 tff(9366,plain,
% 87.01/87.22 (~m_cell_v_ack(c_e_h_2, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9365, 9357])).
% 87.01/87.22 tff(9367,plain,
% 87.01/87.22 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)) | m_cell_v_ack(c_e_h_2, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)) | m_cell_v_ack(c_e_h_2, s8))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9368,plain,
% 87.01/87.22 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)) | m_cell_v_ack(c_e_h_2, s8))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9369,plain,
% 87.01/87.22 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)) | m_cell_v_ack(c_e_h_2, s8)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9368, 9367])).
% 87.01/87.22 tff(9370,plain,
% 87.01/87.22 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9369, 848, 9366])).
% 87.01/87.22 tff(9371,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s8)), introduced(assumption)).
% 87.01/87.22 tff(9372,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s9)), introduced(assumption)).
% 87.01/87.22 tff(9373,assumption,(node6(c_e_h_2, c_j, s8, s9)), introduced(assumption)).
% 87.01/87.22 tff(9374,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | (~node6(c_e_h_2, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | (~node6(c_e_h_2, c_j, s8, s9)))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9375,plain,
% 87.01/87.22 (((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | (~node6(c_e_h_2, c_j, s8, s9)))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9376,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | (~node6(c_e_h_2, c_j, s8, s9))))),
% 87.01/87.22 inference(monotonicity,[status(thm)],[9375])).
% 87.01/87.22 tff(9377,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | (~node6(c_e_h_2, c_j, s8, s9)))),
% 87.01/87.22 inference(transitivity,[status(thm)],[9376, 9374])).
% 87.01/87.22 tff(9378,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9379,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | (~node6(c_e_h_2, c_j, s8, s9))),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9378, 9377])).
% 87.01/87.22 tff(9380,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9379, 899, 9372, 9371, 9373])).
% 87.01/87.22 tff(9381,plain,((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9382,plain,
% 87.01/87.22 (~node6(c_e_h_2, c_j, s8, s9)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9381, 9372, 9371])).
% 87.01/87.22 tff(9383,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)), introduced(assumption)).
% 87.01/87.22 tff(9384,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)), introduced(assumption)).
% 87.01/87.22 tff(9385,assumption,(node5(c_e_h_2, c_j, s8, s9)), introduced(assumption)).
% 87.01/87.22 tff(9386,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9)))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9387,plain,
% 87.01/87.22 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9)))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9388,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9))))),
% 87.01/87.22 inference(monotonicity,[status(thm)],[9387])).
% 87.01/87.22 tff(9389,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9)))),
% 87.01/87.22 inference(transitivity,[status(thm)],[9388, 9386])).
% 87.01/87.22 tff(9390,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9391,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | (~node5(c_e_h_2, c_j, s8, s9))),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9390, 9389])).
% 87.01/87.22 tff(9392,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9391, 862, 9372, 9385, 9384, 9383])).
% 87.01/87.22 tff(9393,plain,((~node5(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9394,plain,
% 87.01/87.22 (~node5(c_e_h_2, c_j, s8, s9)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9393, 9372, 9384, 9383])).
% 87.01/87.22 tff(9395,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node5(c_e_h_2, c_j, s8, s9) | node6(c_e_h_2, c_j, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_2, c_j, s8, s9) | node6(c_e_h_2, c_j, s8, s9))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9396,plain,
% 87.01/87.22 ((node6(c_e_h_2, c_j, s8, s9) | node5(c_e_h_2, c_j, s8, s9) | (~trans(s8, s9))) <=> ((~trans(s8, s9)) | node5(c_e_h_2, c_j, s8, s9) | node6(c_e_h_2, c_j, s8, s9))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9397,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s8, s9) | node5(c_e_h_2, c_j, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node5(c_e_h_2, c_j, s8, s9) | node6(c_e_h_2, c_j, s8, s9)))),
% 87.01/87.22 inference(monotonicity,[status(thm)],[9396])).
% 87.01/87.22 tff(9398,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s8, s9) | node5(c_e_h_2, c_j, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_2, c_j, s8, s9) | node6(c_e_h_2, c_j, s8, s9))),
% 87.01/87.22 inference(transitivity,[status(thm)],[9397, 9395])).
% 87.01/87.22 tff(9399,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s8, s9) | node5(c_e_h_2, c_j, s8, s9) | (~trans(s8, s9)))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9400,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_2, c_j, s8, s9) | node6(c_e_h_2, c_j, s8, s9)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9399, 9398])).
% 87.01/87.22 tff(9401,plain,
% 87.01/87.22 (node5(c_e_h_2, c_j, s8, s9) | node6(c_e_h_2, c_j, s8, s9)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9400, 881, 2636])).
% 87.01/87.22 tff(9402,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9401, 9394, 9382])).
% 87.01/87.22 tff(9403,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s8) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9404,plain,
% 87.01/87.22 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s8) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9403, 9370])).
% 87.01/87.22 tff(9405,plain,
% 87.01/87.22 (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9404, 9253, 9251])).
% 87.01/87.22 tff(9406,plain,
% 87.01/87.22 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9407,plain,
% 87.01/87.22 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9408,plain,
% 87.01/87.22 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9407, 9406])).
% 87.01/87.22 tff(9409,plain,
% 87.01/87.22 (~m_c_h_element_v_in2(c_e_h_2, c_h, s9)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9408, 309, 9405])).
% 87.01/87.22 tff(9410,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s9)), introduced(assumption)).
% 87.01/87.22 tff(9411,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s10)), introduced(assumption)).
% 87.01/87.22 tff(9412,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s9)), introduced(assumption)).
% 87.01/87.22 tff(9413,assumption,(node15(c_e_h_2, c_h, s9, s10)), introduced(assumption)).
% 87.01/87.22 tff(9414,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node15(c_e_h_2, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node15(c_e_h_2, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9415,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node15(c_e_h_2, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9416,plain,
% 87.01/87.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node15(c_e_h_2, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9415, 9414])).
% 87.01/87.22 tff(9417,plain,
% 87.01/87.22 ($false),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9416, 173, 9411, 9412, 9413])).
% 87.01/87.22 tff(9418,plain,((~node15(c_e_h_2, c_h, s9, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.22 tff(9419,plain,
% 87.01/87.22 (~node15(c_e_h_2, c_h, s9, s10)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9418, 9411, 9412])).
% 87.01/87.22 tff(9420,assumption,(~node15(c_e_h_2, c_h, s9, s10)), introduced(assumption)).
% 87.01/87.22 tff(9421,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s9)), introduced(assumption)).
% 87.01/87.22 tff(9422,plain,
% 87.01/87.22 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | m_c_h_element_v_in2(c_e_h_2, c_h, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | m_c_h_element_v_in2(c_e_h_2, c_h, s9))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9423,plain,
% 87.01/87.22 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | m_c_h_element_v_in2(c_e_h_2, c_h, s9))),
% 87.01/87.22 inference(quant_inst,[status(thm)],[])).
% 87.01/87.22 tff(9424,plain,
% 87.01/87.22 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | m_c_h_element_v_in2(c_e_h_2, c_h, s9)),
% 87.01/87.22 inference(modus_ponens,[status(thm)],[9423, 9422])).
% 87.01/87.22 tff(9425,plain,
% 87.01/87.22 ((~node16(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9424, 228, 9410])).
% 87.01/87.22 tff(9426,plain,
% 87.01/87.22 (~node16(c_e_h_2, c_h, s9)),
% 87.01/87.22 inference(unit_resolution,[status(thm)],[9425, 9421])).
% 87.01/87.22 tff(9427,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node14(c_e_h_2, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node14(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9428,plain,
% 87.01/87.22 (((~node14(c_e_h_2, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node14(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.22 inference(rewrite,[status(thm)],[])).
% 87.01/87.22 tff(9429,plain,
% 87.01/87.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node14(c_e_h_2, c_h, s9, s10))))),
% 87.01/87.23 inference(monotonicity,[status(thm)],[9428])).
% 87.01/87.23 tff(9430,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node14(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(transitivity,[status(thm)],[9429, 9427])).
% 87.01/87.23 tff(9431,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9432,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node14(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9431, 9430])).
% 87.01/87.23 tff(9433,plain,
% 87.01/87.23 (m_c_h_element_v_in1(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node14(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9432, 283])).
% 87.01/87.23 tff(9434,plain,
% 87.01/87.23 (~node14(c_e_h_2, c_h, s9, s10)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9433, 9421, 9411])).
% 87.01/87.23 tff(9435,assumption,(~node19(c_e_h_2, c_h, s9, s10)), introduced(assumption)).
% 87.01/87.23 tff(9436,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_2, c_h, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9437,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9438,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_2, c_h, s9, s10)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9437, 9436])).
% 87.01/87.23 tff(9439,plain,
% 87.01/87.23 ($false),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9438, 141, 3175, 9435])).
% 87.01/87.23 tff(9440,plain,(node19(c_e_h_2, c_h, s9, s10)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.23 tff(9441,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)) | node15(c_e_h_2, c_h, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)) | node15(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9442,plain,
% 87.01/87.23 ((node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | node15(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10))) <=> (node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)) | node15(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9443,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | node15(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)) | node15(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(monotonicity,[status(thm)],[9442])).
% 87.01/87.23 tff(9444,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | node15(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)) | node15(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(transitivity,[status(thm)],[9443, 9441])).
% 87.01/87.23 tff(9445,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | node15(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9446,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)) | node15(c_e_h_2, c_h, s9, s10)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9445, 9444])).
% 87.01/87.23 tff(9447,plain,
% 87.01/87.23 (node16(c_e_h_2, c_h, s9) | node14(c_e_h_2, c_h, s9, s10) | node15(c_e_h_2, c_h, s9, s10)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9446, 189, 9440])).
% 87.01/87.23 tff(9448,plain,
% 87.01/87.23 ($false),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9447, 9434, 9426, 9420])).
% 87.01/87.23 tff(9449,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s9) | node15(c_e_h_2, c_h, s9, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.23 tff(9450,plain,
% 87.01/87.23 (m_c_h_element_v_in1(c_e_h_2, c_h, s9)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9449, 9419, 9411, 9410])).
% 87.01/87.23 tff(9451,plain,
% 87.01/87.23 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s9)))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9452,plain,
% 87.01/87.23 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~node17(c_e_h_2, c_h, s9))) <=> ((~node17(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s9)))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9453,plain,
% 87.01/87.23 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~node17(c_e_h_2, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s9))))),
% 87.01/87.23 inference(monotonicity,[status(thm)],[9452])).
% 87.01/87.23 tff(9454,plain,
% 87.01/87.23 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~node17(c_e_h_2, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s9)))),
% 87.01/87.23 inference(transitivity,[status(thm)],[9453, 9451])).
% 87.01/87.23 tff(9455,plain,
% 87.01/87.23 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~node17(c_e_h_2, c_h, s9)))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9456,plain,
% 87.01/87.23 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s9)) | m_c_h_element_v_in2(c_e_h_2, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s9))),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9455, 9454])).
% 87.01/87.23 tff(9457,plain,
% 87.01/87.23 ((~node17(c_e_h_2, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s9))),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9456, 209, 9410])).
% 87.01/87.23 tff(9458,plain,
% 87.01/87.23 (~node17(c_e_h_2, c_h, s9)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9457, 9450])).
% 87.01/87.23 tff(9459,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s9) | node18(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s9) | node18(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9460,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s9) | node18(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9461,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s9) | node18(c_e_h_2, c_h, s9, s10) | (~node19(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9460, 9459])).
% 87.01/87.23 tff(9462,plain,
% 87.01/87.23 (node17(c_e_h_2, c_h, s9) | node18(c_e_h_2, c_h, s9, s10)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9461, 156, 9440])).
% 87.01/87.23 tff(9463,plain,
% 87.01/87.23 (node18(c_e_h_2, c_h, s9, s10)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9462, 9458])).
% 87.01/87.23 tff(9464,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node18(c_e_h_2, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node18(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9465,plain,
% 87.01/87.23 (((~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~node18(c_e_h_2, c_h, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node18(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9466,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~node18(c_e_h_2, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node18(c_e_h_2, c_h, s9, s10))))),
% 87.01/87.23 inference(monotonicity,[status(thm)],[9465])).
% 87.01/87.23 tff(9467,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~node18(c_e_h_2, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node18(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(transitivity,[status(thm)],[9466, 9464])).
% 87.01/87.23 tff(9468,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~node18(c_e_h_2, c_h, s9, s10)))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9469,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | (~node18(c_e_h_2, c_h, s9, s10))),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9468, 9467])).
% 87.01/87.23 tff(9470,plain,
% 87.01/87.23 ($false),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9469, 124, 9411, 9412, 9463])).
% 87.01/87.23 tff(9471,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | m_c_h_element_v_in2(c_e_h_2, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.23 tff(9472,plain,
% 87.01/87.23 (~m_c_h_element_v_out(c_e_h_2, c_h, s10)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9471, 9409, 9003])).
% 87.01/87.23 tff(9473,plain,
% 87.01/87.23 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s10))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9474,plain,
% 87.01/87.23 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s10))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9475,plain,
% 87.01/87.23 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s10)) | m_c_h_element_v_out(c_e_h_2, c_h, s10)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9474, 9473])).
% 87.01/87.23 tff(9476,plain,
% 87.01/87.23 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s10)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9475, 23, 9472])).
% 87.01/87.23 tff(9477,plain,
% 87.01/87.23 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s10))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9478,plain,
% 87.01/87.23 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s10))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9479,plain,
% 87.01/87.23 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s10)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9478, 9477])).
% 87.01/87.23 tff(9480,plain,
% 87.01/87.23 (~node20(c_e_h_2, c_i, s10)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9479, 37, 9476])).
% 87.01/87.23 tff(9481,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s11)), introduced(assumption)).
% 87.01/87.23 tff(9482,assumption,(node22(c_e_h_2, c_i, s10, s11)), introduced(assumption)).
% 87.01/87.23 tff(9483,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node22(c_e_h_2, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node22(c_e_h_2, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9484,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node22(c_e_h_2, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9485,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node22(c_e_h_2, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9484, 9483])).
% 87.01/87.23 tff(9486,plain,
% 87.01/87.23 ($false),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9485, 107, 9069, 9481, 9482])).
% 87.01/87.23 tff(9487,plain,((~node22(c_e_h_2, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s11))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.23 tff(9488,plain,
% 87.01/87.23 (~node22(c_e_h_2, c_i, s10, s11)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9487, 9481, 9069])).
% 87.01/87.23 tff(9489,assumption,(~node20(c_e_h_2, c_i, s10)), introduced(assumption)).
% 87.01/87.23 tff(9490,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node21(c_e_h_2, c_i, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node21(c_e_h_2, c_i, s10, s11)))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9491,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node21(c_e_h_2, c_i, s10, s11)))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9492,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node21(c_e_h_2, c_i, s10, s11))),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9491, 9490])).
% 87.01/87.23 tff(9493,plain,
% 87.01/87.23 (node20(c_e_h_2, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | (~node21(c_e_h_2, c_i, s10, s11))),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9492, 51])).
% 87.01/87.23 tff(9494,plain,
% 87.01/87.23 (~node21(c_e_h_2, c_i, s10, s11)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9493, 9481, 9489])).
% 87.01/87.23 tff(9495,assumption,(~node22(c_e_h_2, c_i, s10, s11)), introduced(assumption)).
% 87.01/87.23 tff(9496,assumption,(~node21(c_e_h_2, c_i, s10, s11)), introduced(assumption)).
% 87.01/87.23 tff(9497,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_2, c_i, s10, s11) | node22(c_e_h_2, c_i, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_2, c_i, s10, s11) | node22(c_e_h_2, c_i, s10, s11))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9498,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_2, c_i, s10, s11) | node22(c_e_h_2, c_i, s10, s11))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9499,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_2, c_i, s10, s11) | node22(c_e_h_2, c_i, s10, s11)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9498, 9497])).
% 87.01/87.23 tff(9500,plain,
% 87.01/87.23 ($false),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9499, 81, 3778, 9496, 9495])).
% 87.01/87.23 tff(9501,plain,(node21(c_e_h_2, c_i, s10, s11) | node22(c_e_h_2, c_i, s10, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.23 tff(9502,plain,
% 87.01/87.23 ($false),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9501, 9494, 9488])).
% 87.01/87.23 tff(9503,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s11)) | node20(c_e_h_2, c_i, s10) | m_and_h_gate_v_out(c_e_h_2, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.23 tff(9504,plain,
% 87.01/87.23 (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9503, 9480, 9067])).
% 87.01/87.23 tff(9505,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s11)), introduced(assumption)).
% 87.01/87.23 tff(9506,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s11)), introduced(assumption)).
% 87.01/87.23 tff(9507,plain,
% 87.01/87.23 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9508,plain,
% 87.01/87.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9509,plain,
% 87.01/87.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9508, 9507])).
% 87.01/87.23 tff(9510,plain,
% 87.01/87.23 ($false),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9509, 365, 9506, 9505])).
% 87.01/87.23 tff(9511,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s11)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.23 tff(9512,plain,
% 87.01/87.23 (~m_c_h_element_v_in2(c_e_h_2, c_e, s11)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9511, 9504])).
% 87.01/87.23 tff(9513,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s12)), introduced(assumption)).
% 87.01/87.23 tff(9514,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s11)), introduced(assumption)).
% 87.01/87.23 tff(9515,assumption,(node18(c_e_h_2, c_e, s11, s12)), introduced(assumption)).
% 87.01/87.23 tff(9516,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_2, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9517,plain,
% 87.01/87.23 (((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11) | (~node18(c_e_h_2, c_e, s11, s12))) <=> ((~node18(c_e_h_2, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9518,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11) | (~node18(c_e_h_2, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_2, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11)))),
% 87.01/87.23 inference(monotonicity,[status(thm)],[9517])).
% 87.01/87.23 tff(9519,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11) | (~node18(c_e_h_2, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11))),
% 87.01/87.23 inference(transitivity,[status(thm)],[9518, 9516])).
% 87.01/87.23 tff(9520,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11) | (~node18(c_e_h_2, c_e, s11, s12)))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9521,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9520, 9519])).
% 87.01/87.23 tff(9522,plain,
% 87.01/87.23 ($false),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9521, 124, 9515, 9513, 9514])).
% 87.01/87.23 tff(9523,plain,((~node18(c_e_h_2, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.23 tff(9524,plain,
% 87.01/87.23 (~node18(c_e_h_2, c_e, s11, s12)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9523, 9514, 9513])).
% 87.01/87.23 tff(9525,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_2, c_e, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_2, c_e, s11, s12))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9526,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_2, c_e, s11, s12))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9527,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_2, c_e, s11, s12)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9526, 9525])).
% 87.01/87.23 tff(9528,plain,
% 87.01/87.23 (node19(c_e_h_2, c_e, s11, s12)),
% 87.01/87.23 inference(unit_resolution,[status(thm)],[9527, 141, 4461])).
% 87.01/87.23 tff(9529,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s11, s12)) | node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s11, s12)) | node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9530,plain,
% 87.01/87.23 ((node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12) | (~node19(c_e_h_2, c_e, s11, s12))) <=> ((~node19(c_e_h_2, c_e, s11, s12)) | node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12))),
% 87.01/87.23 inference(rewrite,[status(thm)],[])).
% 87.01/87.23 tff(9531,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12) | (~node19(c_e_h_2, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s11, s12)) | node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12)))),
% 87.01/87.23 inference(monotonicity,[status(thm)],[9530])).
% 87.01/87.23 tff(9532,plain,
% 87.01/87.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12) | (~node19(c_e_h_2, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s11, s12)) | node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12))),
% 87.01/87.23 inference(transitivity,[status(thm)],[9531, 9529])).
% 87.01/87.23 tff(9533,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12) | (~node19(c_e_h_2, c_e, s11, s12)))),
% 87.01/87.23 inference(quant_inst,[status(thm)],[])).
% 87.01/87.23 tff(9534,plain,
% 87.01/87.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s11, s12)) | node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12)),
% 87.01/87.23 inference(modus_ponens,[status(thm)],[9533, 9532])).
% 87.01/87.23 tff(9535,plain,
% 87.01/87.23 (node17(c_e_h_2, c_e, s11) | node18(c_e_h_2, c_e, s11, s12)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9534, 156, 9528])).
% 87.01/87.24 tff(9536,plain,
% 87.01/87.24 (node17(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9535, 9524])).
% 87.01/87.24 tff(9537,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s11)), introduced(assumption)).
% 87.01/87.24 tff(9538,plain,
% 87.01/87.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s11)))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9539,plain,
% 87.01/87.24 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~node17(c_e_h_2, c_e, s11))) <=> ((~node17(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s11)))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9540,plain,
% 87.01/87.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~node17(c_e_h_2, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s11))))),
% 87.01/87.24 inference(monotonicity,[status(thm)],[9539])).
% 87.01/87.24 tff(9541,plain,
% 87.01/87.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~node17(c_e_h_2, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s11)))),
% 87.01/87.24 inference(transitivity,[status(thm)],[9540, 9538])).
% 87.01/87.24 tff(9542,plain,
% 87.01/87.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~node17(c_e_h_2, c_e, s11)))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9543,plain,
% 87.01/87.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s11)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9542, 9541])).
% 87.01/87.24 tff(9544,plain,
% 87.01/87.24 ((~node17(c_e_h_2, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9543, 209, 9537])).
% 87.01/87.24 tff(9545,plain,
% 87.01/87.24 (~m_c_h_element_v_in1(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9544, 9536])).
% 87.01/87.24 tff(9546,plain,
% 87.01/87.24 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11) | m_c_h_element_v_in2(c_e_h_2, c_e, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11) | m_c_h_element_v_in2(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9547,plain,
% 87.01/87.24 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11) | m_c_h_element_v_in2(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9548,plain,
% 87.01/87.24 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11) | m_c_h_element_v_in2(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9547, 9546])).
% 87.01/87.24 tff(9549,plain,
% 87.01/87.24 ((~node16(c_e_h_2, c_e, s11)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9548, 228, 9537])).
% 87.01/87.24 tff(9550,plain,
% 87.01/87.24 (~node16(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9549, 9545])).
% 87.01/87.24 tff(9551,assumption,(node15(c_e_h_2, c_e, s11, s12)), introduced(assumption)).
% 87.01/87.24 tff(9552,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node15(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node15(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9553,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node15(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9554,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node15(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9553, 9552])).
% 87.01/87.24 tff(9555,plain,
% 87.01/87.24 ($false),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9554, 173, 9551, 9513, 9514])).
% 87.01/87.24 tff(9556,plain,((~node15(c_e_h_2, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.24 tff(9557,plain,
% 87.01/87.24 (~node15(c_e_h_2, c_e, s11, s12)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9556, 9514, 9513])).
% 87.01/87.24 tff(9558,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s11, s12)) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | node16(c_e_h_2, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s11, s12)) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | node16(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9559,plain,
% 87.01/87.24 ((node16(c_e_h_2, c_e, s11) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | (~node19(c_e_h_2, c_e, s11, s12))) <=> ((~node19(c_e_h_2, c_e, s11, s12)) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | node16(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9560,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s11) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | (~node19(c_e_h_2, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s11, s12)) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | node16(c_e_h_2, c_e, s11)))),
% 87.01/87.24 inference(monotonicity,[status(thm)],[9559])).
% 87.01/87.24 tff(9561,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s11) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | (~node19(c_e_h_2, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s11, s12)) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | node16(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(transitivity,[status(thm)],[9560, 9558])).
% 87.01/87.24 tff(9562,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s11) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | (~node19(c_e_h_2, c_e, s11, s12)))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9563,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s11, s12)) | node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | node16(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9562, 9561])).
% 87.01/87.24 tff(9564,plain,
% 87.01/87.24 (node14(c_e_h_2, c_e, s11, s12) | node15(c_e_h_2, c_e, s11, s12) | node16(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9563, 189, 9528])).
% 87.01/87.24 tff(9565,plain,
% 87.01/87.24 (node14(c_e_h_2, c_e, s11, s12)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9564, 9557, 9550])).
% 87.01/87.24 tff(9566,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9567,plain,
% 87.01/87.24 (((~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9568,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11)))),
% 87.01/87.24 inference(monotonicity,[status(thm)],[9567])).
% 87.01/87.24 tff(9569,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11))),
% 87.01/87.24 inference(transitivity,[status(thm)],[9568, 9566])).
% 87.01/87.24 tff(9570,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9571,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | (~node14(c_e_h_2, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s11)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9570, 9569])).
% 87.01/87.24 tff(9572,plain,
% 87.01/87.24 ($false),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9571, 283, 9565, 9513, 9545])).
% 87.01/87.24 tff(9573,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s11) | (~m_c_h_element_v_out(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.24 tff(9574,plain,
% 87.01/87.24 (~m_c_h_element_v_out(c_e_h_2, c_e, s12)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9573, 9512, 9212])).
% 87.01/87.24 tff(9575,plain,
% 87.01/87.24 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s12))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9576,plain,
% 87.01/87.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s12))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9577,plain,
% 87.01/87.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s12)) | m_c_h_element_v_out(c_e_h_2, c_e, s12)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9576, 9575])).
% 87.01/87.24 tff(9578,plain,
% 87.01/87.24 (~m_and_h_gate_v_in1(c_e_h_2, c_r, s12)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9577, 1884, 9574])).
% 87.01/87.24 tff(9579,plain,
% 87.01/87.24 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s12))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9580,plain,
% 87.01/87.24 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s12))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9581,plain,
% 87.01/87.24 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s12)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9580, 9579])).
% 87.01/87.24 tff(9582,plain,
% 87.01/87.24 (~node20(c_e_h_2, c_r, s12)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9581, 37, 9578])).
% 87.01/87.24 tff(9583,assumption,(~node20(c_e_h_2, c_r, s12)), introduced(assumption)).
% 87.01/87.24 tff(9584,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s13)), introduced(assumption)).
% 87.01/87.24 tff(9585,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s12) | (~node21(c_e_h_2, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s12) | (~node21(c_e_h_2, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9586,plain,
% 87.01/87.24 ((node20(c_e_h_2, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | (~node21(c_e_h_2, c_r, s12, s13))) <=> (node20(c_e_h_2, c_r, s12) | (~node21(c_e_h_2, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9587,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | (~node21(c_e_h_2, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s12) | (~node21(c_e_h_2, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13))))),
% 87.01/87.24 inference(monotonicity,[status(thm)],[9586])).
% 87.01/87.24 tff(9588,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | (~node21(c_e_h_2, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s12) | (~node21(c_e_h_2, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)))),
% 87.01/87.24 inference(transitivity,[status(thm)],[9587, 9585])).
% 87.01/87.24 tff(9589,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | (~node21(c_e_h_2, c_r, s12, s13)))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9590,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s12) | (~node21(c_e_h_2, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13))),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9589, 9588])).
% 87.01/87.24 tff(9591,plain,
% 87.01/87.24 (node20(c_e_h_2, c_r, s12) | (~node21(c_e_h_2, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13))),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9590, 51])).
% 87.01/87.24 tff(9592,plain,
% 87.01/87.24 (~node21(c_e_h_2, c_r, s12, s13)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9591, 9584, 9583])).
% 87.01/87.24 tff(9593,plain,
% 87.01/87.24 (succ(s12, s13) <=> succ(s12, s13)),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9594,axiom,(succ(s12, s13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound13')).
% 87.01/87.24 tff(9595,plain,
% 87.01/87.24 (succ(s12, s13)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9594, 9593])).
% 87.01/87.24 tff(9596,plain,
% 87.01/87.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9597,plain,
% 87.01/87.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9598,plain,
% 87.01/87.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9597, 9596])).
% 87.01/87.24 tff(9599,plain,
% 87.01/87.24 (trans(s12, s13)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9598, 9595, 64])).
% 87.01/87.24 tff(9600,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_2, c_r, s12, s13) | node22(c_e_h_2, c_r, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_2, c_r, s12, s13) | node22(c_e_h_2, c_r, s12, s13))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9601,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_2, c_r, s12, s13) | node22(c_e_h_2, c_r, s12, s13))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9602,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_2, c_r, s12, s13) | node22(c_e_h_2, c_r, s12, s13)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9601, 9600])).
% 87.01/87.24 tff(9603,plain,
% 87.01/87.24 (node21(c_e_h_2, c_r, s12, s13) | node22(c_e_h_2, c_r, s12, s13)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9602, 81, 9599])).
% 87.01/87.24 tff(9604,plain,
% 87.01/87.24 (node22(c_e_h_2, c_r, s12, s13)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9603, 9592])).
% 87.01/87.24 tff(9605,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s12)), introduced(assumption)).
% 87.01/87.24 tff(9606,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | (~node22(c_e_h_2, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | (~node22(c_e_h_2, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9607,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | (~node22(c_e_h_2, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9608,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | (~node22(c_e_h_2, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9607, 9606])).
% 87.01/87.24 tff(9609,plain,
% 87.01/87.24 ($false),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9608, 107, 9584, 9605, 9604])).
% 87.01/87.24 tff(9610,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12) | node20(c_e_h_2, c_r, s12)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.24 tff(9611,plain,
% 87.01/87.24 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s12)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9610, 9582])).
% 87.01/87.24 tff(9612,plain,
% 87.01/87.24 (~m_and_h_gate_v_out(c_e_h_2, c_r, s13)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9611, 4474])).
% 87.01/87.24 tff(9613,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s11)), introduced(assumption)).
% 87.01/87.24 tff(9614,plain,
% 87.01/87.24 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9250, 9245])).
% 87.01/87.24 tff(9615,plain,
% 87.01/87.24 (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9404, 9614, 9371])).
% 87.01/87.24 tff(9616,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s9)), introduced(assumption)).
% 87.01/87.24 tff(9617,assumption,(node22(c_e_h_2, c_l, s8, s9)), introduced(assumption)).
% 87.01/87.24 tff(9618,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | (~node22(c_e_h_2, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | (~node22(c_e_h_2, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9619,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | (~node22(c_e_h_2, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9620,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | (~node22(c_e_h_2, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9619, 9618])).
% 87.01/87.24 tff(9621,plain,
% 87.01/87.24 ($false),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9620, 107, 9616, 9245, 9617])).
% 87.01/87.24 tff(9622,plain,((~node22(c_e_h_2, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.24 tff(9623,plain,
% 87.01/87.24 (~node22(c_e_h_2, c_l, s8, s9)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9622, 9616, 9245])).
% 87.01/87.24 tff(9624,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_l, s8, s9) | node22(c_e_h_2, c_l, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_l, s8, s9) | node22(c_e_h_2, c_l, s8, s9))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9625,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_l, s8, s9) | node22(c_e_h_2, c_l, s8, s9))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9626,plain,
% 87.01/87.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_l, s8, s9) | node22(c_e_h_2, c_l, s8, s9)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9625, 9624])).
% 87.01/87.24 tff(9627,plain,
% 87.01/87.24 (node21(c_e_h_2, c_l, s8, s9) | node22(c_e_h_2, c_l, s8, s9)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9626, 81, 2636])).
% 87.01/87.24 tff(9628,plain,
% 87.01/87.24 (node21(c_e_h_2, c_l, s8, s9)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9627, 9623])).
% 87.01/87.24 tff(9629,plain,
% 87.01/87.24 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9630,plain,
% 87.01/87.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9631,plain,
% 87.01/87.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9630, 9629])).
% 87.01/87.24 tff(9632,plain,
% 87.01/87.24 ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9631, 1638])).
% 87.01/87.24 tff(9633,plain,
% 87.01/87.24 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s8)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9632, 2613])).
% 87.01/87.24 tff(9634,plain,
% 87.01/87.24 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s8))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.24 tff(9635,plain,
% 87.01/87.24 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s8))),
% 87.01/87.24 inference(quant_inst,[status(thm)],[])).
% 87.01/87.24 tff(9636,plain,
% 87.01/87.24 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s8)),
% 87.01/87.24 inference(modus_ponens,[status(thm)],[9635, 9634])).
% 87.01/87.24 tff(9637,plain,
% 87.01/87.24 (~node20(c_e_h_2, c_l, s8)),
% 87.01/87.24 inference(unit_resolution,[status(thm)],[9636, 1535, 9633])).
% 87.01/87.24 tff(9638,plain,
% 87.01/87.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | node20(c_e_h_2, c_l, s8) | (~node21(c_e_h_2, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | node20(c_e_h_2, c_l, s8) | (~node21(c_e_h_2, c_l, s8, s9)))),
% 87.01/87.24 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9639,plain,
% 87.01/87.25 ((node20(c_e_h_2, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | (~node21(c_e_h_2, c_l, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | node20(c_e_h_2, c_l, s8) | (~node21(c_e_h_2, c_l, s8, s9)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9640,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | (~node21(c_e_h_2, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | node20(c_e_h_2, c_l, s8) | (~node21(c_e_h_2, c_l, s8, s9))))),
% 87.01/87.25 inference(monotonicity,[status(thm)],[9639])).
% 87.01/87.25 tff(9641,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | (~node21(c_e_h_2, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | node20(c_e_h_2, c_l, s8) | (~node21(c_e_h_2, c_l, s8, s9)))),
% 87.01/87.25 inference(transitivity,[status(thm)],[9640, 9638])).
% 87.01/87.25 tff(9642,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | (~node21(c_e_h_2, c_l, s8, s9)))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9643,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | node20(c_e_h_2, c_l, s8) | (~node21(c_e_h_2, c_l, s8, s9))),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9642, 9641])).
% 87.01/87.25 tff(9644,plain,
% 87.01/87.25 ($false),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9643, 51, 9616, 9637, 9628])).
% 87.01/87.25 tff(9645,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.25 tff(9646,plain,
% 87.01/87.25 (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9645, 9245])).
% 87.01/87.25 tff(9647,plain,
% 87.01/87.25 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9648,plain,
% 87.01/87.25 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9649,plain,
% 87.01/87.25 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9)),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9648, 9647])).
% 87.01/87.25 tff(9650,plain,
% 87.01/87.25 ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9649, 801])).
% 87.01/87.25 tff(9651,plain,
% 87.01/87.25 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9650, 9646])).
% 87.01/87.25 tff(9652,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)), introduced(assumption)).
% 87.01/87.25 tff(9653,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s9)), introduced(assumption)).
% 87.01/87.25 tff(9654,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s10)), introduced(assumption)).
% 87.01/87.25 tff(9655,assumption,(node6(c_e_h_2, c_j, s9, s10)), introduced(assumption)).
% 87.01/87.25 tff(9656,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node6(c_e_h_2, c_j, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node6(c_e_h_2, c_j, s9, s10)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9657,plain,
% 87.01/87.25 (((~node6(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node6(c_e_h_2, c_j, s9, s10)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9658,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node6(c_e_h_2, c_j, s9, s10))))),
% 87.01/87.25 inference(monotonicity,[status(thm)],[9657])).
% 87.01/87.25 tff(9659,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node6(c_e_h_2, c_j, s9, s10)))),
% 87.01/87.25 inference(transitivity,[status(thm)],[9658, 9656])).
% 87.01/87.25 tff(9660,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9661,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node6(c_e_h_2, c_j, s9, s10))),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9660, 9659])).
% 87.01/87.25 tff(9662,plain,
% 87.01/87.25 ($false),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9661, 899, 9654, 9653, 9655])).
% 87.01/87.25 tff(9663,plain,((~node6(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.25 tff(9664,plain,
% 87.01/87.25 (~node6(c_e_h_2, c_j, s9, s10)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9663, 9654, 9653])).
% 87.01/87.25 tff(9665,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s7)), introduced(assumption)).
% 87.01/87.25 tff(9666,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s8)), introduced(assumption)).
% 87.01/87.25 tff(9667,assumption,(node18(c_e_h_1, c_f, s7, s8)), introduced(assumption)).
% 87.01/87.25 tff(9668,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9669,plain,
% 87.01/87.25 (((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~node18(c_e_h_1, c_f, s7, s8))) <=> ((~node18(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9670,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~node18(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 87.01/87.25 inference(monotonicity,[status(thm)],[9669])).
% 87.01/87.25 tff(9671,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~node18(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(transitivity,[status(thm)],[9670, 9668])).
% 87.01/87.25 tff(9672,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~node18(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9673,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9672, 9671])).
% 87.01/87.25 tff(9674,plain,
% 87.01/87.25 ($false),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9673, 124, 9666, 9667, 9665])).
% 87.01/87.25 tff(9675,plain,((~node18(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.25 tff(9676,plain,
% 87.01/87.25 (~node18(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9675, 9666, 9665])).
% 87.01/87.25 tff(9677,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_f, s7, s8))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9678,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_f, s7, s8))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9679,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9678, 9677])).
% 87.01/87.25 tff(9680,plain,
% 87.01/87.25 (node19(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9679, 141, 2152])).
% 87.01/87.25 tff(9681,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s7) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s7) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9682,plain,
% 87.01/87.25 ((node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8))) <=> (node17(c_e_h_1, c_f, s7) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9683,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s7) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(monotonicity,[status(thm)],[9682])).
% 87.01/87.25 tff(9684,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s7) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8))),
% 87.01/87.25 inference(transitivity,[status(thm)],[9683, 9681])).
% 87.01/87.25 tff(9685,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9686,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s7) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9685, 9684])).
% 87.01/87.25 tff(9687,plain,
% 87.01/87.25 (node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9686, 156, 9680])).
% 87.01/87.25 tff(9688,plain,
% 87.01/87.25 (node17(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9687, 9676])).
% 87.01/87.25 tff(9689,plain,
% 87.01/87.25 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9690,plain,
% 87.01/87.25 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9691,plain,
% 87.01/87.25 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9690, 9689])).
% 87.01/87.25 tff(9692,plain,
% 87.01/87.25 (~m_c_h_element_v_in2(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9691, 2218, 7209])).
% 87.01/87.25 tff(9693,plain,
% 87.01/87.25 (~node18(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9675, 9665, 9666])).
% 87.01/87.25 tff(9694,plain,
% 87.01/87.25 (node17(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9687, 9693])).
% 87.01/87.25 tff(9695,assumption,(~node14(c_e_h_1, c_f, s7, s8)), introduced(assumption)).
% 87.01/87.25 tff(9696,assumption,(node15(c_e_h_1, c_f, s7, s8)), introduced(assumption)).
% 87.01/87.25 tff(9697,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node15(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node15(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9698,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node15(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9699,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node15(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9698, 9697])).
% 87.01/87.25 tff(9700,plain,
% 87.01/87.25 ($false),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9699, 173, 9666, 9696, 9665])).
% 87.01/87.25 tff(9701,plain,((~node15(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.25 tff(9702,plain,
% 87.01/87.25 (~node15(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9701, 9665, 9666])).
% 87.01/87.25 tff(9703,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s7) | node15(c_e_h_1, c_f, s7, s8) | node14(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s7) | node15(c_e_h_1, c_f, s7, s8) | node14(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9704,plain,
% 87.01/87.25 ((node16(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8))) <=> (node16(c_e_h_1, c_f, s7) | node15(c_e_h_1, c_f, s7, s8) | node14(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9705,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s7) | node15(c_e_h_1, c_f, s7, s8) | node14(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8))))),
% 87.01/87.25 inference(monotonicity,[status(thm)],[9704])).
% 87.01/87.25 tff(9706,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s7) | node15(c_e_h_1, c_f, s7, s8) | node14(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(transitivity,[status(thm)],[9705, 9703])).
% 87.01/87.25 tff(9707,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9708,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s7) | node15(c_e_h_1, c_f, s7, s8) | node14(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8))),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9707, 9706])).
% 87.01/87.25 tff(9709,plain,
% 87.01/87.25 (node16(c_e_h_1, c_f, s7) | node15(c_e_h_1, c_f, s7, s8) | node14(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9708, 189, 9680])).
% 87.01/87.25 tff(9710,plain,
% 87.01/87.25 (node16(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9709, 9702, 9695])).
% 87.01/87.25 tff(9711,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s7)), introduced(assumption)).
% 87.01/87.25 tff(9712,plain,
% 87.01/87.25 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9713,plain,
% 87.01/87.25 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9714,plain,
% 87.01/87.25 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9713, 9712])).
% 87.01/87.25 tff(9715,plain,
% 87.01/87.25 ((~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9714, 228, 9711])).
% 87.01/87.25 tff(9716,plain,
% 87.01/87.25 (m_c_h_element_v_in1(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9715, 9710])).
% 87.01/87.25 tff(9717,plain,
% 87.01/87.25 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | (~node17(c_e_h_1, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | (~node17(c_e_h_1, c_f, s7)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9718,plain,
% 87.01/87.25 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | (~node17(c_e_h_1, c_f, s7)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9719,plain,
% 87.01/87.25 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | (~node17(c_e_h_1, c_f, s7))))),
% 87.01/87.25 inference(monotonicity,[status(thm)],[9718])).
% 87.01/87.25 tff(9720,plain,
% 87.01/87.25 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | (~node17(c_e_h_1, c_f, s7)))),
% 87.01/87.25 inference(transitivity,[status(thm)],[9719, 9717])).
% 87.01/87.25 tff(9721,plain,
% 87.01/87.25 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9722,plain,
% 87.01/87.25 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | (~node17(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9721, 9720])).
% 87.01/87.25 tff(9723,plain,
% 87.01/87.25 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | (~node17(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9722, 209, 9711])).
% 87.01/87.25 tff(9724,plain,
% 87.01/87.25 ($false),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9723, 9716, 9694])).
% 87.01/87.25 tff(9725,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.25 tff(9726,plain,
% 87.01/87.25 (m_c_h_element_v_out(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9725, 9692])).
% 87.01/87.25 tff(9727,plain,
% 87.01/87.25 (node14(c_e_h_1, c_f, s7, s8)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9726, 9666, 9665])).
% 87.01/87.25 tff(9728,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s7)), introduced(assumption)).
% 87.01/87.25 tff(9729,assumption,(node14(c_e_h_1, c_f, s7, s8)), introduced(assumption)).
% 87.01/87.25 tff(9730,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node14(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node14(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9731,plain,
% 87.01/87.25 (((~node14(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node14(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(rewrite,[status(thm)],[])).
% 87.01/87.25 tff(9732,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node14(c_e_h_1, c_f, s7, s8))))),
% 87.01/87.25 inference(monotonicity,[status(thm)],[9731])).
% 87.01/87.25 tff(9733,plain,
% 87.01/87.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node14(c_e_h_1, c_f, s7, s8)))),
% 87.01/87.25 inference(transitivity,[status(thm)],[9732, 9730])).
% 87.01/87.25 tff(9734,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)))),
% 87.01/87.25 inference(quant_inst,[status(thm)],[])).
% 87.01/87.25 tff(9735,plain,
% 87.01/87.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node14(c_e_h_1, c_f, s7, s8))),
% 87.01/87.25 inference(modus_ponens,[status(thm)],[9734, 9733])).
% 87.01/87.25 tff(9736,plain,
% 87.01/87.25 ($false),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9735, 283, 9666, 9729, 9728])).
% 87.01/87.25 tff(9737,plain,((~node14(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.25 tff(9738,plain,
% 87.01/87.25 (m_c_h_element_v_in1(c_e_h_1, c_f, s7)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9737, 9727, 9666])).
% 87.01/87.25 tff(9739,plain,
% 87.01/87.25 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | (~node17(c_e_h_1, c_f, s7))),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9722, 209, 9692])).
% 87.01/87.25 tff(9740,plain,
% 87.01/87.25 ($false),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9739, 9738, 9688])).
% 87.01/87.25 tff(9741,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.25 tff(9742,plain,
% 87.01/87.25 (~m_c_h_element_v_out(c_e_h_1, c_f, s8)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9741, 9321])).
% 87.01/87.25 tff(9743,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)), introduced(assumption)).
% 87.01/87.25 tff(9744,plain,
% 87.01/87.25 (~node20(c_e_h_1, c_q, s7)),
% 87.01/87.25 inference(unit_resolution,[status(thm)],[9329, 37, 9743])).
% 87.01/87.25 tff(9745,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s9)), introduced(assumption)).
% 87.01/87.25 tff(9746,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s8)), introduced(assumption)).
% 87.01/87.25 tff(9747,plain,
% 87.01/87.25 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9748,plain,
% 87.01/87.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9749,plain,
% 87.01/87.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s8)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9748, 9747])).
% 87.01/87.26 tff(9750,plain,
% 87.01/87.26 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9749, 1666, 9746])).
% 87.01/87.26 tff(9751,plain,
% 87.01/87.26 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s8))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9752,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s8))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9753,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s8)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9752, 9751])).
% 87.01/87.26 tff(9754,plain,
% 87.01/87.26 (~node20(c_e_h_1, c_q, s8)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9753, 37, 9750])).
% 87.01/87.26 tff(9755,assumption,(~node20(c_e_h_1, c_q, s8)), introduced(assumption)).
% 87.01/87.26 tff(9756,assumption,(node21(c_e_h_1, c_q, s8, s9)), introduced(assumption)).
% 87.01/87.26 tff(9757,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node21(c_e_h_1, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node21(c_e_h_1, c_q, s8, s9)))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9758,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node21(c_e_h_1, c_q, s8, s9)))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9759,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node21(c_e_h_1, c_q, s8, s9))),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9758, 9757])).
% 87.01/87.26 tff(9760,plain,
% 87.01/87.26 ($false),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9759, 51, 9745, 9756, 9755])).
% 87.01/87.26 tff(9761,plain,((~node21(c_e_h_1, c_q, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | node20(c_e_h_1, c_q, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.26 tff(9762,plain,
% 87.01/87.26 (~node21(c_e_h_1, c_q, s8, s9)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9761, 9754, 9745])).
% 87.01/87.26 tff(9763,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9764,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9765,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9764, 9763])).
% 87.01/87.26 tff(9766,plain,
% 87.01/87.26 (node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9765, 81, 2636])).
% 87.01/87.26 tff(9767,plain,
% 87.01/87.26 (node22(c_e_h_1, c_q, s8, s9)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9766, 9762])).
% 87.01/87.26 tff(9768,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node22(c_e_h_1, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node22(c_e_h_1, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9769,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node22(c_e_h_1, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9770,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node22(c_e_h_1, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9769, 9768])).
% 87.01/87.26 tff(9771,plain,
% 87.01/87.26 (m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9770, 107, 9745, 9767])).
% 87.01/87.26 tff(9772,plain,
% 87.01/87.26 (~node21(c_e_h_1, c_q, s7, s8)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9340, 9771, 9744])).
% 87.01/87.26 tff(9773,plain,
% 87.01/87.26 (node22(c_e_h_1, c_q, s7, s8)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9354, 9772])).
% 87.01/87.26 tff(9774,plain,
% 87.01/87.26 ($false),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9347, 107, 9771, 9343, 9773])).
% 87.01/87.26 tff(9775,plain,(m_and_h_gate_v_in1(c_e_h_1, c_q, s7) | m_and_h_gate_v_out(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.26 tff(9776,plain,
% 87.01/87.26 (m_and_h_gate_v_in1(c_e_h_1, c_q, s7) | m_and_h_gate_v_out(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9775, 9742])).
% 87.01/87.26 tff(9777,plain,
% 87.01/87.26 (m_and_h_gate_v_out(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9776, 9326])).
% 87.01/87.26 tff(9778,plain,
% 87.01/87.26 (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9777, 8781])).
% 87.01/87.26 tff(9779,plain,
% 87.01/87.26 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s9))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9780,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s9))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9781,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s9)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9780, 9779])).
% 87.01/87.26 tff(9782,plain,
% 87.01/87.26 (node3(c_e_h_1, c_e_h_2, s9)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9781, 817, 814])).
% 87.01/87.26 tff(9783,plain,
% 87.01/87.26 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s9)) | (~node3(c_e_h_1, c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s9)) | (~node3(c_e_h_1, c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9784,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s9)) | (~node3(c_e_h_1, c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9785,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s9)) | (~node3(c_e_h_1, c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9784, 9783])).
% 87.01/87.26 tff(9786,plain,
% 87.01/87.26 ((~m_cell_v_ack(c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9785, 836, 9782])).
% 87.01/87.26 tff(9787,plain,
% 87.01/87.26 (~m_cell_v_ack(c_e_h_2, s9)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9786, 9778])).
% 87.01/87.26 tff(9788,plain,
% 87.01/87.26 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)) | m_cell_v_ack(c_e_h_2, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)) | m_cell_v_ack(c_e_h_2, s9))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9789,plain,
% 87.01/87.26 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)) | m_cell_v_ack(c_e_h_2, s9))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9790,plain,
% 87.01/87.26 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)) | m_cell_v_ack(c_e_h_2, s9)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9789, 9788])).
% 87.01/87.26 tff(9791,plain,
% 87.01/87.26 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9790, 848, 9787])).
% 87.01/87.26 tff(9792,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)), introduced(assumption)).
% 87.01/87.26 tff(9793,assumption,(node5(c_e_h_2, c_j, s9, s10)), introduced(assumption)).
% 87.01/87.26 tff(9794,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node5(c_e_h_2, c_j, s9, s10)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node5(c_e_h_2, c_j, s9, s10)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9795,plain,
% 87.01/87.26 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9) | (~node5(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10))) <=> (m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node5(c_e_h_2, c_j, s9, s10)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9796,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9) | (~node5(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node5(c_e_h_2, c_j, s9, s10)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9)))),
% 87.01/87.26 inference(monotonicity,[status(thm)],[9795])).
% 87.01/87.26 tff(9797,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9) | (~node5(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node5(c_e_h_2, c_j, s9, s10)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9))),
% 87.01/87.26 inference(transitivity,[status(thm)],[9796, 9794])).
% 87.01/87.26 tff(9798,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9) | (~node5(c_e_h_2, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9799,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | (~node5(c_e_h_2, c_j, s9, s10)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9798, 9797])).
% 87.01/87.26 tff(9800,plain,
% 87.01/87.26 ($false),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9799, 862, 9652, 9654, 9793, 9792])).
% 87.01/87.26 tff(9801,plain,((~node5(c_e_h_2, c_j, s9, s10)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.26 tff(9802,plain,
% 87.01/87.26 ((~node5(c_e_h_2, c_j, s9, s10)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s10))),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9801, 9791])).
% 87.01/87.26 tff(9803,plain,
% 87.01/87.26 (~node5(c_e_h_2, c_j, s9, s10)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9802, 9654, 9652])).
% 87.01/87.26 tff(9804,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node5(c_e_h_2, c_j, s9, s10) | node6(c_e_h_2, c_j, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_2, c_j, s9, s10) | node6(c_e_h_2, c_j, s9, s10))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9805,plain,
% 87.01/87.26 ((node6(c_e_h_2, c_j, s9, s10) | node5(c_e_h_2, c_j, s9, s10) | (~trans(s9, s10))) <=> ((~trans(s9, s10)) | node5(c_e_h_2, c_j, s9, s10) | node6(c_e_h_2, c_j, s9, s10))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9806,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s9, s10) | node5(c_e_h_2, c_j, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node5(c_e_h_2, c_j, s9, s10) | node6(c_e_h_2, c_j, s9, s10)))),
% 87.01/87.26 inference(monotonicity,[status(thm)],[9805])).
% 87.01/87.26 tff(9807,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s9, s10) | node5(c_e_h_2, c_j, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_2, c_j, s9, s10) | node6(c_e_h_2, c_j, s9, s10))),
% 87.01/87.26 inference(transitivity,[status(thm)],[9806, 9804])).
% 87.01/87.26 tff(9808,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s9, s10) | node5(c_e_h_2, c_j, s9, s10) | (~trans(s9, s10)))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9809,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_2, c_j, s9, s10) | node6(c_e_h_2, c_j, s9, s10)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9808, 9807])).
% 87.01/87.26 tff(9810,plain,
% 87.01/87.26 (node5(c_e_h_2, c_j, s9, s10) | node6(c_e_h_2, c_j, s9, s10)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9809, 881, 3175])).
% 87.01/87.26 tff(9811,plain,
% 87.01/87.26 ($false),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9810, 9803, 9664])).
% 87.01/87.26 tff(9812,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s10)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s9) | m_or_h_gate_v_out(c_e_h_2, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.26 tff(9813,plain,
% 87.01/87.26 (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9812, 9653, 9652])).
% 87.01/87.26 tff(9814,plain,
% 87.01/87.26 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9815,plain,
% 87.01/87.26 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9816,plain,
% 87.01/87.26 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9815, 9814])).
% 87.01/87.26 tff(9817,plain,
% 87.01/87.26 (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9816, 309, 9813])).
% 87.01/87.26 tff(9818,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s10)), introduced(assumption)).
% 87.01/87.26 tff(9819,assumption,(node18(c_e_h_2, c_h, s10, s11)), introduced(assumption)).
% 87.01/87.26 tff(9820,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node18(c_e_h_2, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node18(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9821,plain,
% 87.01/87.26 (((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~node18(c_e_h_2, c_h, s10, s11))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node18(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9822,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~node18(c_e_h_2, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node18(c_e_h_2, c_h, s10, s11))))),
% 87.01/87.26 inference(monotonicity,[status(thm)],[9821])).
% 87.01/87.26 tff(9823,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~node18(c_e_h_2, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node18(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(transitivity,[status(thm)],[9822, 9820])).
% 87.01/87.26 tff(9824,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~node18(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9825,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node18(c_e_h_2, c_h, s10, s11))),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9824, 9823])).
% 87.01/87.26 tff(9826,plain,
% 87.01/87.26 ($false),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9825, 124, 9818, 9613, 9819])).
% 87.01/87.26 tff(9827,plain,((~node18(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.26 tff(9828,plain,
% 87.01/87.26 (~node18(c_e_h_2, c_h, s10, s11)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9827, 9613, 9818])).
% 87.01/87.26 tff(9829,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_2, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_2, c_h, s10, s11))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9830,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_2, c_h, s10, s11))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9831,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_2, c_h, s10, s11)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9830, 9829])).
% 87.01/87.26 tff(9832,plain,
% 87.01/87.26 (node19(c_e_h_2, c_h, s10, s11)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9831, 141, 3778])).
% 87.01/87.26 tff(9833,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s10) | node18(c_e_h_2, c_h, s10, s11) | (~node19(c_e_h_2, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s10) | node18(c_e_h_2, c_h, s10, s11) | (~node19(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9834,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s10) | node18(c_e_h_2, c_h, s10, s11) | (~node19(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9835,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s10) | node18(c_e_h_2, c_h, s10, s11) | (~node19(c_e_h_2, c_h, s10, s11))),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9834, 9833])).
% 87.01/87.26 tff(9836,plain,
% 87.01/87.26 (node17(c_e_h_2, c_h, s10) | node18(c_e_h_2, c_h, s10, s11)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9835, 156, 9832])).
% 87.01/87.26 tff(9837,plain,
% 87.01/87.26 (node17(c_e_h_2, c_h, s10)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9836, 9828])).
% 87.01/87.26 tff(9838,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s10)), introduced(assumption)).
% 87.01/87.26 tff(9839,plain,
% 87.01/87.26 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | (~node17(c_e_h_2, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | (~node17(c_e_h_2, c_h, s10)))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9840,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | (~node17(c_e_h_2, c_h, s10)))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9841,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | (~node17(c_e_h_2, c_h, s10))),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9840, 9839])).
% 87.01/87.26 tff(9842,plain,
% 87.01/87.26 ((~m_c_h_element_v_in2(c_e_h_2, c_h, s10)) | (~node17(c_e_h_2, c_h, s10))),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9841, 245, 9838])).
% 87.01/87.26 tff(9843,plain,
% 87.01/87.26 (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9842, 9837])).
% 87.01/87.26 tff(9844,plain,
% 87.01/87.26 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s10)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | m_c_h_element_v_in2(c_e_h_2, c_h, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s10)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | m_c_h_element_v_in2(c_e_h_2, c_h, s10))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9845,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s10)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | m_c_h_element_v_in2(c_e_h_2, c_h, s10))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9846,plain,
% 87.01/87.26 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s10)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | m_c_h_element_v_in2(c_e_h_2, c_h, s10)),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9845, 9844])).
% 87.01/87.26 tff(9847,plain,
% 87.01/87.26 ((~node16(c_e_h_2, c_h, s10)) | m_c_h_element_v_in2(c_e_h_2, c_h, s10)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9846, 228, 9838])).
% 87.01/87.26 tff(9848,plain,
% 87.01/87.26 (~node16(c_e_h_2, c_h, s10)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9847, 9843])).
% 87.01/87.26 tff(9849,assumption,(node14(c_e_h_2, c_h, s10, s11)), introduced(assumption)).
% 87.01/87.26 tff(9850,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~node14(c_e_h_2, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~node14(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9851,plain,
% 87.01/87.26 (((~node14(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~node14(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(rewrite,[status(thm)],[])).
% 87.01/87.26 tff(9852,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~node14(c_e_h_2, c_h, s10, s11))))),
% 87.01/87.26 inference(monotonicity,[status(thm)],[9851])).
% 87.01/87.26 tff(9853,plain,
% 87.01/87.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~node14(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.26 inference(transitivity,[status(thm)],[9852, 9850])).
% 87.01/87.26 tff(9854,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)))),
% 87.01/87.26 inference(quant_inst,[status(thm)],[])).
% 87.01/87.26 tff(9855,plain,
% 87.01/87.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10) | (~node14(c_e_h_2, c_h, s10, s11))),
% 87.01/87.26 inference(modus_ponens,[status(thm)],[9854, 9853])).
% 87.01/87.26 tff(9856,plain,
% 87.01/87.26 ($false),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9855, 283, 9613, 9838, 9849])).
% 87.01/87.26 tff(9857,plain,((~node14(c_e_h_2, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.26 tff(9858,plain,
% 87.01/87.26 (~node14(c_e_h_2, c_h, s10, s11)),
% 87.01/87.26 inference(unit_resolution,[status(thm)],[9857, 9613, 9838])).
% 87.01/87.27 tff(9859,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s10) | node14(c_e_h_2, c_h, s10, s11) | node15(c_e_h_2, c_h, s10, s11) | (~node19(c_e_h_2, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s10) | node14(c_e_h_2, c_h, s10, s11) | node15(c_e_h_2, c_h, s10, s11) | (~node19(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9860,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s10) | node14(c_e_h_2, c_h, s10, s11) | node15(c_e_h_2, c_h, s10, s11) | (~node19(c_e_h_2, c_h, s10, s11)))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9861,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s10) | node14(c_e_h_2, c_h, s10, s11) | node15(c_e_h_2, c_h, s10, s11) | (~node19(c_e_h_2, c_h, s10, s11))),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9860, 9859])).
% 87.01/87.27 tff(9862,plain,
% 87.01/87.27 (node16(c_e_h_2, c_h, s10) | node14(c_e_h_2, c_h, s10, s11) | node15(c_e_h_2, c_h, s10, s11)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9861, 189, 9832])).
% 87.01/87.27 tff(9863,plain,
% 87.01/87.27 (node15(c_e_h_2, c_h, s10, s11)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9862, 9858, 9848])).
% 87.01/87.27 tff(9864,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node15(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node15(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9865,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node15(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9866,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | (~node15(c_e_h_2, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9865, 9864])).
% 87.01/87.27 tff(9867,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9866, 173, 9818, 9613, 9863])).
% 87.01/87.27 tff(9868,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s10) | m_c_h_element_v_in1(c_e_h_2, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9869,plain,
% 87.01/87.27 (m_c_h_element_v_in1(c_e_h_2, c_h, s10)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9868, 9613, 9818])).
% 87.01/87.27 tff(9870,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s10)), introduced(assumption)).
% 87.01/87.27 tff(9871,plain,
% 87.01/87.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s10)) | m_c_h_element_v_in2(c_e_h_2, c_h, s10) | (~node17(c_e_h_2, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s10)) | m_c_h_element_v_in2(c_e_h_2, c_h, s10) | (~node17(c_e_h_2, c_h, s10)))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9872,plain,
% 87.01/87.27 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s10)) | m_c_h_element_v_in2(c_e_h_2, c_h, s10) | (~node17(c_e_h_2, c_h, s10)))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9873,plain,
% 87.01/87.27 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s10)) | m_c_h_element_v_in2(c_e_h_2, c_h, s10) | (~node17(c_e_h_2, c_h, s10))),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9872, 9871])).
% 87.01/87.27 tff(9874,plain,
% 87.01/87.27 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s10)) | (~node17(c_e_h_2, c_h, s10))),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9873, 209, 9870])).
% 87.01/87.27 tff(9875,plain,
% 87.01/87.27 (~node17(c_e_h_2, c_h, s10)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9874, 9869])).
% 87.01/87.27 tff(9876,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9836, 9875, 9828])).
% 87.01/87.27 tff(9877,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s10) | m_c_h_element_v_out(c_e_h_2, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9878,plain,
% 87.01/87.27 (m_c_h_element_v_out(c_e_h_2, c_h, s10)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9877, 9817, 9613])).
% 87.01/87.27 tff(9879,plain,
% 87.01/87.27 (m_c_h_element_v_in2(c_e_h_2, c_h, s9)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9471, 9878, 9412])).
% 87.01/87.27 tff(9880,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9408, 309, 9653, 9879])).
% 87.01/87.27 tff(9881,plain,(m_or_h_gate_v_out(c_e_h_2, c_j, s9) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9882,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9881, 9651, 9615, 9412, 9613])).
% 87.01/87.27 tff(9883,plain,(m_and_h_gate_v_out(c_e_h_2, c_l, s8) | m_c_h_element_v_out(c_e_h_2, c_h, s9) | (~m_c_h_element_v_out(c_e_h_2, c_h, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9884,plain,
% 87.01/87.27 (~m_c_h_element_v_out(c_e_h_2, c_h, s11)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9883, 9253, 9243, 9003])).
% 87.01/87.27 tff(9885,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_i, s11)), introduced(assumption)).
% 87.01/87.27 tff(9886,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s11)), introduced(assumption)).
% 87.01/87.27 tff(9887,plain,
% 87.01/87.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s11))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9888,plain,
% 87.01/87.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s11))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9889,plain,
% 87.01/87.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s11)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9888, 9887])).
% 87.01/87.27 tff(9890,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9889, 23, 9886, 9885])).
% 87.01/87.27 tff(9891,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_i, s11)) | m_c_h_element_v_out(c_e_h_2, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9892,plain,
% 87.01/87.27 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s11)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9891, 9884])).
% 87.01/87.27 tff(9893,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_i, s11)), introduced(assumption)).
% 87.01/87.27 tff(9894,assumption,(node20(c_e_h_2, c_i, s11)), introduced(assumption)).
% 87.01/87.27 tff(9895,plain,
% 87.01/87.27 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s11))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9896,plain,
% 87.01/87.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s11))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9897,plain,
% 87.01/87.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s11)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9896, 9895])).
% 87.01/87.27 tff(9898,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9897, 37, 9894, 9893])).
% 87.01/87.27 tff(9899,plain,((~node20(c_e_h_2, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9900,plain,
% 87.01/87.27 (~node20(c_e_h_2, c_i, s11)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9899, 9892])).
% 87.01/87.27 tff(9901,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s12)), introduced(assumption)).
% 87.01/87.27 tff(9902,assumption,(node22(c_e_h_2, c_i, s11, s12)), introduced(assumption)).
% 87.01/87.27 tff(9903,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | (~node22(c_e_h_2, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | (~node22(c_e_h_2, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9904,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | (~node22(c_e_h_2, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9905,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | (~node22(c_e_h_2, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9904, 9903])).
% 87.01/87.27 tff(9906,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9905, 107, 9506, 9901, 9902])).
% 87.01/87.27 tff(9907,plain,((~node22(c_e_h_2, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s12))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9908,plain,
% 87.01/87.27 (~node22(c_e_h_2, c_i, s11, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9907, 9901, 9506])).
% 87.01/87.27 tff(9909,assumption,(~node20(c_e_h_2, c_i, s11)), introduced(assumption)).
% 87.01/87.27 tff(9910,assumption,(node21(c_e_h_2, c_i, s11, s12)), introduced(assumption)).
% 87.01/87.27 tff(9911,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | (~node21(c_e_h_2, c_i, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | (~node21(c_e_h_2, c_i, s11, s12)))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9912,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | (~node21(c_e_h_2, c_i, s11, s12)))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9913,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | (~node21(c_e_h_2, c_i, s11, s12))),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9912, 9911])).
% 87.01/87.27 tff(9914,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9913, 51, 9901, 9909, 9910])).
% 87.01/87.27 tff(9915,plain,((~node21(c_e_h_2, c_i, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | node20(c_e_h_2, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9916,plain,
% 87.01/87.27 (~node21(c_e_h_2, c_i, s11, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9915, 9901, 9909])).
% 87.01/87.27 tff(9917,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_2, c_i, s11, s12) | node22(c_e_h_2, c_i, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_2, c_i, s11, s12) | node22(c_e_h_2, c_i, s11, s12))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9918,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_2, c_i, s11, s12) | node22(c_e_h_2, c_i, s11, s12))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9919,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_2, c_i, s11, s12) | node22(c_e_h_2, c_i, s11, s12)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9918, 9917])).
% 87.01/87.27 tff(9920,plain,
% 87.01/87.27 (node21(c_e_h_2, c_i, s11, s12) | node22(c_e_h_2, c_i, s11, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9919, 81, 4461])).
% 87.01/87.27 tff(9921,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9920, 9916, 9908])).
% 87.01/87.27 tff(9922,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s12)) | node20(c_e_h_2, c_i, s11) | m_and_h_gate_v_out(c_e_h_2, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9923,plain,
% 87.01/87.27 (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9922, 9504, 9900])).
% 87.01/87.27 tff(9924,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s12)), introduced(assumption)).
% 87.01/87.27 tff(9925,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s12)), introduced(assumption)).
% 87.01/87.27 tff(9926,plain,
% 87.01/87.27 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9927,plain,
% 87.01/87.27 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9928,plain,
% 87.01/87.27 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9927, 9926])).
% 87.01/87.27 tff(9929,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9928, 365, 9925, 9924])).
% 87.01/87.27 tff(9930,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9931,plain,
% 87.01/87.27 (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9930, 9923])).
% 87.01/87.27 tff(9932,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s12)), introduced(assumption)).
% 87.01/87.27 tff(9933,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s13)), introduced(assumption)).
% 87.01/87.27 tff(9934,assumption,(node18(c_e_h_2, c_e, s12, s13)), introduced(assumption)).
% 87.01/87.27 tff(9935,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12) | (~node18(c_e_h_2, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12) | (~node18(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9936,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12) | (~node18(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9937,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12) | (~node18(c_e_h_2, c_e, s12, s13))),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9936, 9935])).
% 87.01/87.27 tff(9938,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9937, 124, 9934, 9932, 9933])).
% 87.01/87.27 tff(9939,plain,((~node18(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9940,plain,
% 87.01/87.27 (~node18(c_e_h_2, c_e, s12, s13)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9939, 9933, 9932])).
% 87.01/87.27 tff(9941,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_2, c_e, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_2, c_e, s12, s13))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9942,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_2, c_e, s12, s13))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9943,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_2, c_e, s12, s13)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9942, 9941])).
% 87.01/87.27 tff(9944,plain,
% 87.01/87.27 (node19(c_e_h_2, c_e, s12, s13)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9943, 141, 9599])).
% 87.01/87.27 tff(9945,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s12, s13)) | node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s12, s13)) | node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9946,plain,
% 87.01/87.27 ((node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13))) <=> ((~node19(c_e_h_2, c_e, s12, s13)) | node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9947,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s12, s13)) | node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.27 inference(monotonicity,[status(thm)],[9946])).
% 87.01/87.27 tff(9948,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s12, s13)) | node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13))),
% 87.01/87.27 inference(transitivity,[status(thm)],[9947, 9945])).
% 87.01/87.27 tff(9949,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9950,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s12, s13)) | node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9949, 9948])).
% 87.01/87.27 tff(9951,plain,
% 87.01/87.27 (node17(c_e_h_2, c_e, s12) | node18(c_e_h_2, c_e, s12, s13)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9950, 156, 9944])).
% 87.01/87.27 tff(9952,plain,
% 87.01/87.27 (node17(c_e_h_2, c_e, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9951, 9940])).
% 87.01/87.27 tff(9953,assumption,(node15(c_e_h_2, c_e, s12, s13)), introduced(assumption)).
% 87.01/87.27 tff(9954,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | (~node15(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | (~node15(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9955,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | (~node15(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9956,plain,
% 87.01/87.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | (~node15(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9955, 9954])).
% 87.01/87.27 tff(9957,plain,
% 87.01/87.27 ($false),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9956, 173, 9953, 9932, 9933])).
% 87.01/87.27 tff(9958,plain,((~node15(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s12) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.27 tff(9959,plain,
% 87.01/87.27 (~node15(c_e_h_2, c_e, s12, s13)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9958, 9933, 9932])).
% 87.01/87.27 tff(9960,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s12)), introduced(assumption)).
% 87.01/87.27 tff(9961,assumption,(~node15(c_e_h_2, c_e, s12, s13)), introduced(assumption)).
% 87.01/87.27 tff(9962,assumption,(node17(c_e_h_2, c_e, s12)), introduced(assumption)).
% 87.01/87.27 tff(9963,plain,
% 87.01/87.27 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9964,plain,
% 87.01/87.27 ((m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | (~node17(c_e_h_2, c_e, s12))) <=> ((~node17(c_e_h_2, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9965,plain,
% 87.01/87.27 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | (~node17(c_e_h_2, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12)))),
% 87.01/87.27 inference(monotonicity,[status(thm)],[9964])).
% 87.01/87.27 tff(9966,plain,
% 87.01/87.27 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | (~node17(c_e_h_2, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12))),
% 87.01/87.27 inference(transitivity,[status(thm)],[9965, 9963])).
% 87.01/87.27 tff(9967,plain,
% 87.01/87.27 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | (~node17(c_e_h_2, c_e, s12)))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9968,plain,
% 87.01/87.27 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9967, 9966])).
% 87.01/87.27 tff(9969,plain,
% 87.01/87.27 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9968, 245, 9962])).
% 87.01/87.27 tff(9970,plain,
% 87.01/87.27 (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9969, 9960])).
% 87.01/87.27 tff(9971,plain,
% 87.01/87.27 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | m_c_h_element_v_in2(c_e_h_2, c_e, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | m_c_h_element_v_in2(c_e_h_2, c_e, s12))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9972,plain,
% 87.01/87.27 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | m_c_h_element_v_in2(c_e_h_2, c_e, s12))),
% 87.01/87.27 inference(quant_inst,[status(thm)],[])).
% 87.01/87.27 tff(9973,plain,
% 87.01/87.27 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s12)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | m_c_h_element_v_in2(c_e_h_2, c_e, s12)),
% 87.01/87.27 inference(modus_ponens,[status(thm)],[9972, 9971])).
% 87.01/87.27 tff(9974,plain,
% 87.01/87.27 (~node16(c_e_h_2, c_e, s12)),
% 87.01/87.27 inference(unit_resolution,[status(thm)],[9973, 228, 9960, 9970])).
% 87.01/87.27 tff(9975,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s12) | node15(c_e_h_2, c_e, s12, s13) | node14(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s12) | node15(c_e_h_2, c_e, s12, s13) | node14(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9976,plain,
% 87.01/87.27 ((node16(c_e_h_2, c_e, s12) | node14(c_e_h_2, c_e, s12, s13) | node15(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13))) <=> (node16(c_e_h_2, c_e, s12) | node15(c_e_h_2, c_e, s12, s13) | node14(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.27 inference(rewrite,[status(thm)],[])).
% 87.01/87.27 tff(9977,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s12) | node14(c_e_h_2, c_e, s12, s13) | node15(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s12) | node15(c_e_h_2, c_e, s12, s13) | node14(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13))))),
% 87.01/87.27 inference(monotonicity,[status(thm)],[9976])).
% 87.01/87.27 tff(9978,plain,
% 87.01/87.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s12) | node14(c_e_h_2, c_e, s12, s13) | node15(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s12) | node15(c_e_h_2, c_e, s12, s13) | node14(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.28 inference(transitivity,[status(thm)],[9977, 9975])).
% 87.01/87.28 tff(9979,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s12) | node14(c_e_h_2, c_e, s12, s13) | node15(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(9980,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s12) | node15(c_e_h_2, c_e, s12, s13) | node14(c_e_h_2, c_e, s12, s13) | (~node19(c_e_h_2, c_e, s12, s13))),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[9979, 9978])).
% 87.01/87.28 tff(9981,plain,
% 87.01/87.28 (node16(c_e_h_2, c_e, s12) | node15(c_e_h_2, c_e, s12, s13) | node14(c_e_h_2, c_e, s12, s13)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9980, 189, 9944])).
% 87.01/87.28 tff(9982,plain,
% 87.01/87.28 (node14(c_e_h_2, c_e, s12, s13)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9981, 9974, 9961])).
% 87.01/87.28 tff(9983,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~node14(c_e_h_2, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~node14(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(9984,plain,
% 87.01/87.28 (((~node14(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~node14(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(9985,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~node14(c_e_h_2, c_e, s12, s13))))),
% 87.01/87.28 inference(monotonicity,[status(thm)],[9984])).
% 87.01/87.28 tff(9986,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~node14(c_e_h_2, c_e, s12, s13)))),
% 87.01/87.28 inference(transitivity,[status(thm)],[9985, 9983])).
% 87.01/87.28 tff(9987,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(9988,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~node14(c_e_h_2, c_e, s12, s13))),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[9987, 9986])).
% 87.01/87.28 tff(9989,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9988, 283, 9982, 9933, 9960])).
% 87.01/87.28 tff(9990,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s12) | (~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | node15(c_e_h_2, c_e, s12, s13) | (~node17(c_e_h_2, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(9991,plain,
% 87.01/87.28 (m_c_h_element_v_in1(c_e_h_2, c_e, s12)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9990, 9959, 9933, 9952])).
% 87.01/87.28 tff(9992,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s12)), introduced(assumption)).
% 87.01/87.28 tff(9993,plain,
% 87.01/87.28 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s12)))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(9994,plain,
% 87.01/87.28 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~node17(c_e_h_2, c_e, s12))) <=> ((~node17(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s12)))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(9995,plain,
% 87.01/87.28 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~node17(c_e_h_2, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s12))))),
% 87.01/87.28 inference(monotonicity,[status(thm)],[9994])).
% 87.01/87.28 tff(9996,plain,
% 87.01/87.28 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~node17(c_e_h_2, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s12)))),
% 87.01/87.28 inference(transitivity,[status(thm)],[9995, 9993])).
% 87.01/87.28 tff(9997,plain,
% 87.01/87.28 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~node17(c_e_h_2, c_e, s12)))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(9998,plain,
% 87.01/87.28 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s12))),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[9997, 9996])).
% 87.01/87.28 tff(9999,plain,
% 87.01/87.28 ((~node17(c_e_h_2, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s12))),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9998, 209, 9992])).
% 87.01/87.28 tff(10000,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9999, 9991, 9952])).
% 87.01/87.28 tff(10001,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s13)) | m_c_h_element_v_in2(c_e_h_2, c_e, s12) | m_c_h_element_v_out(c_e_h_2, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10002,plain,
% 87.01/87.28 (~m_c_h_element_v_out(c_e_h_2, c_e, s13)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10001, 9931, 9574])).
% 87.01/87.28 tff(10003,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_r, s13)), introduced(assumption)).
% 87.01/87.28 tff(10004,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s13)), introduced(assumption)).
% 87.01/87.28 tff(10005,plain,
% 87.01/87.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s13))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10006,plain,
% 87.01/87.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s13))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10007,plain,
% 87.01/87.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s13)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10006, 10005])).
% 87.01/87.28 tff(10008,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10007, 1884, 10004, 10003])).
% 87.01/87.28 tff(10009,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_r, s13)) | m_c_h_element_v_out(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10010,plain,
% 87.01/87.28 (~m_and_h_gate_v_in1(c_e_h_2, c_r, s13)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10009, 10002])).
% 87.01/87.28 tff(10011,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_r, s13)), introduced(assumption)).
% 87.01/87.28 tff(10012,assumption,(node20(c_e_h_2, c_r, s13)), introduced(assumption)).
% 87.01/87.28 tff(10013,plain,
% 87.01/87.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s13))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10014,plain,
% 87.01/87.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s13))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10015,plain,
% 87.01/87.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s13)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10014, 10013])).
% 87.01/87.28 tff(10016,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10015, 37, 10012, 10011])).
% 87.01/87.28 tff(10017,plain,((~node20(c_e_h_2, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10018,plain,
% 87.01/87.28 (~node20(c_e_h_2, c_r, s13)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10017, 10010])).
% 87.01/87.28 tff(10019,assumption,(~node20(c_e_h_2, c_r, s13)), introduced(assumption)).
% 87.01/87.28 tff(10020,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s14)), introduced(assumption)).
% 87.01/87.28 tff(10021,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node21(c_e_h_2, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node21(c_e_h_2, c_r, s13, s14)))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10022,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node21(c_e_h_2, c_r, s13, s14)))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10023,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node21(c_e_h_2, c_r, s13, s14))),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10022, 10021])).
% 87.01/87.28 tff(10024,plain,
% 87.01/87.28 (node20(c_e_h_2, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node21(c_e_h_2, c_r, s13, s14))),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10023, 51])).
% 87.01/87.28 tff(10025,plain,
% 87.01/87.28 (~node21(c_e_h_2, c_r, s13, s14)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10024, 10020, 10019])).
% 87.01/87.28 tff(10026,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s13)), introduced(assumption)).
% 87.01/87.28 tff(10027,assumption,(node22(c_e_h_2, c_r, s13, s14)), introduced(assumption)).
% 87.01/87.28 tff(10028,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node22(c_e_h_2, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node22(c_e_h_2, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10029,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node22(c_e_h_2, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10030,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | (~node22(c_e_h_2, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10029, 10028])).
% 87.01/87.28 tff(10031,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10030, 107, 10026, 10020, 10027])).
% 87.01/87.28 tff(10032,plain,((~node22(c_e_h_2, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s14))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10033,plain,
% 87.01/87.28 (~node22(c_e_h_2, c_r, s13, s14)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10032, 10020, 10026])).
% 87.01/87.28 tff(10034,plain,
% 87.01/87.28 (succ(s13, s14) <=> succ(s13, s14)),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10035,axiom,(succ(s13, s14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound14')).
% 87.01/87.28 tff(10036,plain,
% 87.01/87.28 (succ(s13, s14)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10035, 10034])).
% 87.01/87.28 tff(10037,plain,
% 87.01/87.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10038,plain,
% 87.01/87.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10039,plain,
% 87.01/87.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10038, 10037])).
% 87.01/87.28 tff(10040,plain,
% 87.01/87.28 (trans(s13, s14)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10039, 10036, 64])).
% 87.01/87.28 tff(10041,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_2, c_r, s13, s14) | node22(c_e_h_2, c_r, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_2, c_r, s13, s14) | node22(c_e_h_2, c_r, s13, s14))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10042,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_2, c_r, s13, s14) | node22(c_e_h_2, c_r, s13, s14))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10043,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_2, c_r, s13, s14) | node22(c_e_h_2, c_r, s13, s14)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10042, 10041])).
% 87.01/87.28 tff(10044,plain,
% 87.01/87.28 (node21(c_e_h_2, c_r, s13, s14) | node22(c_e_h_2, c_r, s13, s14)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10043, 81, 10040])).
% 87.01/87.28 tff(10045,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10044, 10033, 10025])).
% 87.01/87.28 tff(10046,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13) | node20(c_e_h_2, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10047,plain,
% 87.01/87.28 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10046, 10018])).
% 87.01/87.28 tff(10048,plain,
% 87.01/87.28 (~m_and_h_gate_v_out(c_e_h_2, c_r, s14)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10047, 9612])).
% 87.01/87.28 tff(10049,plain,
% 87.01/87.28 (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9645, 9243])).
% 87.01/87.28 tff(10050,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s11)), introduced(assumption)).
% 87.01/87.28 tff(10051,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s9)), introduced(assumption)).
% 87.01/87.28 tff(10052,plain,
% 87.01/87.28 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9650, 10051])).
% 87.01/87.28 tff(10053,plain,
% 87.01/87.28 (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[9812, 10052, 9653])).
% 87.01/87.28 tff(10054,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s10)), introduced(assumption)).
% 87.01/87.28 tff(10055,assumption,(node21(c_e_h_2, c_l, s9, s10)), introduced(assumption)).
% 87.01/87.28 tff(10056,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_l, s9)), introduced(assumption)).
% 87.01/87.28 tff(10057,plain,
% 87.01/87.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10058,plain,
% 87.01/87.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10059,plain,
% 87.01/87.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10058, 10057])).
% 87.01/87.28 tff(10060,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10059, 1638, 3682, 10056])).
% 87.01/87.28 tff(10061,plain,((~m_and_h_gate_v_in2(c_e_h_2, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10062,plain,
% 87.01/87.28 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s9)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10061, 3142])).
% 87.01/87.28 tff(10063,assumption,(node20(c_e_h_2, c_l, s9)), introduced(assumption)).
% 87.01/87.28 tff(10064,plain,
% 87.01/87.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s9))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10065,plain,
% 87.01/87.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s9))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10066,plain,
% 87.01/87.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s9)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10065, 10064])).
% 87.01/87.28 tff(10067,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10066, 1535, 10063, 10062])).
% 87.01/87.28 tff(10068,plain,(~node20(c_e_h_2, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10069,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | (~node21(c_e_h_2, c_l, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | (~node21(c_e_h_2, c_l, s9, s10)))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10070,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | (~node21(c_e_h_2, c_l, s9, s10)))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10071,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | (~node21(c_e_h_2, c_l, s9, s10))),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10070, 10069])).
% 87.01/87.28 tff(10072,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10071, 51, 10054, 10068, 10055])).
% 87.01/87.28 tff(10073,plain,((~node21(c_e_h_2, c_l, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s10))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10074,plain,
% 87.01/87.28 (~node21(c_e_h_2, c_l, s9, s10)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10073, 10054])).
% 87.01/87.28 tff(10075,assumption,(node22(c_e_h_2, c_l, s9, s10)), introduced(assumption)).
% 87.01/87.28 tff(10076,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | (~node22(c_e_h_2, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | (~node22(c_e_h_2, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10077,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | (~node22(c_e_h_2, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10078,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | (~node22(c_e_h_2, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10077, 10076])).
% 87.01/87.28 tff(10079,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10078, 107, 10051, 10054, 10075])).
% 87.01/87.28 tff(10080,plain,((~node22(c_e_h_2, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s10))), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10081,plain,
% 87.01/87.28 (~node22(c_e_h_2, c_l, s9, s10)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10080, 10054, 10051])).
% 87.01/87.28 tff(10082,plain,
% 87.01/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_l, s9, s10) | node22(c_e_h_2, c_l, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_l, s9, s10) | node22(c_e_h_2, c_l, s9, s10))),
% 87.01/87.28 inference(rewrite,[status(thm)],[])).
% 87.01/87.28 tff(10083,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_l, s9, s10) | node22(c_e_h_2, c_l, s9, s10))),
% 87.01/87.28 inference(quant_inst,[status(thm)],[])).
% 87.01/87.28 tff(10084,plain,
% 87.01/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_l, s9, s10) | node22(c_e_h_2, c_l, s9, s10)),
% 87.01/87.28 inference(modus_ponens,[status(thm)],[10083, 10082])).
% 87.01/87.28 tff(10085,plain,
% 87.01/87.28 (node21(c_e_h_2, c_l, s9, s10) | node22(c_e_h_2, c_l, s9, s10)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10084, 81, 3175])).
% 87.01/87.28 tff(10086,plain,
% 87.01/87.28 ($false),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10085, 10081, 10074])).
% 87.01/87.28 tff(10087,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 87.01/87.28 tff(10088,plain,
% 87.01/87.28 (~m_and_h_gate_v_out(c_e_h_2, c_l, s10)),
% 87.01/87.28 inference(unit_resolution,[status(thm)],[10087, 10051])).
% 87.01/87.28 tff(10089,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s10)), introduced(assumption)).
% 87.10/87.28 tff(10090,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s10)), introduced(assumption)).
% 87.10/87.28 tff(10091,plain,
% 87.10/87.28 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10))),
% 87.10/87.28 inference(rewrite,[status(thm)],[])).
% 87.10/87.28 tff(10092,plain,
% 87.10/87.28 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10))),
% 87.10/87.28 inference(quant_inst,[status(thm)],[])).
% 87.10/87.28 tff(10093,plain,
% 87.10/87.28 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10)),
% 87.10/87.28 inference(modus_ponens,[status(thm)],[10092, 10091])).
% 87.10/87.28 tff(10094,plain,
% 87.10/87.28 ($false),
% 87.10/87.28 inference(unit_resolution,[status(thm)],[10093, 801, 10090, 10089])).
% 87.10/87.28 tff(10095,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s10)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.28 tff(10096,plain,
% 87.10/87.28 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s10)),
% 87.10/87.28 inference(unit_resolution,[status(thm)],[10095, 10088])).
% 87.10/87.28 tff(10097,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s10)), introduced(assumption)).
% 87.10/87.28 tff(10098,assumption,(node6(c_e_h_2, c_j, s10, s11)), introduced(assumption)).
% 87.10/87.28 tff(10099,plain,
% 87.10/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10) | (~node6(c_e_h_2, c_j, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10) | (~node6(c_e_h_2, c_j, s10, s11)))),
% 87.10/87.28 inference(rewrite,[status(thm)],[])).
% 87.10/87.28 tff(10100,plain,
% 87.10/87.28 (((~node6(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10)) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10) | (~node6(c_e_h_2, c_j, s10, s11)))),
% 87.10/87.28 inference(rewrite,[status(thm)],[])).
% 87.10/87.28 tff(10101,plain,
% 87.10/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10) | (~node6(c_e_h_2, c_j, s10, s11))))),
% 87.10/87.28 inference(monotonicity,[status(thm)],[10100])).
% 87.10/87.28 tff(10102,plain,
% 87.10/87.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10) | (~node6(c_e_h_2, c_j, s10, s11)))),
% 87.10/87.28 inference(transitivity,[status(thm)],[10101, 10099])).
% 87.10/87.28 tff(10103,plain,
% 87.10/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10))),
% 87.10/87.28 inference(quant_inst,[status(thm)],[])).
% 87.10/87.28 tff(10104,plain,
% 87.10/87.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10) | (~node6(c_e_h_2, c_j, s10, s11))),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10103, 10102])).
% 87.10/87.29 tff(10105,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10104, 899, 10097, 10050, 10098])).
% 87.10/87.29 tff(10106,plain,((~node6(c_e_h_2, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11))), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10107,plain,
% 87.10/87.29 (~node6(c_e_h_2, c_j, s10, s11)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10106, 10050, 10097])).
% 87.10/87.29 tff(10108,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s10)), introduced(assumption)).
% 87.10/87.29 tff(10109,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s10)), introduced(assumption)).
% 87.10/87.29 tff(10110,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s8)), introduced(assumption)).
% 87.10/87.29 tff(10111,plain,
% 87.10/87.29 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10112,plain,
% 87.10/87.29 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10113,plain,
% 87.10/87.29 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10112, 10111])).
% 87.10/87.29 tff(10114,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10113, 2218, 8202, 10110])).
% 87.10/87.29 tff(10115,plain,(~m_c_h_element_v_in2(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10116,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s9)), introduced(assumption)).
% 87.10/87.29 tff(10117,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s8)), introduced(assumption)).
% 87.10/87.29 tff(10118,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s8)), introduced(assumption)).
% 87.10/87.29 tff(10119,assumption,(~node15(c_e_h_1, c_f, s8, s9)), introduced(assumption)).
% 87.10/87.29 tff(10120,assumption,(node14(c_e_h_1, c_f, s8, s9)), introduced(assumption)).
% 87.10/87.29 tff(10121,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node14(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node14(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10122,plain,
% 87.10/87.29 (((~node14(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node14(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10123,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node14(c_e_h_1, c_f, s8, s9))))),
% 87.10/87.29 inference(monotonicity,[status(thm)],[10122])).
% 87.10/87.29 tff(10124,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node14(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(transitivity,[status(thm)],[10123, 10121])).
% 87.10/87.29 tff(10125,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10126,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node14(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10125, 10124])).
% 87.10/87.29 tff(10127,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10126, 283, 10116, 10120, 10118])).
% 87.10/87.29 tff(10128,plain,((~node14(c_e_h_1, c_f, s8, s9)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10129,plain,
% 87.10/87.29 (~node14(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10128, 10118, 10116])).
% 87.10/87.29 tff(10130,plain,
% 87.10/87.29 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10131,plain,
% 87.10/87.29 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10132,plain,
% 87.10/87.29 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10131, 10130])).
% 87.10/87.29 tff(10133,plain,
% 87.10/87.29 ((~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10132, 228, 10117])).
% 87.10/87.29 tff(10134,plain,
% 87.10/87.29 (~node16(c_e_h_1, c_f, s8)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10133, 10118])).
% 87.10/87.29 tff(10135,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10136,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10137,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10136, 10135])).
% 87.10/87.29 tff(10138,plain,
% 87.10/87.29 (node19(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10137, 141, 2636])).
% 87.10/87.29 tff(10139,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node16(c_e_h_1, c_f, s8) | node15(c_e_h_1, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node16(c_e_h_1, c_f, s8) | node15(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10140,plain,
% 87.10/87.29 ((node16(c_e_h_1, c_f, s8) | node14(c_e_h_1, c_f, s8, s9) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9))) <=> (node14(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node16(c_e_h_1, c_f, s8) | node15(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10141,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s8) | node14(c_e_h_1, c_f, s8, s9) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node16(c_e_h_1, c_f, s8) | node15(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(monotonicity,[status(thm)],[10140])).
% 87.10/87.29 tff(10142,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s8) | node14(c_e_h_1, c_f, s8, s9) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node16(c_e_h_1, c_f, s8) | node15(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(transitivity,[status(thm)],[10141, 10139])).
% 87.10/87.29 tff(10143,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s8) | node14(c_e_h_1, c_f, s8, s9) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10144,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node16(c_e_h_1, c_f, s8) | node15(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10143, 10142])).
% 87.10/87.29 tff(10145,plain,
% 87.10/87.29 (node14(c_e_h_1, c_f, s8, s9) | node16(c_e_h_1, c_f, s8) | node15(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10144, 189, 10138])).
% 87.10/87.29 tff(10146,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10145, 10134, 10129, 10119])).
% 87.10/87.29 tff(10147,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s8) | node15(c_e_h_1, c_f, s8, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10148,plain,
% 87.10/87.29 (node15(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10147, 10116, 10117, 10118])).
% 87.10/87.29 tff(10149,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node15(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node15(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10150,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node15(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10151,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node15(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10150, 10149])).
% 87.10/87.29 tff(10152,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10151, 173, 9746, 10116, 10148])).
% 87.10/87.29 tff(10153,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | m_c_h_element_v_in1(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10154,plain,
% 87.10/87.29 (m_c_h_element_v_in1(c_e_h_1, c_f, s8)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10153, 9746, 10117, 10116])).
% 87.10/87.29 tff(10155,plain,
% 87.10/87.29 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10156,plain,
% 87.10/87.29 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10157,plain,
% 87.10/87.29 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8))))),
% 87.10/87.29 inference(monotonicity,[status(thm)],[10156])).
% 87.10/87.29 tff(10158,plain,
% 87.10/87.29 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)))),
% 87.10/87.29 inference(transitivity,[status(thm)],[10157, 10155])).
% 87.10/87.29 tff(10159,plain,
% 87.10/87.29 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10160,plain,
% 87.10/87.29 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8))),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10159, 10158])).
% 87.10/87.29 tff(10161,plain,
% 87.10/87.29 ((~node17(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8))),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10160, 209, 10117])).
% 87.10/87.29 tff(10162,plain,
% 87.10/87.29 (~node17(c_e_h_1, c_f, s8)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10161, 10154])).
% 87.10/87.29 tff(10163,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s8, s9)) | node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s8, s9)) | node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10164,plain,
% 87.10/87.29 ((node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9))) <=> ((~node19(c_e_h_1, c_f, s8, s9)) | node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10165,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s8, s9)) | node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(monotonicity,[status(thm)],[10164])).
% 87.10/87.29 tff(10166,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s8, s9)) | node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(transitivity,[status(thm)],[10165, 10163])).
% 87.10/87.29 tff(10167,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10168,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s8, s9)) | node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10167, 10166])).
% 87.10/87.29 tff(10169,plain,
% 87.10/87.29 (node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10168, 156, 10138])).
% 87.10/87.29 tff(10170,plain,
% 87.10/87.29 (node18(c_e_h_1, c_f, s8, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10169, 10162])).
% 87.10/87.29 tff(10171,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node18(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node18(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10172,plain,
% 87.10/87.29 (((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~node18(c_e_h_1, c_f, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node18(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10173,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~node18(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node18(c_e_h_1, c_f, s8, s9))))),
% 87.10/87.29 inference(monotonicity,[status(thm)],[10172])).
% 87.10/87.29 tff(10174,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~node18(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node18(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(transitivity,[status(thm)],[10173, 10171])).
% 87.10/87.29 tff(10175,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~node18(c_e_h_1, c_f, s8, s9)))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10176,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node18(c_e_h_1, c_f, s8, s9))),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10175, 10174])).
% 87.10/87.29 tff(10177,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10176, 124, 9746, 10116, 10170])).
% 87.10/87.29 tff(10178,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10179,plain,
% 87.10/87.29 ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10178, 9742])).
% 87.10/87.29 tff(10180,plain,
% 87.10/87.29 (~m_c_h_element_v_out(c_e_h_1, c_f, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10179, 10115])).
% 87.10/87.29 tff(10181,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s9)), introduced(assumption)).
% 87.10/87.29 tff(10182,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s9)), introduced(assumption)).
% 87.10/87.29 tff(10183,plain,
% 87.10/87.29 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10184,plain,
% 87.10/87.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10185,plain,
% 87.10/87.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10184, 10183])).
% 87.10/87.29 tff(10186,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10185, 1666, 10182, 10181])).
% 87.10/87.29 tff(10187,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10188,plain,
% 87.10/87.29 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10187, 10180])).
% 87.10/87.29 tff(10189,assumption,(node20(c_e_h_1, c_q, s9)), introduced(assumption)).
% 87.10/87.29 tff(10190,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)), introduced(assumption)).
% 87.10/87.29 tff(10191,plain,
% 87.10/87.29 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10192,plain,
% 87.10/87.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10193,plain,
% 87.10/87.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10192, 10191])).
% 87.10/87.29 tff(10194,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10193, 37, 10190, 10189])).
% 87.10/87.29 tff(10195,plain,((~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10196,plain,
% 87.10/87.29 (~node20(c_e_h_1, c_q, s9)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10195, 10188])).
% 87.10/87.29 tff(10197,assumption,(~node20(c_e_h_1, c_q, s9)), introduced(assumption)).
% 87.10/87.29 tff(10198,assumption,(node21(c_e_h_1, c_q, s9, s10)), introduced(assumption)).
% 87.10/87.29 tff(10199,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node21(c_e_h_1, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node21(c_e_h_1, c_q, s9, s10)))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10200,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node21(c_e_h_1, c_q, s9, s10)))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10201,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node21(c_e_h_1, c_q, s9, s10))),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10200, 10199])).
% 87.10/87.29 tff(10202,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10201, 51, 10109, 10198, 10197])).
% 87.10/87.29 tff(10203,plain,((~node21(c_e_h_1, c_q, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | node20(c_e_h_1, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10204,plain,
% 87.10/87.29 ((~node21(c_e_h_1, c_q, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10))),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10203, 10196])).
% 87.10/87.29 tff(10205,plain,
% 87.10/87.29 (~node21(c_e_h_1, c_q, s9, s10)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10204, 10109])).
% 87.10/87.29 tff(10206,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s9)), introduced(assumption)).
% 87.10/87.29 tff(10207,assumption,(node22(c_e_h_1, c_q, s9, s10)), introduced(assumption)).
% 87.10/87.29 tff(10208,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node22(c_e_h_1, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node22(c_e_h_1, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10209,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node22(c_e_h_1, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10210,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node22(c_e_h_1, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)),
% 87.10/87.29 inference(modus_ponens,[status(thm)],[10209, 10208])).
% 87.10/87.29 tff(10211,plain,
% 87.10/87.29 ($false),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10210, 107, 10109, 10206, 10207])).
% 87.10/87.29 tff(10212,plain,((~node22(c_e_h_1, c_q, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.29 tff(10213,plain,
% 87.10/87.29 (~node22(c_e_h_1, c_q, s9, s10)),
% 87.10/87.29 inference(unit_resolution,[status(thm)],[10212, 10109, 10206])).
% 87.10/87.29 tff(10214,plain,
% 87.10/87.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10))),
% 87.10/87.29 inference(rewrite,[status(thm)],[])).
% 87.10/87.29 tff(10215,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10))),
% 87.10/87.29 inference(quant_inst,[status(thm)],[])).
% 87.10/87.29 tff(10216,plain,
% 87.10/87.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10)),
% 87.10/87.30 inference(modus_ponens,[status(thm)],[10215, 10214])).
% 87.10/87.30 tff(10217,plain,
% 87.10/87.30 (node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10)),
% 87.10/87.30 inference(unit_resolution,[status(thm)],[10216, 81, 3175])).
% 87.10/87.30 tff(10218,plain,
% 87.10/87.30 ($false),
% 87.10/87.30 inference(unit_resolution,[status(thm)],[10217, 10213, 10205])).
% 87.10/87.30 tff(10219,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.30 tff(10220,plain,
% 87.10/87.30 (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)),
% 87.10/87.30 inference(unit_resolution,[status(thm)],[10219, 9778])).
% 87.10/87.30 tff(10221,assumption,(~node3(c_e_h_1, c_e_h_2, s10)), introduced(assumption)).
% 87.10/87.30 tff(10222,plain,
% 87.10/87.30 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s10))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s10))),
% 87.10/87.30 inference(rewrite,[status(thm)],[])).
% 87.10/87.30 tff(10223,plain,
% 87.10/87.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s10))),
% 87.10/87.30 inference(quant_inst,[status(thm)],[])).
% 87.10/87.30 tff(10224,plain,
% 87.10/87.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s10)),
% 87.10/87.30 inference(modus_ponens,[status(thm)],[10223, 10222])).
% 87.10/87.30 tff(10225,plain,
% 87.10/87.30 ($false),
% 87.10/87.30 inference(unit_resolution,[status(thm)],[10224, 817, 814, 10221])).
% 87.10/87.30 tff(10226,plain,(node3(c_e_h_1, c_e_h_2, s10)), inference(lemma,lemma(discharge,[]))).
% 87.10/87.30 tff(10227,plain,
% 87.10/87.30 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s10)) | (~node3(c_e_h_1, c_e_h_2, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s10)) | (~node3(c_e_h_1, c_e_h_2, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))),
% 87.10/87.30 inference(rewrite,[status(thm)],[])).
% 87.10/87.30 tff(10228,plain,
% 87.10/87.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s10)) | (~node3(c_e_h_1, c_e_h_2, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))),
% 87.10/87.30 inference(quant_inst,[status(thm)],[])).
% 87.10/87.30 tff(10229,plain,
% 87.10/87.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s10)) | (~node3(c_e_h_1, c_e_h_2, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10)),
% 87.10/87.30 inference(modus_ponens,[status(thm)],[10228, 10227])).
% 87.10/87.30 tff(10230,plain,
% 87.10/87.30 ((~m_cell_v_ack(c_e_h_2, s10)) | (~node3(c_e_h_1, c_e_h_2, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10)),
% 87.10/87.30 inference(unit_resolution,[status(thm)],[10229, 836])).
% 87.10/87.30 tff(10231,plain,
% 87.10/87.30 ((~m_cell_v_ack(c_e_h_2, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10)),
% 87.10/87.30 inference(unit_resolution,[status(thm)],[10230, 10226])).
% 87.10/87.30 tff(10232,plain,
% 87.10/87.30 (~m_cell_v_ack(c_e_h_2, s10)),
% 87.10/87.30 inference(unit_resolution,[status(thm)],[10231, 10220])).
% 87.10/87.30 tff(10233,plain,
% 87.10/87.30 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s10)) | m_cell_v_ack(c_e_h_2, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s10)) | m_cell_v_ack(c_e_h_2, s10))),
% 87.10/87.30 inference(rewrite,[status(thm)],[])).
% 87.10/87.30 tff(10234,plain,
% 87.10/87.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s10)) | m_cell_v_ack(c_e_h_2, s10))),
% 87.10/87.30 inference(quant_inst,[status(thm)],[])).
% 87.10/87.30 tff(10235,plain,
% 87.10/87.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s10)) | m_cell_v_ack(c_e_h_2, s10)),
% 87.10/87.30 inference(modus_ponens,[status(thm)],[10234, 10233])).
% 87.11/87.30 tff(10236,plain,
% 87.11/87.30 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s10)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10235, 848, 10232])).
% 87.11/87.30 tff(10237,assumption,(node5(c_e_h_2, c_j, s10, s11)), introduced(assumption)).
% 87.11/87.30 tff(10238,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s10)), introduced(assumption)).
% 87.11/87.30 tff(10239,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11)))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10240,plain,
% 87.11/87.30 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11))) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11)))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10241,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11))))),
% 87.11/87.30 inference(monotonicity,[status(thm)],[10240])).
% 87.11/87.30 tff(10242,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11)))),
% 87.11/87.30 inference(transitivity,[status(thm)],[10241, 10239])).
% 87.11/87.30 tff(10243,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10244,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | (~node5(c_e_h_2, c_j, s10, s11))),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10243, 10242])).
% 87.11/87.30 tff(10245,plain,
% 87.11/87.30 ($false),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10244, 862, 10050, 10238, 10108, 10237])).
% 87.11/87.30 tff(10246,plain,((~node5(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s10) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.30 tff(10247,plain,
% 87.11/87.30 ((~node5(c_e_h_2, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10246, 10236])).
% 87.11/87.30 tff(10248,plain,
% 87.11/87.30 (~node5(c_e_h_2, c_j, s10, s11)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10247, 10050, 10108])).
% 87.11/87.30 tff(10249,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node5(c_e_h_2, c_j, s10, s11) | node6(c_e_h_2, c_j, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_2, c_j, s10, s11) | node6(c_e_h_2, c_j, s10, s11))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10250,plain,
% 87.11/87.30 ((node6(c_e_h_2, c_j, s10, s11) | node5(c_e_h_2, c_j, s10, s11) | (~trans(s10, s11))) <=> ((~trans(s10, s11)) | node5(c_e_h_2, c_j, s10, s11) | node6(c_e_h_2, c_j, s10, s11))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10251,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s10, s11) | node5(c_e_h_2, c_j, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node5(c_e_h_2, c_j, s10, s11) | node6(c_e_h_2, c_j, s10, s11)))),
% 87.11/87.30 inference(monotonicity,[status(thm)],[10250])).
% 87.11/87.30 tff(10252,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s10, s11) | node5(c_e_h_2, c_j, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_2, c_j, s10, s11) | node6(c_e_h_2, c_j, s10, s11))),
% 87.11/87.30 inference(transitivity,[status(thm)],[10251, 10249])).
% 87.11/87.30 tff(10253,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s10, s11) | node5(c_e_h_2, c_j, s10, s11) | (~trans(s10, s11)))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10254,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_2, c_j, s10, s11) | node6(c_e_h_2, c_j, s10, s11)),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10253, 10252])).
% 87.11/87.30 tff(10255,plain,
% 87.11/87.30 (node5(c_e_h_2, c_j, s10, s11) | node6(c_e_h_2, c_j, s10, s11)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10254, 881, 3778])).
% 87.11/87.30 tff(10256,plain,
% 87.11/87.30 ($false),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10255, 10248, 10107])).
% 87.11/87.30 tff(10257,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s10) | m_or_h_gate_v_out(c_e_h_2, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.30 tff(10258,plain,
% 87.11/87.30 ($false),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10257, 10096, 10053, 10050])).
% 87.11/87.30 tff(10259,plain,(m_and_h_gate_v_out(c_e_h_2, c_l, s9) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.30 tff(10260,plain,
% 87.11/87.30 (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10259, 9405, 10049])).
% 87.11/87.30 tff(10261,assumption,(m_c_h_element_v_in2(c_e_h_2, c_h, s11)), introduced(assumption)).
% 87.11/87.30 tff(10262,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s11)), introduced(assumption)).
% 87.11/87.30 tff(10263,plain,
% 87.11/87.30 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10264,plain,
% 87.11/87.30 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10265,plain,
% 87.11/87.30 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11)),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10264, 10263])).
% 87.11/87.30 tff(10266,plain,
% 87.11/87.30 ($false),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10265, 309, 10262, 10261])).
% 87.11/87.30 tff(10267,plain,((~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.30 tff(10268,plain,
% 87.11/87.30 (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10267, 10260])).
% 87.11/87.30 tff(10269,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s12)), introduced(assumption)).
% 87.11/87.30 tff(10270,assumption,(node18(c_e_h_2, c_h, s11, s12)), introduced(assumption)).
% 87.11/87.30 tff(10271,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node18(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node18(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10272,plain,
% 87.11/87.30 (((~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~node18(c_e_h_2, c_h, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node18(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10273,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~node18(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node18(c_e_h_2, c_h, s11, s12))))),
% 87.11/87.30 inference(monotonicity,[status(thm)],[10272])).
% 87.11/87.30 tff(10274,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~node18(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node18(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.30 inference(transitivity,[status(thm)],[10273, 10271])).
% 87.11/87.30 tff(10275,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~node18(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10276,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node18(c_e_h_2, c_h, s11, s12))),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10275, 10274])).
% 87.11/87.30 tff(10277,plain,
% 87.11/87.30 ($false),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10276, 124, 10269, 10270, 9886])).
% 87.11/87.30 tff(10278,plain,((~node18(c_e_h_2, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.30 tff(10279,plain,
% 87.11/87.30 (~node18(c_e_h_2, c_h, s11, s12)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10278, 10269, 9886])).
% 87.11/87.30 tff(10280,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s11)), introduced(assumption)).
% 87.11/87.30 tff(10281,assumption,(node14(c_e_h_2, c_h, s11, s12)), introduced(assumption)).
% 87.11/87.30 tff(10282,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node14(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node14(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10283,plain,
% 87.11/87.30 (((~node14(c_e_h_2, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node14(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10284,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node14(c_e_h_2, c_h, s11, s12))))),
% 87.11/87.30 inference(monotonicity,[status(thm)],[10283])).
% 87.11/87.30 tff(10285,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node14(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.30 inference(transitivity,[status(thm)],[10284, 10282])).
% 87.11/87.30 tff(10286,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10287,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node14(c_e_h_2, c_h, s11, s12))),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10286, 10285])).
% 87.11/87.30 tff(10288,plain,
% 87.11/87.30 ($false),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10287, 283, 10269, 10280, 10281])).
% 87.11/87.30 tff(10289,plain,((~node14(c_e_h_2, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.30 tff(10290,plain,
% 87.11/87.30 (~node14(c_e_h_2, c_h, s11, s12)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10289, 10269, 10280])).
% 87.11/87.30 tff(10291,assumption,(node15(c_e_h_2, c_h, s11, s12)), introduced(assumption)).
% 87.11/87.30 tff(10292,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node15(c_e_h_2, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node15(c_e_h_2, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10293,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node15(c_e_h_2, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10294,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | (~node15(c_e_h_2, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11)),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10293, 10292])).
% 87.11/87.30 tff(10295,plain,
% 87.11/87.30 ($false),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10294, 173, 10269, 10291, 9886])).
% 87.11/87.30 tff(10296,plain,((~node15(c_e_h_2, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.30 tff(10297,plain,
% 87.11/87.30 (~node15(c_e_h_2, c_h, s11, s12)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10296, 9886, 10269])).
% 87.11/87.30 tff(10298,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_2, c_h, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_2, c_h, s11, s12))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10299,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_2, c_h, s11, s12))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10300,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_2, c_h, s11, s12)),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10299, 10298])).
% 87.11/87.30 tff(10301,plain,
% 87.11/87.30 (node19(c_e_h_2, c_h, s11, s12)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10300, 141, 4461])).
% 87.11/87.30 tff(10302,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)) | node15(c_e_h_2, c_h, s11, s12) | node16(c_e_h_2, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)) | node15(c_e_h_2, c_h, s11, s12) | node16(c_e_h_2, c_h, s11))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10303,plain,
% 87.11/87.30 ((node16(c_e_h_2, c_h, s11) | node14(c_e_h_2, c_h, s11, s12) | node15(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12))) <=> (node14(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)) | node15(c_e_h_2, c_h, s11, s12) | node16(c_e_h_2, c_h, s11))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10304,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s11) | node14(c_e_h_2, c_h, s11, s12) | node15(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)) | node15(c_e_h_2, c_h, s11, s12) | node16(c_e_h_2, c_h, s11)))),
% 87.11/87.30 inference(monotonicity,[status(thm)],[10303])).
% 87.11/87.30 tff(10305,plain,
% 87.11/87.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s11) | node14(c_e_h_2, c_h, s11, s12) | node15(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)) | node15(c_e_h_2, c_h, s11, s12) | node16(c_e_h_2, c_h, s11))),
% 87.11/87.30 inference(transitivity,[status(thm)],[10304, 10302])).
% 87.11/87.30 tff(10306,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s11) | node14(c_e_h_2, c_h, s11, s12) | node15(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10307,plain,
% 87.11/87.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)) | node15(c_e_h_2, c_h, s11, s12) | node16(c_e_h_2, c_h, s11)),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10306, 10305])).
% 87.11/87.30 tff(10308,plain,
% 87.11/87.30 (node14(c_e_h_2, c_h, s11, s12) | node15(c_e_h_2, c_h, s11, s12) | node16(c_e_h_2, c_h, s11)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10307, 189, 10301])).
% 87.11/87.30 tff(10309,plain,
% 87.11/87.30 (node16(c_e_h_2, c_h, s11)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10308, 10297, 10290])).
% 87.11/87.30 tff(10310,plain,
% 87.11/87.30 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | m_c_h_element_v_in2(c_e_h_2, c_h, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | m_c_h_element_v_in2(c_e_h_2, c_h, s11))),
% 87.11/87.30 inference(rewrite,[status(thm)],[])).
% 87.11/87.30 tff(10311,plain,
% 87.11/87.30 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | m_c_h_element_v_in2(c_e_h_2, c_h, s11))),
% 87.11/87.30 inference(quant_inst,[status(thm)],[])).
% 87.11/87.30 tff(10312,plain,
% 87.11/87.30 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s11)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | m_c_h_element_v_in2(c_e_h_2, c_h, s11)),
% 87.11/87.30 inference(modus_ponens,[status(thm)],[10311, 10310])).
% 87.11/87.30 tff(10313,plain,
% 87.11/87.30 ((~node16(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10312, 228, 10280])).
% 87.11/87.30 tff(10314,plain,
% 87.11/87.30 (m_c_h_element_v_in2(c_e_h_2, c_h, s11)),
% 87.11/87.30 inference(unit_resolution,[status(thm)],[10313, 10309])).
% 87.11/87.31 tff(10315,plain,
% 87.11/87.31 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)))),
% 87.11/87.31 inference(rewrite,[status(thm)],[])).
% 87.11/87.31 tff(10316,plain,
% 87.11/87.31 ((m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)))),
% 87.11/87.31 inference(rewrite,[status(thm)],[])).
% 87.11/87.31 tff(10317,plain,
% 87.11/87.31 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11))))),
% 87.11/87.31 inference(monotonicity,[status(thm)],[10316])).
% 87.11/87.31 tff(10318,plain,
% 87.11/87.31 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)))),
% 87.11/87.31 inference(transitivity,[status(thm)],[10317, 10315])).
% 87.11/87.31 tff(10319,plain,
% 87.11/87.31 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)))),
% 87.11/87.31 inference(quant_inst,[status(thm)],[])).
% 87.11/87.31 tff(10320,plain,
% 87.11/87.31 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11))),
% 87.11/87.31 inference(modus_ponens,[status(thm)],[10319, 10318])).
% 87.11/87.31 tff(10321,plain,
% 87.11/87.31 ((~node17(c_e_h_2, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s11))),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10320, 245, 10280])).
% 87.11/87.31 tff(10322,plain,
% 87.11/87.31 (~node17(c_e_h_2, c_h, s11)),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10321, 10314])).
% 87.11/87.31 tff(10323,plain,
% 87.11/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s11, s12) | node17(c_e_h_2, c_h, s11) | (~node19(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s11, s12) | node17(c_e_h_2, c_h, s11) | (~node19(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.31 inference(rewrite,[status(thm)],[])).
% 87.11/87.31 tff(10324,plain,
% 87.11/87.31 ((node17(c_e_h_2, c_h, s11) | node18(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12))) <=> (node18(c_e_h_2, c_h, s11, s12) | node17(c_e_h_2, c_h, s11) | (~node19(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.31 inference(rewrite,[status(thm)],[])).
% 87.11/87.31 tff(10325,plain,
% 87.11/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s11) | node18(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s11, s12) | node17(c_e_h_2, c_h, s11) | (~node19(c_e_h_2, c_h, s11, s12))))),
% 87.11/87.31 inference(monotonicity,[status(thm)],[10324])).
% 87.11/87.31 tff(10326,plain,
% 87.11/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s11) | node18(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s11, s12) | node17(c_e_h_2, c_h, s11) | (~node19(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.31 inference(transitivity,[status(thm)],[10325, 10323])).
% 87.11/87.31 tff(10327,plain,
% 87.11/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s11) | node18(c_e_h_2, c_h, s11, s12) | (~node19(c_e_h_2, c_h, s11, s12)))),
% 87.11/87.31 inference(quant_inst,[status(thm)],[])).
% 87.11/87.31 tff(10328,plain,
% 87.11/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s11, s12) | node17(c_e_h_2, c_h, s11) | (~node19(c_e_h_2, c_h, s11, s12))),
% 87.11/87.31 inference(modus_ponens,[status(thm)],[10327, 10326])).
% 87.11/87.31 tff(10329,plain,
% 87.11/87.31 (node18(c_e_h_2, c_h, s11, s12) | node17(c_e_h_2, c_h, s11)),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10328, 156, 10301])).
% 87.11/87.31 tff(10330,plain,
% 87.11/87.31 (node18(c_e_h_2, c_h, s11, s12)),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10329, 10322])).
% 87.11/87.31 tff(10331,plain,
% 87.11/87.31 ($false),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10276, 124, 10269, 10330, 9886])).
% 87.11/87.31 tff(10332,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s11) | (~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.31 tff(10333,plain,
% 87.11/87.31 (m_c_h_element_v_in1(c_e_h_2, c_h, s11)),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10332, 10269, 9886])).
% 87.11/87.31 tff(10334,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s11)), introduced(assumption)).
% 87.11/87.31 tff(10335,plain,
% 87.11/87.31 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11))),
% 87.11/87.31 inference(rewrite,[status(thm)],[])).
% 87.11/87.31 tff(10336,plain,
% 87.11/87.31 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11))),
% 87.11/87.31 inference(rewrite,[status(thm)],[])).
% 87.11/87.31 tff(10337,plain,
% 87.11/87.31 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11)))),
% 87.11/87.31 inference(monotonicity,[status(thm)],[10336])).
% 87.11/87.31 tff(10338,plain,
% 87.11/87.31 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11))),
% 87.11/87.31 inference(transitivity,[status(thm)],[10337, 10335])).
% 87.11/87.31 tff(10339,plain,
% 87.11/87.31 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11) | (~node17(c_e_h_2, c_h, s11)))),
% 87.11/87.31 inference(quant_inst,[status(thm)],[])).
% 87.11/87.31 tff(10340,plain,
% 87.11/87.31 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11)),
% 87.11/87.31 inference(modus_ponens,[status(thm)],[10339, 10338])).
% 87.11/87.31 tff(10341,plain,
% 87.11/87.31 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s11)) | (~node17(c_e_h_2, c_h, s11))),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10340, 209, 10334])).
% 87.11/87.31 tff(10342,plain,
% 87.11/87.31 (~node17(c_e_h_2, c_h, s11)),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10341, 10333])).
% 87.11/87.31 tff(10343,plain,
% 87.11/87.31 ($false),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10329, 10342, 10279])).
% 87.11/87.31 tff(10344,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s11) | m_c_h_element_v_out(c_e_h_2, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.11/87.31 tff(10345,plain,
% 87.11/87.31 (~m_c_h_element_v_out(c_e_h_2, c_h, s12)),
% 87.11/87.31 inference(unit_resolution,[status(thm)],[10344, 10268, 9884])).
% 87.11/87.31 tff(10346,plain,
% 87.11/87.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s12))),
% 87.11/87.31 inference(rewrite,[status(thm)],[])).
% 87.11/87.31 tff(10347,plain,
% 87.11/87.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s12))),
% 87.11/87.31 inference(quant_inst,[status(thm)],[])).
% 87.11/87.31 tff(10348,plain,
% 87.11/87.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s12)) | m_c_h_element_v_out(c_e_h_2, c_h, s12)),
% 87.11/87.31 inference(modus_ponens,[status(thm)],[10347, 10346])).
% 87.12/87.31 tff(10349,plain,
% 87.12/87.31 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s12)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10348, 23, 10345])).
% 87.12/87.31 tff(10350,plain,
% 87.12/87.31 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s12))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10351,plain,
% 87.12/87.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s12))),
% 87.12/87.31 inference(quant_inst,[status(thm)],[])).
% 87.12/87.31 tff(10352,plain,
% 87.12/87.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s12)),
% 87.12/87.31 inference(modus_ponens,[status(thm)],[10351, 10350])).
% 87.12/87.31 tff(10353,plain,
% 87.12/87.31 (~node20(c_e_h_2, c_i, s12)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10352, 37, 10349])).
% 87.12/87.31 tff(10354,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s13)), introduced(assumption)).
% 87.12/87.31 tff(10355,assumption,(~node20(c_e_h_2, c_i, s12)), introduced(assumption)).
% 87.12/87.31 tff(10356,assumption,(node21(c_e_h_2, c_i, s12, s13)), introduced(assumption)).
% 87.12/87.31 tff(10357,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s12) | (~node21(c_e_h_2, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s12) | (~node21(c_e_h_2, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10358,plain,
% 87.12/87.31 ((node20(c_e_h_2, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | (~node21(c_e_h_2, c_i, s12, s13))) <=> (node20(c_e_h_2, c_i, s12) | (~node21(c_e_h_2, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10359,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | (~node21(c_e_h_2, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s12) | (~node21(c_e_h_2, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13))))),
% 87.12/87.31 inference(monotonicity,[status(thm)],[10358])).
% 87.12/87.31 tff(10360,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | (~node21(c_e_h_2, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s12) | (~node21(c_e_h_2, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)))),
% 87.12/87.31 inference(transitivity,[status(thm)],[10359, 10357])).
% 87.12/87.31 tff(10361,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | (~node21(c_e_h_2, c_i, s12, s13)))),
% 87.12/87.31 inference(quant_inst,[status(thm)],[])).
% 87.12/87.31 tff(10362,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s12) | (~node21(c_e_h_2, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13))),
% 87.12/87.31 inference(modus_ponens,[status(thm)],[10361, 10360])).
% 87.12/87.31 tff(10363,plain,
% 87.12/87.31 ($false),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10362, 51, 10356, 10354, 10355])).
% 87.12/87.31 tff(10364,plain,((~node21(c_e_h_2, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | node20(c_e_h_2, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.31 tff(10365,plain,
% 87.12/87.31 (~node21(c_e_h_2, c_i, s12, s13)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10364, 10354, 10355])).
% 87.12/87.31 tff(10366,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_2, c_i, s12, s13) | node22(c_e_h_2, c_i, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_2, c_i, s12, s13) | node22(c_e_h_2, c_i, s12, s13))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10367,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_2, c_i, s12, s13) | node22(c_e_h_2, c_i, s12, s13))),
% 87.12/87.31 inference(quant_inst,[status(thm)],[])).
% 87.12/87.31 tff(10368,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_2, c_i, s12, s13) | node22(c_e_h_2, c_i, s12, s13)),
% 87.12/87.31 inference(modus_ponens,[status(thm)],[10367, 10366])).
% 87.12/87.31 tff(10369,plain,
% 87.12/87.31 (node21(c_e_h_2, c_i, s12, s13) | node22(c_e_h_2, c_i, s12, s13)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10368, 81, 9599])).
% 87.12/87.31 tff(10370,plain,
% 87.12/87.31 (node22(c_e_h_2, c_i, s12, s13)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10369, 10365])).
% 87.12/87.31 tff(10371,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | (~node22(c_e_h_2, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | (~node22(c_e_h_2, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10372,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | (~node22(c_e_h_2, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12))),
% 87.12/87.31 inference(quant_inst,[status(thm)],[])).
% 87.12/87.31 tff(10373,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | (~node22(c_e_h_2, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12)),
% 87.12/87.31 inference(modus_ponens,[status(thm)],[10372, 10371])).
% 87.12/87.31 tff(10374,plain,
% 87.12/87.31 ($false),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10373, 107, 10370, 10354, 9925])).
% 87.12/87.31 tff(10375,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s12) | node20(c_e_h_2, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.31 tff(10376,plain,
% 87.12/87.31 (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10375, 9923, 10353])).
% 87.12/87.31 tff(10377,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s13)), introduced(assumption)).
% 87.12/87.31 tff(10378,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s13)), introduced(assumption)).
% 87.12/87.31 tff(10379,plain,
% 87.12/87.31 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10380,plain,
% 87.12/87.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13))),
% 87.12/87.31 inference(quant_inst,[status(thm)],[])).
% 87.12/87.31 tff(10381,plain,
% 87.12/87.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13)),
% 87.12/87.31 inference(modus_ponens,[status(thm)],[10380, 10379])).
% 87.12/87.31 tff(10382,plain,
% 87.12/87.31 ($false),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10381, 365, 10378, 10377])).
% 87.12/87.31 tff(10383,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.31 tff(10384,plain,
% 87.12/87.31 (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10383, 10376])).
% 87.12/87.31 tff(10385,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s14)), introduced(assumption)).
% 87.12/87.31 tff(10386,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s13)), introduced(assumption)).
% 87.12/87.31 tff(10387,assumption,(~node16(c_e_h_2, c_e, s13)), introduced(assumption)).
% 87.12/87.31 tff(10388,assumption,(node14(c_e_h_2, c_e, s13, s14)), introduced(assumption)).
% 87.12/87.31 tff(10389,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node14(c_e_h_2, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node14(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10390,plain,
% 87.12/87.31 (((~node14(c_e_h_2, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node14(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10391,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node14(c_e_h_2, c_e, s13, s14))))),
% 87.12/87.31 inference(monotonicity,[status(thm)],[10390])).
% 87.12/87.31 tff(10392,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node14(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.31 inference(transitivity,[status(thm)],[10391, 10389])).
% 87.12/87.31 tff(10393,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)))),
% 87.12/87.31 inference(quant_inst,[status(thm)],[])).
% 87.12/87.31 tff(10394,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node14(c_e_h_2, c_e, s13, s14))),
% 87.12/87.31 inference(modus_ponens,[status(thm)],[10393, 10392])).
% 87.12/87.31 tff(10395,plain,
% 87.12/87.31 ($false),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10394, 283, 10388, 10385, 10386])).
% 87.12/87.31 tff(10396,plain,((~node14(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.31 tff(10397,plain,
% 87.12/87.31 (~node14(c_e_h_2, c_e, s13, s14)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10396, 10385, 10386])).
% 87.12/87.31 tff(10398,assumption,(node15(c_e_h_2, c_e, s13, s14)), introduced(assumption)).
% 87.12/87.31 tff(10399,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node15(c_e_h_2, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node15(c_e_h_2, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10400,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node15(c_e_h_2, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13))),
% 87.12/87.31 inference(quant_inst,[status(thm)],[])).
% 87.12/87.31 tff(10401,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | (~node15(c_e_h_2, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13)),
% 87.12/87.31 inference(modus_ponens,[status(thm)],[10400, 10399])).
% 87.12/87.31 tff(10402,plain,
% 87.12/87.31 ($false),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10401, 173, 10398, 10385, 10004])).
% 87.12/87.31 tff(10403,plain,((~node15(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.31 tff(10404,plain,
% 87.12/87.31 (~node15(c_e_h_2, c_e, s13, s14)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10403, 10385, 10004])).
% 87.12/87.31 tff(10405,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_2, c_e, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_2, c_e, s13, s14))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10406,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_2, c_e, s13, s14))),
% 87.12/87.31 inference(quant_inst,[status(thm)],[])).
% 87.12/87.31 tff(10407,plain,
% 87.12/87.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_2, c_e, s13, s14)),
% 87.12/87.31 inference(modus_ponens,[status(thm)],[10406, 10405])).
% 87.12/87.31 tff(10408,plain,
% 87.12/87.31 (node19(c_e_h_2, c_e, s13, s14)),
% 87.12/87.31 inference(unit_resolution,[status(thm)],[10407, 141, 10040])).
% 87.12/87.31 tff(10409,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s13) | node15(c_e_h_2, c_e, s13, s14) | node14(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s13) | node15(c_e_h_2, c_e, s13, s14) | node14(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10410,plain,
% 87.12/87.31 ((node16(c_e_h_2, c_e, s13) | node14(c_e_h_2, c_e, s13, s14) | node15(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14))) <=> (node16(c_e_h_2, c_e, s13) | node15(c_e_h_2, c_e, s13, s14) | node14(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.31 inference(rewrite,[status(thm)],[])).
% 87.12/87.31 tff(10411,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s13) | node14(c_e_h_2, c_e, s13, s14) | node15(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s13) | node15(c_e_h_2, c_e, s13, s14) | node14(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14))))),
% 87.12/87.31 inference(monotonicity,[status(thm)],[10410])).
% 87.12/87.31 tff(10412,plain,
% 87.12/87.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s13) | node14(c_e_h_2, c_e, s13, s14) | node15(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s13) | node15(c_e_h_2, c_e, s13, s14) | node14(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.32 inference(transitivity,[status(thm)],[10411, 10409])).
% 87.12/87.32 tff(10413,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s13) | node14(c_e_h_2, c_e, s13, s14) | node15(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10414,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s13) | node15(c_e_h_2, c_e, s13, s14) | node14(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14))),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10413, 10412])).
% 87.12/87.32 tff(10415,plain,
% 87.12/87.32 (node16(c_e_h_2, c_e, s13) | node15(c_e_h_2, c_e, s13, s14) | node14(c_e_h_2, c_e, s13, s14)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10414, 189, 10408])).
% 87.12/87.32 tff(10416,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10415, 10404, 10397, 10387])).
% 87.12/87.32 tff(10417,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | node16(c_e_h_2, c_e, s13) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | m_c_h_element_v_in1(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10418,plain,
% 87.12/87.32 (node16(c_e_h_2, c_e, s13)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10417, 10386, 10385, 10004])).
% 87.12/87.32 tff(10419,assumption,(node18(c_e_h_2, c_e, s13, s14)), introduced(assumption)).
% 87.12/87.32 tff(10420,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10421,plain,
% 87.12/87.32 (((~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10422,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14))))),
% 87.12/87.32 inference(monotonicity,[status(thm)],[10421])).
% 87.12/87.32 tff(10423,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)))),
% 87.12/87.32 inference(transitivity,[status(thm)],[10422, 10420])).
% 87.12/87.32 tff(10424,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10425,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | (~node18(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14))),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10424, 10423])).
% 87.12/87.32 tff(10426,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10425, 124, 10419, 10385, 10004])).
% 87.12/87.32 tff(10427,plain,((~node18(c_e_h_2, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10428,plain,
% 87.12/87.32 (~node18(c_e_h_2, c_e, s13, s14)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10427, 10004, 10385])).
% 87.12/87.32 tff(10429,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s13) | node18(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s13) | node18(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10430,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s13) | node18(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14)))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10431,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s13) | node18(c_e_h_2, c_e, s13, s14) | (~node19(c_e_h_2, c_e, s13, s14))),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10430, 10429])).
% 87.12/87.32 tff(10432,plain,
% 87.12/87.32 (node17(c_e_h_2, c_e, s13) | node18(c_e_h_2, c_e, s13, s14)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10431, 156, 10408])).
% 87.12/87.32 tff(10433,plain,
% 87.12/87.32 (node17(c_e_h_2, c_e, s13)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10432, 10428])).
% 87.12/87.32 tff(10434,plain,
% 87.12/87.32 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10435,plain,
% 87.12/87.32 ((m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10436,plain,
% 87.12/87.32 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13)))),
% 87.12/87.32 inference(monotonicity,[status(thm)],[10435])).
% 87.12/87.32 tff(10437,plain,
% 87.12/87.32 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13))),
% 87.12/87.32 inference(transitivity,[status(thm)],[10436, 10434])).
% 87.12/87.32 tff(10438,plain,
% 87.12/87.32 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10439,plain,
% 87.12/87.32 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | (~node17(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10438, 10437])).
% 87.12/87.32 tff(10440,plain,
% 87.12/87.32 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10439, 245, 10433])).
% 87.12/87.32 tff(10441,plain,
% 87.12/87.32 (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10440, 10386])).
% 87.12/87.32 tff(10442,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s13)), introduced(assumption)).
% 87.12/87.32 tff(10443,assumption,(node16(c_e_h_2, c_e, s13)), introduced(assumption)).
% 87.12/87.32 tff(10444,plain,
% 87.12/87.32 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | m_c_h_element_v_in2(c_e_h_2, c_e, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | m_c_h_element_v_in2(c_e_h_2, c_e, s13))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10445,plain,
% 87.12/87.32 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | m_c_h_element_v_in2(c_e_h_2, c_e, s13))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10446,plain,
% 87.12/87.32 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | m_c_h_element_v_in2(c_e_h_2, c_e, s13)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10445, 10444])).
% 87.12/87.32 tff(10447,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10446, 228, 10443, 10386, 10442])).
% 87.12/87.32 tff(10448,plain,((~node16(c_e_h_2, c_e, s13)) | m_c_h_element_v_in1(c_e_h_2, c_e, s13) | m_c_h_element_v_in2(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10449,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10448, 10441, 10418, 10386])).
% 87.12/87.32 tff(10450,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s13) | (~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10451,plain,
% 87.12/87.32 (m_c_h_element_v_in1(c_e_h_2, c_e, s13)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10450, 10385, 10004])).
% 87.12/87.32 tff(10452,plain,
% 87.12/87.32 (~node18(c_e_h_2, c_e, s13, s14)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10427, 10385, 10004])).
% 87.12/87.32 tff(10453,plain,
% 87.12/87.32 (node17(c_e_h_2, c_e, s13)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10432, 10452])).
% 87.12/87.32 tff(10454,plain,
% 87.12/87.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s13)))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10455,plain,
% 87.12/87.32 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s13)) | m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s13)))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10456,plain,
% 87.12/87.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s13)) | m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s13))))),
% 87.12/87.32 inference(monotonicity,[status(thm)],[10455])).
% 87.12/87.32 tff(10457,plain,
% 87.12/87.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s13)) | m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s13)))),
% 87.12/87.32 inference(transitivity,[status(thm)],[10456, 10454])).
% 87.12/87.32 tff(10458,plain,
% 87.12/87.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s13)) | m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10459,plain,
% 87.12/87.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s13) | (~node17(c_e_h_2, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s13))),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10458, 10457])).
% 87.12/87.32 tff(10460,plain,
% 87.12/87.32 ((~node17(c_e_h_2, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s13))),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10459, 209, 10442])).
% 87.12/87.32 tff(10461,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10460, 10453, 10451])).
% 87.12/87.32 tff(10462,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s13) | m_c_h_element_v_out(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10463,plain,
% 87.12/87.32 (~m_c_h_element_v_out(c_e_h_2, c_e, s14)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10462, 10002, 10384])).
% 87.12/87.32 tff(10464,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_r, s14)), introduced(assumption)).
% 87.12/87.32 tff(10465,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s14)), introduced(assumption)).
% 87.12/87.32 tff(10466,plain,
% 87.12/87.32 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s14))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10467,plain,
% 87.12/87.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s14))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10468,plain,
% 87.12/87.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s14)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10467, 10466])).
% 87.12/87.32 tff(10469,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10468, 1884, 10465, 10464])).
% 87.12/87.32 tff(10470,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_r, s14)) | m_c_h_element_v_out(c_e_h_2, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10471,plain,
% 87.12/87.32 (~m_and_h_gate_v_in1(c_e_h_2, c_r, s14)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10470, 10463])).
% 87.12/87.32 tff(10472,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_r, s14)), introduced(assumption)).
% 87.12/87.32 tff(10473,assumption,(node20(c_e_h_2, c_r, s14)), introduced(assumption)).
% 87.12/87.32 tff(10474,plain,
% 87.12/87.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s14))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10475,plain,
% 87.12/87.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s14))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10476,plain,
% 87.12/87.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s14)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10475, 10474])).
% 87.12/87.32 tff(10477,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10476, 37, 10473, 10472])).
% 87.12/87.32 tff(10478,plain,((~node20(c_e_h_2, c_r, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s14)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10479,plain,
% 87.12/87.32 (~node20(c_e_h_2, c_r, s14)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10478, 10471])).
% 87.12/87.32 tff(10480,assumption,(~node20(c_e_h_2, c_r, s14)), introduced(assumption)).
% 87.12/87.32 tff(10481,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s15)), introduced(assumption)).
% 87.12/87.32 tff(10482,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | node20(c_e_h_2, c_r, s14) | (~node21(c_e_h_2, c_r, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | node20(c_e_h_2, c_r, s14) | (~node21(c_e_h_2, c_r, s14, s15)))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10483,plain,
% 87.12/87.32 ((node20(c_e_h_2, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | (~node21(c_e_h_2, c_r, s14, s15))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | node20(c_e_h_2, c_r, s14) | (~node21(c_e_h_2, c_r, s14, s15)))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10484,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | (~node21(c_e_h_2, c_r, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | node20(c_e_h_2, c_r, s14) | (~node21(c_e_h_2, c_r, s14, s15))))),
% 87.12/87.32 inference(monotonicity,[status(thm)],[10483])).
% 87.12/87.32 tff(10485,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | (~node21(c_e_h_2, c_r, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | node20(c_e_h_2, c_r, s14) | (~node21(c_e_h_2, c_r, s14, s15)))),
% 87.12/87.32 inference(transitivity,[status(thm)],[10484, 10482])).
% 87.12/87.32 tff(10486,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | (~node21(c_e_h_2, c_r, s14, s15)))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10487,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | node20(c_e_h_2, c_r, s14) | (~node21(c_e_h_2, c_r, s14, s15))),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10486, 10485])).
% 87.12/87.32 tff(10488,plain,
% 87.12/87.32 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | node20(c_e_h_2, c_r, s14) | (~node21(c_e_h_2, c_r, s14, s15))),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10487, 51])).
% 87.12/87.32 tff(10489,plain,
% 87.12/87.32 (~node21(c_e_h_2, c_r, s14, s15)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10488, 10481, 10480])).
% 87.12/87.32 tff(10490,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s14)), introduced(assumption)).
% 87.12/87.32 tff(10491,assumption,(node22(c_e_h_2, c_r, s14, s15)), introduced(assumption)).
% 87.12/87.32 tff(10492,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | (~node22(c_e_h_2, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | (~node22(c_e_h_2, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10493,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | (~node22(c_e_h_2, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10494,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | (~node22(c_e_h_2, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10493, 10492])).
% 87.12/87.32 tff(10495,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10494, 107, 10490, 10481, 10491])).
% 87.12/87.32 tff(10496,plain,((~node22(c_e_h_2, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s15))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10497,plain,
% 87.12/87.32 (~node22(c_e_h_2, c_r, s14, s15)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10496, 10481, 10490])).
% 87.12/87.32 tff(10498,plain,
% 87.12/87.32 (succ(s14, s15) <=> succ(s14, s15)),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10499,axiom,(succ(s14, s15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound15')).
% 87.12/87.32 tff(10500,plain,
% 87.12/87.32 (succ(s14, s15)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10499, 10498])).
% 87.12/87.32 tff(10501,plain,
% 87.12/87.32 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10502,plain,
% 87.12/87.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10503,plain,
% 87.12/87.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10502, 10501])).
% 87.12/87.32 tff(10504,plain,
% 87.12/87.32 (trans(s14, s15)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10503, 10500, 64])).
% 87.12/87.32 tff(10505,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_2, c_r, s14, s15) | node22(c_e_h_2, c_r, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_2, c_r, s14, s15) | node22(c_e_h_2, c_r, s14, s15))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10506,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_2, c_r, s14, s15) | node22(c_e_h_2, c_r, s14, s15))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10507,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_2, c_r, s14, s15) | node22(c_e_h_2, c_r, s14, s15)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10506, 10505])).
% 87.12/87.32 tff(10508,plain,
% 87.12/87.32 (node21(c_e_h_2, c_r, s14, s15) | node22(c_e_h_2, c_r, s14, s15)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10507, 81, 10504])).
% 87.12/87.32 tff(10509,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10508, 10497, 10489])).
% 87.12/87.32 tff(10510,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14) | node20(c_e_h_2, c_r, s14)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10511,plain,
% 87.12/87.32 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10510, 10479])).
% 87.12/87.32 tff(10512,plain,
% 87.12/87.32 (~m_and_h_gate_v_out(c_e_h_2, c_r, s15)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10511, 10048])).
% 87.12/87.32 tff(10513,plain,
% 87.12/87.32 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10514,plain,
% 87.12/87.32 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10515,plain,
% 87.12/87.32 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s15)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10514, 10513])).
% 87.12/87.32 tff(10516,plain,
% 87.12/87.32 (~m_user_v_ack(c_e_h_2, c_u, s15)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10515, 4481, 10512])).
% 87.12/87.32 tff(10517,plain,
% 87.12/87.32 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s15) | (~node25(s15)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s15) | (~node25(s15)))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10518,plain,
% 87.12/87.32 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s15) | (~node25(s15)))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10519,plain,
% 87.12/87.32 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s15) | (~node25(s15))),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10518, 10517])).
% 87.12/87.32 tff(10520,plain,
% 87.12/87.32 (~node25(s15)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10519, 4492, 10516])).
% 87.12/87.32 tff(10521,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s13)), introduced(assumption)).
% 87.12/87.32 tff(10522,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s7)), introduced(assumption)).
% 87.12/87.32 tff(10523,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s6)), introduced(assumption)).
% 87.12/87.32 tff(10524,assumption,(node21(c_e_h_3, c_q, s5, s6)), introduced(assumption)).
% 87.12/87.32 tff(10525,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s4)), introduced(assumption)).
% 87.12/87.32 tff(10526,assumption,(node22(c_e_h_3, c_i, s3, s4)), introduced(assumption)).
% 87.12/87.32 tff(10527,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s3)), introduced(assumption)).
% 87.12/87.32 tff(10528,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10529,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10530,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10529, 10528])).
% 87.12/87.32 tff(10531,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10530, 107, 10527, 10525, 10526])).
% 87.12/87.32 tff(10532,plain,((~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10533,plain,
% 87.12/87.32 ((~node22(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10532, 7723])).
% 87.12/87.32 tff(10534,plain,
% 87.12/87.32 (~node22(c_e_h_3, c_i, s3, s4)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10533, 10525])).
% 87.12/87.32 tff(10535,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s3)), introduced(assumption)).
% 87.12/87.32 tff(10536,assumption,(node15(c_e_h_3, c_h, s2, s3)), introduced(assumption)).
% 87.12/87.32 tff(10537,plain,
% 87.12/87.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10538,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10539,plain,
% 87.12/87.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10538, 10537])).
% 87.12/87.32 tff(10540,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10539, 173, 7621, 10535, 10536])).
% 87.12/87.32 tff(10541,plain,((~node15(c_e_h_3, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10542,plain,
% 87.12/87.32 (~node15(c_e_h_3, c_h, s2, s3)),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10541, 10535])).
% 87.12/87.32 tff(10543,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s2)), introduced(assumption)).
% 87.12/87.32 tff(10544,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s0)), introduced(assumption)).
% 87.12/87.32 tff(10545,plain,
% 87.12/87.32 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 87.12/87.32 inference(quant_inst,[status(thm)],[])).
% 87.12/87.32 tff(10546,plain,
% 87.12/87.32 ($false),
% 87.12/87.32 inference(unit_resolution,[status(thm)],[10545, 94, 10544])).
% 87.12/87.32 tff(10547,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s0)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.32 tff(10548,plain,
% 87.12/87.32 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X)))),
% 87.12/87.32 inference(bind,[status(th)],[])).
% 87.12/87.32 tff(10549,plain,
% 87.12/87.32 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 87.12/87.32 inference(quant_intro,[status(thm)],[10548])).
% 87.12/87.32 tff(10550,plain,
% 87.12/87.32 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 87.12/87.32 inference(rewrite,[status(thm)],[])).
% 87.12/87.32 tff(10551,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_48')).
% 87.12/87.32 tff(10552,plain,
% 87.12/87.32 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10551, 10550])).
% 87.12/87.32 tff(10553,plain,(
% 87.12/87.32 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 87.12/87.32 inference(skolemize,[status(sab)],[10552])).
% 87.12/87.32 tff(10554,plain,
% 87.12/87.32 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 87.12/87.32 inference(modus_ponens,[status(thm)],[10553, 10549])).
% 87.12/87.33 tff(10555,plain,
% 87.12/87.33 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10556,plain,
% 87.12/87.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10557,plain,
% 87.12/87.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10556, 10555])).
% 87.12/87.33 tff(10558,plain,
% 87.12/87.33 ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10557, 10554])).
% 87.12/87.33 tff(10559,plain,
% 87.12/87.33 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10558, 10547])).
% 87.12/87.33 tff(10560,plain,
% 87.12/87.33 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s0))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10561,plain,
% 87.12/87.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s0))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10562,plain,
% 87.12/87.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s0)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10561, 10560])).
% 87.12/87.33 tff(10563,plain,
% 87.12/87.33 (~node20(c_e_h_3, c_l, s0)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10562, 37, 10559])).
% 87.12/87.33 tff(10564,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s1)), introduced(assumption)).
% 87.12/87.33 tff(10565,assumption,(node22(c_e_h_3, c_l, s0, s1)), introduced(assumption)).
% 87.12/87.33 tff(10566,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10567,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10568,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10567, 10566])).
% 87.12/87.33 tff(10569,plain,
% 87.12/87.33 ($false),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10568, 107, 10565, 7437, 10564])).
% 87.12/87.33 tff(10570,plain,((~node22(c_e_h_3, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.33 tff(10571,plain,
% 87.12/87.33 (~node22(c_e_h_3, c_l, s0, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10570, 10564])).
% 87.12/87.33 tff(10572,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10573,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10574,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10573, 10572])).
% 87.12/87.33 tff(10575,plain,
% 87.12/87.33 (node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10574, 81, 71])).
% 87.12/87.33 tff(10576,plain,
% 87.12/87.33 (node21(c_e_h_3, c_l, s0, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10575, 10571])).
% 87.12/87.33 tff(10577,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node21(c_e_h_3, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10578,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10579,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node21(c_e_h_3, c_l, s0, s1))),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10578, 10577])).
% 87.12/87.33 tff(10580,plain,
% 87.12/87.33 ($false),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10579, 51, 10576, 10564, 10563])).
% 87.12/87.33 tff(10581,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.33 tff(10582,plain,
% 87.12/87.33 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10583,plain,
% 87.12/87.33 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10584,plain,
% 87.12/87.33 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10583, 10582])).
% 87.12/87.33 tff(10585,plain,
% 87.12/87.33 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10584, 801, 10581])).
% 87.12/87.33 tff(10586,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s1)), introduced(assumption)).
% 87.12/87.33 tff(10587,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s2)), introduced(assumption)).
% 87.12/87.33 tff(10588,assumption,(node6(c_e_h_3, c_j, s1, s2)), introduced(assumption)).
% 87.12/87.33 tff(10589,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2)))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10590,plain,
% 87.12/87.33 (((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2)))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10591,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2))))),
% 87.12/87.33 inference(monotonicity,[status(thm)],[10590])).
% 87.12/87.33 tff(10592,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2)))),
% 87.12/87.33 inference(transitivity,[status(thm)],[10591, 10589])).
% 87.12/87.33 tff(10593,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10594,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2))),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10593, 10592])).
% 87.12/87.33 tff(10595,plain,
% 87.12/87.33 ($false),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10594, 899, 10586, 10587, 10588])).
% 87.12/87.33 tff(10596,plain,((~node6(c_e_h_3, c_j, s1, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.33 tff(10597,plain,
% 87.12/87.33 (~node6(c_e_h_3, c_j, s1, s2)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10596, 10587, 10586])).
% 87.12/87.33 tff(10598,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10599,plain,
% 87.12/87.33 ((node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10600,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2)))),
% 87.12/87.33 inference(monotonicity,[status(thm)],[10599])).
% 87.12/87.33 tff(10601,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2))),
% 87.12/87.33 inference(transitivity,[status(thm)],[10600, 10598])).
% 87.12/87.33 tff(10602,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2)))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10603,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10602, 10601])).
% 87.12/87.33 tff(10604,plain,
% 87.12/87.33 (node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10603, 881, 344])).
% 87.12/87.33 tff(10605,plain,
% 87.12/87.33 (node5(c_e_h_3, c_j, s1, s2)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10604, 10597])).
% 87.12/87.33 tff(10606,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)), introduced(assumption)).
% 87.12/87.33 tff(10607,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s1)), introduced(assumption)).
% 87.12/87.33 tff(10608,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s0)), introduced(assumption)).
% 87.12/87.33 tff(10609,plain,
% 87.12/87.33 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10610,plain,
% 87.12/87.33 ($false),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10609, 13, 10608])).
% 87.12/87.33 tff(10611,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.33 tff(10612,plain,
% 87.12/87.33 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10613,plain,
% 87.12/87.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10614,plain,
% 87.12/87.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)) | m_c_h_element_v_out(c_e_h_2, c_f, s0)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10613, 10612])).
% 87.12/87.33 tff(10615,plain,
% 87.12/87.33 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10614, 1666, 10611])).
% 87.12/87.33 tff(10616,plain,
% 87.12/87.33 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10617,plain,
% 87.12/87.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10618,plain,
% 87.12/87.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10617, 10616])).
% 87.12/87.33 tff(10619,plain,
% 87.12/87.33 (~node20(c_e_h_2, c_q, s0)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10618, 37, 10615])).
% 87.12/87.33 tff(10620,assumption,(node21(c_e_h_2, c_q, s0, s1)), introduced(assumption)).
% 87.12/87.33 tff(10621,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10622,plain,
% 87.12/87.33 ((node20(c_e_h_2, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1))) <=> (node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10623,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1))))),
% 87.12/87.33 inference(monotonicity,[status(thm)],[10622])).
% 87.12/87.33 tff(10624,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)))),
% 87.12/87.33 inference(transitivity,[status(thm)],[10623, 10621])).
% 87.12/87.33 tff(10625,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10626,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10625, 10624])).
% 87.12/87.33 tff(10627,plain,
% 87.12/87.33 ($false),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10626, 51, 10620, 10607, 10619])).
% 87.12/87.33 tff(10628,plain,((~node21(c_e_h_2, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.33 tff(10629,plain,
% 87.12/87.33 (~node21(c_e_h_2, c_q, s0, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10628, 10607])).
% 87.12/87.33 tff(10630,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10631,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10632,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10631, 10630])).
% 87.12/87.33 tff(10633,plain,
% 87.12/87.33 (node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10632, 81, 71])).
% 87.12/87.33 tff(10634,plain,
% 87.12/87.33 (node22(c_e_h_2, c_q, s0, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10633, 10629])).
% 87.12/87.33 tff(10635,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10636,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10637,plain,
% 87.12/87.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10636, 10635])).
% 87.12/87.33 tff(10638,plain,
% 87.12/87.33 ($false),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10637, 107, 10634, 7445, 10607])).
% 87.12/87.33 tff(10639,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.33 tff(10640,plain,
% 87.12/87.33 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s1))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10641,plain,
% 87.12/87.33 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s1))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10642,plain,
% 87.12/87.33 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s1)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10641, 10640])).
% 87.12/87.33 tff(10643,plain,
% 87.12/87.33 (node3(c_e_h_2, c_e_h_3, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10642, 7448, 814])).
% 87.12/87.33 tff(10644,plain,
% 87.12/87.33 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s1)) | (~node3(c_e_h_2, c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s1)) | (~node3(c_e_h_2, c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10645,plain,
% 87.12/87.33 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s1)) | (~node3(c_e_h_2, c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10646,plain,
% 87.12/87.33 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s1)) | (~node3(c_e_h_2, c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10645, 10644])).
% 87.12/87.33 tff(10647,plain,
% 87.12/87.33 ((~m_cell_v_ack(c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10646, 836, 10643])).
% 87.12/87.33 tff(10648,plain,
% 87.12/87.33 (~m_cell_v_ack(c_e_h_3, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10647, 10639])).
% 87.12/87.33 tff(10649,plain,
% 87.12/87.33 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)) | m_cell_v_ack(c_e_h_3, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)) | m_cell_v_ack(c_e_h_3, s1))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10650,plain,
% 87.12/87.33 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)) | m_cell_v_ack(c_e_h_3, s1))),
% 87.12/87.33 inference(quant_inst,[status(thm)],[])).
% 87.12/87.33 tff(10651,plain,
% 87.12/87.33 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)) | m_cell_v_ack(c_e_h_3, s1)),
% 87.12/87.33 inference(modus_ponens,[status(thm)],[10650, 10649])).
% 87.12/87.33 tff(10652,plain,
% 87.12/87.33 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)),
% 87.12/87.33 inference(unit_resolution,[status(thm)],[10651, 848, 10648])).
% 87.12/87.33 tff(10653,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10654,plain,
% 87.12/87.33 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)))),
% 87.12/87.33 inference(rewrite,[status(thm)],[])).
% 87.12/87.33 tff(10655,plain,
% 87.12/87.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2))))),
% 87.12/87.34 inference(monotonicity,[status(thm)],[10654])).
% 87.12/87.34 tff(10656,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)))),
% 87.12/87.34 inference(transitivity,[status(thm)],[10655, 10653])).
% 87.12/87.34 tff(10657,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10658,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2))),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10657, 10656])).
% 87.12/87.34 tff(10659,plain,
% 87.12/87.34 ($false),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10658, 862, 10587, 10652, 10606, 10605])).
% 87.12/87.34 tff(10660,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_out(c_e_h_3, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.34 tff(10661,plain,
% 87.12/87.34 (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10660, 10585, 7492])).
% 87.12/87.34 tff(10662,plain,
% 87.12/87.34 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10663,plain,
% 87.12/87.34 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10664,plain,
% 87.12/87.34 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2)),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10663, 10662])).
% 87.12/87.34 tff(10665,plain,
% 87.12/87.34 (~m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10664, 309, 10661])).
% 87.12/87.34 tff(10666,plain,
% 87.12/87.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10667,plain,
% 87.12/87.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10668,plain,
% 87.12/87.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10667, 10666])).
% 87.12/87.34 tff(10669,plain,
% 87.12/87.34 ((~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10668, 228, 10665])).
% 87.12/87.34 tff(10670,plain,
% 87.12/87.34 (~node16(c_e_h_3, c_h, s2)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10669, 10543])).
% 87.12/87.34 tff(10671,assumption,(node14(c_e_h_3, c_h, s2, s3)), introduced(assumption)).
% 87.12/87.34 tff(10672,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10673,plain,
% 87.12/87.34 (((~node14(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10674,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3))))),
% 87.12/87.34 inference(monotonicity,[status(thm)],[10673])).
% 87.12/87.34 tff(10675,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(transitivity,[status(thm)],[10674, 10672])).
% 87.12/87.34 tff(10676,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10677,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10676, 10675])).
% 87.12/87.34 tff(10678,plain,
% 87.12/87.34 ($false),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10677, 283, 10535, 10543, 10671])).
% 87.12/87.34 tff(10679,plain,((~node14(c_e_h_3, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.34 tff(10680,plain,
% 87.12/87.34 (~node14(c_e_h_3, c_h, s2, s3)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10679, 10543, 10535])).
% 87.12/87.34 tff(10681,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10682,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10683,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3)),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10682, 10681])).
% 87.12/87.34 tff(10684,plain,
% 87.12/87.34 (node19(c_e_h_3, c_h, s2, s3)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10683, 141, 582])).
% 87.12/87.34 tff(10685,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node14(c_e_h_3, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node14(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10686,plain,
% 87.12/87.34 ((node16(c_e_h_3, c_h, s2) | node14(c_e_h_3, c_h, s2, s3) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3))) <=> (node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node14(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10687,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node14(c_e_h_3, c_h, s2, s3) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node14(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(monotonicity,[status(thm)],[10686])).
% 87.12/87.34 tff(10688,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node14(c_e_h_3, c_h, s2, s3) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node14(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(transitivity,[status(thm)],[10687, 10685])).
% 87.12/87.34 tff(10689,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node14(c_e_h_3, c_h, s2, s3) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10690,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)) | node14(c_e_h_3, c_h, s2, s3)),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10689, 10688])).
% 87.12/87.34 tff(10691,plain,
% 87.12/87.34 (node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | node14(c_e_h_3, c_h, s2, s3)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10690, 189, 10684])).
% 87.12/87.34 tff(10692,plain,
% 87.12/87.34 ($false),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10691, 10680, 10670, 10542])).
% 87.12/87.34 tff(10693,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.34 tff(10694,plain,
% 87.12/87.34 (m_c_h_element_v_in1(c_e_h_3, c_h, s2)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10693, 10535])).
% 87.12/87.34 tff(10695,plain,
% 87.12/87.34 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10696,plain,
% 87.12/87.34 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~node17(c_e_h_3, c_h, s2))) <=> ((~node17(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10697,plain,
% 87.12/87.34 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~node17(c_e_h_3, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2))))),
% 87.12/87.34 inference(monotonicity,[status(thm)],[10696])).
% 87.12/87.34 tff(10698,plain,
% 87.12/87.34 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~node17(c_e_h_3, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)))),
% 87.12/87.34 inference(transitivity,[status(thm)],[10697, 10695])).
% 87.12/87.34 tff(10699,plain,
% 87.12/87.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~node17(c_e_h_3, c_h, s2)))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10700,plain,
% 87.12/87.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2))),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10699, 10698])).
% 87.12/87.34 tff(10701,plain,
% 87.12/87.34 ((~node17(c_e_h_3, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2))),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10700, 209, 10665])).
% 87.12/87.34 tff(10702,plain,
% 87.12/87.34 (~node17(c_e_h_3, c_h, s2)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10701, 10694])).
% 87.12/87.34 tff(10703,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10704,plain,
% 87.12/87.34 ((node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3))) <=> (node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10705,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(monotonicity,[status(thm)],[10704])).
% 87.12/87.34 tff(10706,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(transitivity,[status(thm)],[10705, 10703])).
% 87.12/87.34 tff(10707,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10708,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3)),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10707, 10706])).
% 87.12/87.34 tff(10709,plain,
% 87.12/87.34 (node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10708, 156, 10684])).
% 87.12/87.34 tff(10710,plain,
% 87.12/87.34 (node18(c_e_h_3, c_h, s2, s3)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10709, 10702])).
% 87.12/87.34 tff(10711,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10712,plain,
% 87.12/87.34 (((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~node18(c_e_h_3, c_h, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10713,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~node18(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3))))),
% 87.12/87.34 inference(monotonicity,[status(thm)],[10712])).
% 87.12/87.34 tff(10714,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~node18(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(transitivity,[status(thm)],[10713, 10711])).
% 87.12/87.34 tff(10715,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~node18(c_e_h_3, c_h, s2, s3)))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10716,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3))),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10715, 10714])).
% 87.12/87.34 tff(10717,plain,
% 87.12/87.34 ($false),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10716, 124, 7621, 10535, 10710])).
% 87.12/87.34 tff(10718,plain,(~m_c_h_element_v_out(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.34 tff(10719,plain,
% 87.12/87.34 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10720,plain,
% 87.12/87.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10721,plain,
% 87.12/87.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10720, 10719])).
% 87.12/87.34 tff(10722,plain,
% 87.12/87.34 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10721, 23, 10718])).
% 87.12/87.34 tff(10723,plain,
% 87.12/87.34 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s3))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10724,plain,
% 87.12/87.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s3))),
% 87.12/87.34 inference(quant_inst,[status(thm)],[])).
% 87.12/87.34 tff(10725,plain,
% 87.12/87.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s3)),
% 87.12/87.34 inference(modus_ponens,[status(thm)],[10724, 10723])).
% 87.12/87.34 tff(10726,plain,
% 87.12/87.34 (~node20(c_e_h_3, c_i, s3)),
% 87.12/87.34 inference(unit_resolution,[status(thm)],[10725, 37, 10722])).
% 87.12/87.34 tff(10727,assumption,(~node20(c_e_h_3, c_i, s3)), introduced(assumption)).
% 87.12/87.34 tff(10728,assumption,(node21(c_e_h_3, c_i, s3, s4)), introduced(assumption)).
% 87.12/87.34 tff(10729,plain,
% 87.12/87.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4)))),
% 87.12/87.34 inference(rewrite,[status(thm)],[])).
% 87.12/87.34 tff(10730,plain,
% 87.12/87.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4)))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10731,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4))),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10730, 10729])).
% 87.12/87.35 tff(10732,plain,
% 87.12/87.35 ($false),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10731, 51, 10525, 10728, 10727])).
% 87.12/87.35 tff(10733,plain,((~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.35 tff(10734,plain,
% 87.12/87.35 ((~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10733, 10726])).
% 87.12/87.35 tff(10735,plain,
% 87.12/87.35 (~node21(c_e_h_3, c_i, s3, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10734, 10525])).
% 87.12/87.35 tff(10736,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10737,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10738,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10737, 10736])).
% 87.12/87.35 tff(10739,plain,
% 87.12/87.35 (node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10738, 81, 679])).
% 87.12/87.35 tff(10740,plain,
% 87.12/87.35 ($false),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10739, 10735, 10534])).
% 87.12/87.35 tff(10741,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.35 tff(10742,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s4)), introduced(assumption)).
% 87.12/87.35 tff(10743,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s4)), introduced(assumption)).
% 87.12/87.35 tff(10744,plain,
% 87.12/87.35 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10745,plain,
% 87.12/87.35 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10746,plain,
% 87.12/87.35 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10745, 10744])).
% 87.12/87.35 tff(10747,plain,
% 87.12/87.35 ($false),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10746, 2218, 10743, 10742])).
% 87.12/87.35 tff(10748,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.35 tff(10749,plain,
% 87.12/87.35 (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10748, 10741])).
% 87.12/87.35 tff(10750,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s4)), introduced(assumption)).
% 87.12/87.35 tff(10751,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s5)), introduced(assumption)).
% 87.12/87.35 tff(10752,assumption,(node15(c_e_h_3, c_f, s4, s5)), introduced(assumption)).
% 87.12/87.35 tff(10753,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10754,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10755,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10754, 10753])).
% 87.12/87.35 tff(10756,plain,
% 87.12/87.35 ($false),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10755, 173, 10750, 10751, 10752])).
% 87.12/87.35 tff(10757,plain,((~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.35 tff(10758,plain,
% 87.12/87.35 (~node15(c_e_h_3, c_f, s4, s5)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10757, 10751, 10750])).
% 87.12/87.35 tff(10759,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s4)), introduced(assumption)).
% 87.12/87.35 tff(10760,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s4)), introduced(assumption)).
% 87.12/87.35 tff(10761,assumption,(~node15(c_e_h_3, c_f, s4, s5)), introduced(assumption)).
% 87.12/87.35 tff(10762,plain,
% 87.12/87.35 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10763,plain,
% 87.12/87.35 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10764,plain,
% 87.12/87.35 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10763, 10762])).
% 87.12/87.35 tff(10765,plain,
% 87.12/87.35 ((~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10764, 228, 10759])).
% 87.12/87.35 tff(10766,plain,
% 87.12/87.35 (~node16(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10765, 10760])).
% 87.12/87.35 tff(10767,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_f, s4, s5))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10768,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_f, s4, s5))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10769,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_f, s4, s5)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10768, 10767])).
% 87.12/87.35 tff(10770,plain,
% 87.12/87.35 (node19(c_e_h_3, c_f, s4, s5)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10769, 141, 1432])).
% 87.12/87.35 tff(10771,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10772,plain,
% 87.12/87.35 ((node16(c_e_h_3, c_f, s4) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5))) <=> (node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10773,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s4) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4)))),
% 87.12/87.35 inference(monotonicity,[status(thm)],[10772])).
% 87.12/87.35 tff(10774,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s4) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(transitivity,[status(thm)],[10773, 10771])).
% 87.12/87.35 tff(10775,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s4) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10776,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10775, 10774])).
% 87.12/87.35 tff(10777,plain,
% 87.12/87.35 (node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | node16(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10776, 189, 10770])).
% 87.12/87.35 tff(10778,plain,
% 87.12/87.35 (node14(c_e_h_3, c_f, s4, s5)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10777, 10766, 10761])).
% 87.12/87.35 tff(10779,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10780,plain,
% 87.12/87.35 (((~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10781,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4)))),
% 87.12/87.35 inference(monotonicity,[status(thm)],[10780])).
% 87.12/87.35 tff(10782,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(transitivity,[status(thm)],[10781, 10779])).
% 87.12/87.35 tff(10783,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10784,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10783, 10782])).
% 87.12/87.35 tff(10785,plain,
% 87.12/87.35 ($false),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10784, 283, 10751, 10778, 10760])).
% 87.12/87.35 tff(10786,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | node15(c_e_h_3, c_f, s4, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.35 tff(10787,plain,
% 87.12/87.35 (m_c_h_element_v_in1(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10786, 10751, 10759, 10758])).
% 87.12/87.35 tff(10788,assumption,(node18(c_e_h_3, c_f, s4, s5)), introduced(assumption)).
% 87.12/87.35 tff(10789,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5)))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10790,plain,
% 87.12/87.35 (((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~node18(c_e_h_3, c_f, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5)))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10791,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~node18(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5))))),
% 87.12/87.35 inference(monotonicity,[status(thm)],[10790])).
% 87.12/87.35 tff(10792,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~node18(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5)))),
% 87.12/87.35 inference(transitivity,[status(thm)],[10791, 10789])).
% 87.12/87.35 tff(10793,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~node18(c_e_h_3, c_f, s4, s5)))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10794,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5))),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10793, 10792])).
% 87.12/87.35 tff(10795,plain,
% 87.12/87.35 ($false),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10794, 124, 10750, 10751, 10788])).
% 87.12/87.35 tff(10796,plain,((~node18(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.35 tff(10797,plain,
% 87.12/87.35 (~node18(c_e_h_3, c_f, s4, s5)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10796, 10751, 10750])).
% 87.12/87.35 tff(10798,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10799,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10800,plain,
% 87.12/87.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5))),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10799, 10798])).
% 87.12/87.35 tff(10801,plain,
% 87.12/87.35 (node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10800, 156, 10770])).
% 87.12/87.35 tff(10802,plain,
% 87.12/87.35 (node17(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10801, 10797])).
% 87.12/87.35 tff(10803,plain,
% 87.12/87.35 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10804,plain,
% 87.12/87.35 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4))) <=> (m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10805,plain,
% 87.12/87.35 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4))))),
% 87.12/87.35 inference(monotonicity,[status(thm)],[10804])).
% 87.12/87.35 tff(10806,plain,
% 87.12/87.35 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)))),
% 87.12/87.35 inference(transitivity,[status(thm)],[10805, 10803])).
% 87.12/87.35 tff(10807,plain,
% 87.12/87.35 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10808,plain,
% 87.12/87.35 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10807, 10806])).
% 87.12/87.35 tff(10809,plain,
% 87.12/87.35 ((~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4))),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10808, 209, 10759])).
% 87.12/87.35 tff(10810,plain,
% 87.12/87.35 ($false),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10809, 10802, 10787])).
% 87.12/87.35 tff(10811,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.35 tff(10812,plain,
% 87.12/87.35 ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10811, 7998])).
% 87.12/87.35 tff(10813,plain,
% 87.12/87.35 (~m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10812, 10749])).
% 87.12/87.35 tff(10814,plain,
% 87.12/87.35 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10815,plain,
% 87.12/87.35 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10816,plain,
% 87.12/87.35 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10815, 10814])).
% 87.12/87.35 tff(10817,plain,
% 87.12/87.35 (~m_and_h_gate_v_in1(c_e_h_3, c_q, s5)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10816, 1666, 10813])).
% 87.12/87.35 tff(10818,plain,
% 87.12/87.35 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s5))),
% 87.12/87.35 inference(rewrite,[status(thm)],[])).
% 87.12/87.35 tff(10819,plain,
% 87.12/87.35 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s5))),
% 87.12/87.35 inference(quant_inst,[status(thm)],[])).
% 87.12/87.35 tff(10820,plain,
% 87.12/87.35 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s5)),
% 87.12/87.35 inference(modus_ponens,[status(thm)],[10819, 10818])).
% 87.12/87.35 tff(10821,plain,
% 87.12/87.35 (~node20(c_e_h_3, c_q, s5)),
% 87.12/87.35 inference(unit_resolution,[status(thm)],[10820, 37, 10817])).
% 87.12/87.35 tff(10822,plain,
% 87.12/87.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node21(c_e_h_3, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node21(c_e_h_3, c_q, s5, s6)))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10823,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node21(c_e_h_3, c_q, s5, s6)))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10824,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node21(c_e_h_3, c_q, s5, s6))),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10823, 10822])).
% 87.12/87.36 tff(10825,plain,
% 87.12/87.36 ($false),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10824, 51, 10821, 10523, 10524])).
% 87.12/87.36 tff(10826,plain,((~node21(c_e_h_3, c_q, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.36 tff(10827,plain,
% 87.12/87.36 (~node21(c_e_h_3, c_q, s5, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10826, 10523])).
% 87.12/87.36 tff(10828,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10829,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10830,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10829, 10828])).
% 87.12/87.36 tff(10831,plain,
% 87.12/87.36 (node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10830, 81, 1499])).
% 87.12/87.36 tff(10832,plain,
% 87.12/87.36 (node22(c_e_h_3, c_q, s5, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10831, 10827])).
% 87.12/87.36 tff(10833,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s5)), introduced(assumption)).
% 87.12/87.36 tff(10834,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10835,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10836,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10835, 10834])).
% 87.12/87.36 tff(10837,plain,
% 87.12/87.36 ($false),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10836, 107, 10833, 10523, 10832])).
% 87.12/87.36 tff(10838,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.36 tff(10839,plain,
% 87.12/87.36 (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10838, 8025])).
% 87.12/87.36 tff(10840,plain,
% 87.12/87.36 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s6))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10841,plain,
% 87.12/87.36 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s6))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10842,plain,
% 87.12/87.36 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s6)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10841, 10840])).
% 87.12/87.36 tff(10843,plain,
% 87.12/87.36 (node3(c_e_h_3, c_e_h_1, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10842, 3860, 814])).
% 87.12/87.36 tff(10844,plain,
% 87.12/87.36 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s6)) | (~node3(c_e_h_3, c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s6)) | (~node3(c_e_h_3, c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10845,plain,
% 87.12/87.36 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s6)) | (~node3(c_e_h_3, c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10846,plain,
% 87.12/87.36 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s6)) | (~node3(c_e_h_3, c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10845, 10844])).
% 87.12/87.36 tff(10847,plain,
% 87.12/87.36 ((~m_cell_v_ack(c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10846, 836, 10843])).
% 87.12/87.36 tff(10848,plain,
% 87.12/87.36 (~m_cell_v_ack(c_e_h_1, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10847, 10839])).
% 87.12/87.36 tff(10849,plain,
% 87.12/87.36 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)) | m_cell_v_ack(c_e_h_1, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)) | m_cell_v_ack(c_e_h_1, s6))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10850,plain,
% 87.12/87.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)) | m_cell_v_ack(c_e_h_1, s6))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10851,plain,
% 87.12/87.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)) | m_cell_v_ack(c_e_h_1, s6)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10850, 10849])).
% 87.12/87.36 tff(10852,plain,
% 87.12/87.36 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10851, 848, 10848])).
% 87.12/87.36 tff(10853,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s6)), introduced(assumption)).
% 87.12/87.36 tff(10854,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s7)), introduced(assumption)).
% 87.12/87.36 tff(10855,assumption,(node6(c_e_h_1, c_j, s6, s7)), introduced(assumption)).
% 87.12/87.36 tff(10856,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | (~node6(c_e_h_1, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | (~node6(c_e_h_1, c_j, s6, s7)))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10857,plain,
% 87.12/87.36 (((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | (~node6(c_e_h_1, c_j, s6, s7)))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10858,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | (~node6(c_e_h_1, c_j, s6, s7))))),
% 87.12/87.36 inference(monotonicity,[status(thm)],[10857])).
% 87.12/87.36 tff(10859,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | (~node6(c_e_h_1, c_j, s6, s7)))),
% 87.12/87.36 inference(transitivity,[status(thm)],[10858, 10856])).
% 87.12/87.36 tff(10860,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10861,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | (~node6(c_e_h_1, c_j, s6, s7))),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10860, 10859])).
% 87.12/87.36 tff(10862,plain,
% 87.12/87.36 ($false),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10861, 899, 10853, 10854, 10855])).
% 87.12/87.36 tff(10863,plain,((~node6(c_e_h_1, c_j, s6, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.36 tff(10864,plain,
% 87.12/87.36 (~node6(c_e_h_1, c_j, s6, s7)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10863, 10854, 10853])).
% 87.12/87.36 tff(10865,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)), introduced(assumption)).
% 87.12/87.36 tff(10866,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s5)), introduced(assumption)).
% 87.12/87.36 tff(10867,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s6)), introduced(assumption)).
% 87.12/87.36 tff(10868,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10869,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10870,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10869, 10868])).
% 87.12/87.36 tff(10871,plain,
% 87.12/87.36 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10870, 107])).
% 87.12/87.36 tff(10872,plain,
% 87.12/87.36 (~node22(c_e_h_1, c_l, s5, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10871, 10867, 10866])).
% 87.12/87.36 tff(10873,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10874,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10875,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10874, 10873])).
% 87.12/87.36 tff(10876,plain,
% 87.12/87.36 (node21(c_e_h_1, c_l, s5, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10875, 81, 1499, 10872])).
% 87.12/87.36 tff(10877,plain,
% 87.12/87.36 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10878,plain,
% 87.12/87.36 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10879,plain,
% 87.12/87.36 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10878, 10877])).
% 87.12/87.36 tff(10880,plain,
% 87.12/87.36 ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10879, 1638])).
% 87.12/87.36 tff(10881,plain,
% 87.12/87.36 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10880, 5178])).
% 87.12/87.36 tff(10882,plain,
% 87.12/87.36 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s5))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10883,plain,
% 87.12/87.36 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s5))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10884,plain,
% 87.12/87.36 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s5)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10883, 10882])).
% 87.12/87.36 tff(10885,plain,
% 87.12/87.36 (~node20(c_e_h_1, c_l, s5)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10884, 1535, 10881])).
% 87.12/87.36 tff(10886,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node21(c_e_h_1, c_l, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node21(c_e_h_1, c_l, s5, s6)))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10887,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node21(c_e_h_1, c_l, s5, s6)))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10888,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node21(c_e_h_1, c_l, s5, s6))),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10887, 10886])).
% 87.12/87.36 tff(10889,plain,
% 87.12/87.36 ($false),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10888, 51, 10867, 10885, 10876])).
% 87.12/87.36 tff(10890,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.36 tff(10891,plain,
% 87.12/87.36 (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10890, 8070])).
% 87.12/87.36 tff(10892,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s6)), introduced(assumption)).
% 87.12/87.36 tff(10893,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s6)), introduced(assumption)).
% 87.12/87.36 tff(10894,plain,
% 87.12/87.36 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10895,plain,
% 87.12/87.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10896,plain,
% 87.12/87.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10895, 10894])).
% 87.12/87.36 tff(10897,plain,
% 87.12/87.36 ($false),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10896, 801, 10893, 10892])).
% 87.12/87.36 tff(10898,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.36 tff(10899,plain,
% 87.12/87.36 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10898, 10891])).
% 87.12/87.36 tff(10900,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)), introduced(assumption)).
% 87.12/87.36 tff(10901,assumption,(node5(c_e_h_1, c_j, s6, s7)), introduced(assumption)).
% 87.12/87.36 tff(10902,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10903,plain,
% 87.12/87.36 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10904,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7))))),
% 87.12/87.36 inference(monotonicity,[status(thm)],[10903])).
% 87.12/87.36 tff(10905,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)))),
% 87.12/87.36 inference(transitivity,[status(thm)],[10904, 10902])).
% 87.12/87.36 tff(10906,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10907,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7))),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10906, 10905])).
% 87.12/87.36 tff(10908,plain,
% 87.12/87.36 ($false),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10907, 862, 10854, 10901, 10865, 10900])).
% 87.12/87.36 tff(10909,plain,((~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.36 tff(10910,plain,
% 87.12/87.36 ((~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10909, 10899])).
% 87.12/87.36 tff(10911,plain,
% 87.12/87.36 (~node5(c_e_h_1, c_j, s6, s7)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10910, 10854, 10865])).
% 87.12/87.36 tff(10912,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10913,plain,
% 87.12/87.36 ((node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7) | (~trans(s6, s7))) <=> ((~trans(s6, s7)) | node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10914,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7)))),
% 87.12/87.36 inference(monotonicity,[status(thm)],[10913])).
% 87.12/87.36 tff(10915,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7))),
% 87.12/87.36 inference(transitivity,[status(thm)],[10914, 10912])).
% 87.12/87.36 tff(10916,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7) | (~trans(s6, s7)))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10917,plain,
% 87.12/87.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10916, 10915])).
% 87.12/87.36 tff(10918,plain,
% 87.12/87.36 (node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10917, 881, 1552])).
% 87.12/87.36 tff(10919,plain,
% 87.12/87.36 ($false),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10918, 10911, 10864])).
% 87.12/87.36 tff(10920,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | m_or_h_gate_v_out(c_e_h_1, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.36 tff(10921,plain,
% 87.12/87.36 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10920, 10852])).
% 87.12/87.36 tff(10922,plain,
% 87.12/87.36 (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10921, 8084])).
% 87.12/87.36 tff(10923,plain,
% 87.12/87.36 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10924,plain,
% 87.12/87.36 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))),
% 87.12/87.36 inference(quant_inst,[status(thm)],[])).
% 87.12/87.36 tff(10925,plain,
% 87.12/87.36 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7)),
% 87.12/87.36 inference(modus_ponens,[status(thm)],[10924, 10923])).
% 87.12/87.36 tff(10926,plain,
% 87.12/87.36 ($false),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10925, 309, 10922, 10522])).
% 87.12/87.36 tff(10927,plain,(~m_c_h_element_v_in2(c_e_h_1, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.36 tff(10928,plain,
% 87.12/87.36 (~m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[7169, 6695, 8089])).
% 87.12/87.36 tff(10929,plain,
% 87.12/87.36 (m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[8161, 10928])).
% 87.12/87.36 tff(10930,plain,
% 87.12/87.36 (~m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 87.12/87.36 inference(unit_resolution,[status(thm)],[10929, 8088])).
% 87.12/87.36 tff(10931,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s7)), introduced(assumption)).
% 87.12/87.36 tff(10932,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s8)), introduced(assumption)).
% 87.12/87.36 tff(10933,assumption,(node18(c_e_h_1, c_h, s7, s8)), introduced(assumption)).
% 87.12/87.36 tff(10934,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10935,plain,
% 87.12/87.36 (((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~node18(c_e_h_1, c_h, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.36 inference(rewrite,[status(thm)],[])).
% 87.12/87.36 tff(10936,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~node18(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8))))),
% 87.12/87.36 inference(monotonicity,[status(thm)],[10935])).
% 87.12/87.36 tff(10937,plain,
% 87.12/87.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~node18(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(transitivity,[status(thm)],[10936, 10934])).
% 87.12/87.37 tff(10938,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~node18(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10939,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10938, 10937])).
% 87.12/87.37 tff(10940,plain,
% 87.12/87.37 ($false),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10939, 124, 10931, 10932, 10933])).
% 87.12/87.37 tff(10941,plain,((~node18(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.37 tff(10942,plain,
% 87.12/87.37 (~node18(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10941, 10932, 10931])).
% 87.12/87.37 tff(10943,assumption,(node15(c_e_h_1, c_h, s7, s8)), introduced(assumption)).
% 87.12/87.37 tff(10944,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10945,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10946,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10945, 10944])).
% 87.12/87.37 tff(10947,plain,
% 87.12/87.37 ($false),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10946, 173, 10931, 10932, 10943])).
% 87.12/87.37 tff(10948,plain,((~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.37 tff(10949,plain,
% 87.12/87.37 (~node15(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10948, 10932, 10931])).
% 87.12/87.37 tff(10950,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s7)), introduced(assumption)).
% 87.12/87.37 tff(10951,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10952,plain,
% 87.12/87.37 (((~node14(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10953,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8))))),
% 87.12/87.37 inference(monotonicity,[status(thm)],[10952])).
% 87.12/87.37 tff(10954,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(transitivity,[status(thm)],[10953, 10951])).
% 87.12/87.37 tff(10955,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10956,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10955, 10954])).
% 87.12/87.37 tff(10957,plain,
% 87.12/87.37 (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10956, 283])).
% 87.12/87.37 tff(10958,plain,
% 87.12/87.37 (~node14(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10957, 10932, 10950])).
% 87.12/87.37 tff(10959,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10960,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10961,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10960, 10959])).
% 87.12/87.37 tff(10962,plain,
% 87.12/87.37 (node19(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10961, 141, 2152])).
% 87.12/87.37 tff(10963,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10964,plain,
% 87.12/87.37 ((node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8))) <=> (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10965,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(monotonicity,[status(thm)],[10964])).
% 87.12/87.37 tff(10966,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(transitivity,[status(thm)],[10965, 10963])).
% 87.12/87.37 tff(10967,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10968,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10967, 10966])).
% 87.12/87.37 tff(10969,plain,
% 87.12/87.37 (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10968, 189, 10962])).
% 87.12/87.37 tff(10970,plain,
% 87.12/87.37 (node16(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10969, 10958, 10949])).
% 87.12/87.37 tff(10971,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10972,plain,
% 87.12/87.37 ((node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8))) <=> (node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10973,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(monotonicity,[status(thm)],[10972])).
% 87.12/87.37 tff(10974,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8))),
% 87.12/87.37 inference(transitivity,[status(thm)],[10973, 10971])).
% 87.12/87.37 tff(10975,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10976,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10975, 10974])).
% 87.12/87.37 tff(10977,plain,
% 87.12/87.37 (node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10976, 156, 10962])).
% 87.12/87.37 tff(10978,plain,
% 87.12/87.37 (node17(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10977, 10942])).
% 87.12/87.37 tff(10979,plain,
% 87.12/87.37 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7)))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10980,plain,
% 87.12/87.37 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7)))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10981,plain,
% 87.12/87.37 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7))),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10980, 10979])).
% 87.12/87.37 tff(10982,plain,
% 87.12/87.37 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7))),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10981, 245, 10950])).
% 87.12/87.37 tff(10983,plain,
% 87.12/87.37 (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10982, 10978])).
% 87.12/87.37 tff(10984,plain,
% 87.12/87.37 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_in2(c_e_h_1, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_in2(c_e_h_1, c_h, s7))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10985,plain,
% 87.12/87.37 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_in2(c_e_h_1, c_h, s7))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10986,plain,
% 87.12/87.37 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_in2(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10985, 10984])).
% 87.12/87.37 tff(10987,plain,
% 87.12/87.37 ((~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10986, 228, 10950])).
% 87.12/87.37 tff(10988,plain,
% 87.12/87.37 ($false),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10987, 10983, 10970])).
% 87.12/87.37 tff(10989,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_out(c_e_h_1, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.37 tff(10990,plain,
% 87.12/87.37 (m_c_h_element_v_in1(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10989, 10932, 10931])).
% 87.12/87.37 tff(10991,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s7)), introduced(assumption)).
% 87.12/87.37 tff(10992,plain,
% 87.12/87.37 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7)))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10993,plain,
% 87.12/87.37 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7)))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(10994,plain,
% 87.12/87.37 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7))))),
% 87.12/87.37 inference(monotonicity,[status(thm)],[10993])).
% 87.12/87.37 tff(10995,plain,
% 87.12/87.37 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7)))),
% 87.12/87.37 inference(transitivity,[status(thm)],[10994, 10992])).
% 87.12/87.37 tff(10996,plain,
% 87.12/87.37 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(10997,plain,
% 87.12/87.37 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7))),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[10996, 10995])).
% 87.12/87.37 tff(10998,plain,
% 87.12/87.37 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | (~node17(c_e_h_1, c_h, s7))),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10997, 209, 10991])).
% 87.12/87.37 tff(10999,plain,
% 87.12/87.37 (~node17(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10998, 10990])).
% 87.12/87.37 tff(11000,plain,
% 87.12/87.37 ($false),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[10977, 10999, 10942])).
% 87.12/87.37 tff(11001,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | m_c_h_element_v_out(c_e_h_1, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.37 tff(11002,plain,
% 87.12/87.37 ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11001, 10930])).
% 87.12/87.37 tff(11003,plain,
% 87.12/87.37 (~m_c_h_element_v_out(c_e_h_1, c_h, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11002, 10927])).
% 87.12/87.37 tff(11004,plain,
% 87.12/87.37 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(11005,plain,
% 87.12/87.37 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(11006,plain,
% 87.12/87.37 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s8)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[11005, 11004])).
% 87.12/87.37 tff(11007,plain,
% 87.12/87.37 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11006, 23, 11003])).
% 87.12/87.37 tff(11008,plain,
% 87.12/87.37 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s8))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(11009,plain,
% 87.12/87.37 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s8))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(11010,plain,
% 87.12/87.37 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s8)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[11009, 11008])).
% 87.12/87.37 tff(11011,plain,
% 87.12/87.37 (~node20(c_e_h_1, c_i, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11010, 37, 11007])).
% 87.12/87.37 tff(11012,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s9)), introduced(assumption)).
% 87.12/87.37 tff(11013,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(11014,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(11015,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[11014, 11013])).
% 87.12/87.37 tff(11016,plain,
% 87.12/87.37 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11015, 107])).
% 87.12/87.37 tff(11017,plain,
% 87.12/87.37 (~node22(c_e_h_1, c_i, s8, s9)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11016, 11012, 8204])).
% 87.12/87.37 tff(11018,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(11019,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(11020,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[11019, 11018])).
% 87.12/87.37 tff(11021,plain,
% 87.12/87.37 (node21(c_e_h_1, c_i, s8, s9)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11020, 81, 2636, 11017])).
% 87.12/87.37 tff(11022,assumption,(~node20(c_e_h_1, c_i, s8)), introduced(assumption)).
% 87.12/87.37 tff(11023,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node21(c_e_h_1, c_i, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node21(c_e_h_1, c_i, s8, s9)))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(11024,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node21(c_e_h_1, c_i, s8, s9)))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(11025,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node21(c_e_h_1, c_i, s8, s9))),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[11024, 11023])).
% 87.12/87.37 tff(11026,plain,
% 87.12/87.37 ($false),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11025, 51, 11022, 11012, 11021])).
% 87.12/87.37 tff(11027,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | node20(c_e_h_1, c_i, s8) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.37 tff(11028,plain,
% 87.12/87.37 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | node20(c_e_h_1, c_i, s8)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11027, 8202])).
% 87.12/87.37 tff(11029,plain,
% 87.12/87.37 (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11028, 11011])).
% 87.12/87.37 tff(11030,plain,
% 87.12/87.37 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(11031,plain,
% 87.12/87.37 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.37 tff(11032,plain,
% 87.12/87.37 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)),
% 87.12/87.37 inference(modus_ponens,[status(thm)],[11031, 11030])).
% 87.12/87.37 tff(11033,plain,
% 87.12/87.37 (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[11032, 365, 11029])).
% 87.12/87.37 tff(11034,plain,
% 87.12/87.37 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[8312, 1142, 7364])).
% 87.12/87.37 tff(11035,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s9)), introduced(assumption)).
% 87.12/87.37 tff(11036,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)), introduced(assumption)).
% 87.12/87.37 tff(11037,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)), introduced(assumption)).
% 87.12/87.37 tff(11038,plain,
% 87.12/87.37 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[8308, 8303])).
% 87.12/87.37 tff(11039,plain,
% 87.12/87.37 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)),
% 87.12/87.37 inference(unit_resolution,[status(thm)],[8343, 11038, 8315, 8327])).
% 87.12/87.37 tff(11040,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s10)), introduced(assumption)).
% 87.12/87.37 tff(11041,assumption,(node15(c_e_h_1, c_e, s9, s10)), introduced(assumption)).
% 87.12/87.37 tff(11042,plain,
% 87.12/87.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9))),
% 87.12/87.37 inference(rewrite,[status(thm)],[])).
% 87.12/87.37 tff(11043,plain,
% 87.12/87.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9))),
% 87.12/87.37 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11044,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11043, 11042])).
% 87.12/87.38 tff(11045,plain,
% 87.12/87.38 ($false),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11044, 173, 8303, 11041, 11040])).
% 87.12/87.38 tff(11046,plain,((~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.38 tff(11047,plain,
% 87.12/87.38 (~node15(c_e_h_1, c_e, s9, s10)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11046, 11040, 8303])).
% 87.12/87.38 tff(11048,assumption,(node18(c_e_h_1, c_e, s9, s10)), introduced(assumption)).
% 87.12/87.38 tff(11049,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11050,plain,
% 87.12/87.38 (((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~node18(c_e_h_1, c_e, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11051,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~node18(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s9, s10))))),
% 87.12/87.38 inference(monotonicity,[status(thm)],[11050])).
% 87.12/87.38 tff(11052,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~node18(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(transitivity,[status(thm)],[11051, 11049])).
% 87.12/87.38 tff(11053,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~node18(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11054,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s9, s10))),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11053, 11052])).
% 87.12/87.38 tff(11055,plain,
% 87.12/87.38 ($false),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11054, 124, 8303, 11048, 11040])).
% 87.12/87.38 tff(11056,plain,((~node18(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.38 tff(11057,plain,
% 87.12/87.38 (~node18(c_e_h_1, c_e, s9, s10)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11056, 11040, 8303])).
% 87.12/87.38 tff(11058,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_e, s9, s10))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11059,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_e, s9, s10))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11060,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_e, s9, s10)),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11059, 11058])).
% 87.12/87.38 tff(11061,plain,
% 87.12/87.38 (node19(c_e_h_1, c_e, s9, s10)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11060, 141, 3175])).
% 87.12/87.38 tff(11062,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11063,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11064,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10))),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11063, 11062])).
% 87.12/87.38 tff(11065,plain,
% 87.12/87.38 (node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11064, 156, 11061])).
% 87.12/87.38 tff(11066,plain,
% 87.12/87.38 (node17(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11065, 11057])).
% 87.12/87.38 tff(11067,assumption,(node17(c_e_h_1, c_e, s9)), introduced(assumption)).
% 87.12/87.38 tff(11068,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11069,plain,
% 87.12/87.38 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11070,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9))))),
% 87.12/87.38 inference(monotonicity,[status(thm)],[11069])).
% 87.12/87.38 tff(11071,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(transitivity,[status(thm)],[11070, 11068])).
% 87.12/87.38 tff(11072,plain,
% 87.12/87.38 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11073,plain,
% 87.12/87.38 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9))),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11072, 11071])).
% 87.12/87.38 tff(11074,plain,
% 87.12/87.38 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9))),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11073, 209, 11035])).
% 87.12/87.38 tff(11075,plain,
% 87.12/87.38 (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11074, 11067])).
% 87.12/87.38 tff(11076,assumption,(~node15(c_e_h_1, c_e, s9, s10)), introduced(assumption)).
% 87.12/87.38 tff(11077,assumption,(node16(c_e_h_1, c_e, s9)), introduced(assumption)).
% 87.12/87.38 tff(11078,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s9)), introduced(assumption)).
% 87.12/87.38 tff(11079,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11080,plain,
% 87.12/87.38 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11081,plain,
% 87.12/87.38 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11080, 11079])).
% 87.12/87.38 tff(11082,plain,
% 87.12/87.38 (m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11081, 228, 11077])).
% 87.12/87.38 tff(11083,plain,
% 87.12/87.38 (m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11082, 11078])).
% 87.12/87.38 tff(11084,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11085,plain,
% 87.12/87.38 ((m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11086,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9))))),
% 87.12/87.38 inference(monotonicity,[status(thm)],[11085])).
% 87.12/87.38 tff(11087,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(transitivity,[status(thm)],[11086, 11084])).
% 87.12/87.38 tff(11088,plain,
% 87.12/87.38 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11089,plain,
% 87.12/87.38 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9))),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11088, 11087])).
% 87.12/87.38 tff(11090,plain,
% 87.12/87.38 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11089, 245, 11067])).
% 87.12/87.38 tff(11091,plain,
% 87.12/87.38 ($false),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11090, 11083, 11078])).
% 87.12/87.38 tff(11092,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)) | (~node16(c_e_h_1, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.38 tff(11093,plain,
% 87.12/87.38 (m_c_h_element_v_in1(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11092, 11067, 11077])).
% 87.12/87.38 tff(11094,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node16(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node16(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11095,plain,
% 87.12/87.38 (((~node16(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node16(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11096,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node16(c_e_h_1, c_e, s9))))),
% 87.12/87.38 inference(monotonicity,[status(thm)],[11095])).
% 87.12/87.38 tff(11097,plain,
% 87.12/87.38 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node16(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(transitivity,[status(thm)],[11096, 11094])).
% 87.12/87.38 tff(11098,plain,
% 87.12/87.38 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11099,plain,
% 87.12/87.38 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node16(c_e_h_1, c_e, s9))),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11098, 11097])).
% 87.12/87.38 tff(11100,plain,
% 87.12/87.38 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11099, 263, 11077])).
% 87.12/87.38 tff(11101,plain,
% 87.12/87.38 (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11100, 11093])).
% 87.12/87.38 tff(11102,plain,
% 87.12/87.38 (m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9))),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11073, 209, 11067])).
% 87.12/87.38 tff(11103,plain,
% 87.12/87.38 ($false),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11102, 11101, 11093])).
% 87.12/87.38 tff(11104,plain,((~node17(c_e_h_1, c_e, s9)) | (~node16(c_e_h_1, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.38 tff(11105,plain,
% 87.12/87.38 (~node16(c_e_h_1, c_e, s9)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11104, 11067])).
% 87.12/87.38 tff(11106,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node15(c_e_h_1, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node15(c_e_h_1, c_e, s9, s10))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11107,plain,
% 87.12/87.38 ((node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10))) <=> (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node15(c_e_h_1, c_e, s9, s10))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11108,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node15(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(monotonicity,[status(thm)],[11107])).
% 87.12/87.38 tff(11109,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node15(c_e_h_1, c_e, s9, s10))),
% 87.12/87.38 inference(transitivity,[status(thm)],[11108, 11106])).
% 87.12/87.38 tff(11110,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11111,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node15(c_e_h_1, c_e, s9, s10)),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11110, 11109])).
% 87.12/87.38 tff(11112,plain,
% 87.12/87.38 (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11111, 189, 11061])).
% 87.12/87.38 tff(11113,plain,
% 87.12/87.38 (node14(c_e_h_1, c_e, s9, s10)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11112, 11105, 11076])).
% 87.12/87.38 tff(11114,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11115,plain,
% 87.12/87.38 (((~node14(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11116,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10))))),
% 87.12/87.38 inference(monotonicity,[status(thm)],[11115])).
% 87.12/87.38 tff(11117,plain,
% 87.12/87.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10)))),
% 87.12/87.38 inference(transitivity,[status(thm)],[11116, 11114])).
% 87.12/87.38 tff(11118,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))),
% 87.12/87.38 inference(quant_inst,[status(thm)],[])).
% 87.12/87.38 tff(11119,plain,
% 87.12/87.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10))),
% 87.12/87.38 inference(modus_ponens,[status(thm)],[11118, 11117])).
% 87.12/87.38 tff(11120,plain,
% 87.12/87.38 ($false),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11119, 283, 11113, 11075, 11040])).
% 87.12/87.38 tff(11121,plain,((~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | node15(c_e_h_1, c_e, s9, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.38 tff(11122,plain,
% 87.12/87.38 ($false),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11121, 11066, 11047, 11035, 11040])).
% 87.12/87.38 tff(11123,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.38 tff(11124,plain,
% 87.12/87.38 (~m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 87.12/87.38 inference(unit_resolution,[status(thm)],[11123, 8303, 11035])).
% 87.12/87.38 tff(11125,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)), introduced(assumption)).
% 87.12/87.38 tff(11126,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s10)), introduced(assumption)).
% 87.12/87.38 tff(11127,plain,
% 87.12/87.38 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 87.12/87.38 inference(rewrite,[status(thm)],[])).
% 87.12/87.38 tff(11128,plain,
% 87.12/87.38 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11129,plain,
% 87.12/87.39 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11128, 11127])).
% 87.12/87.39 tff(11130,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11129, 976, 11126, 11125])).
% 87.12/87.39 tff(11131,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11132,plain,
% 87.12/87.39 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11131, 11124])).
% 87.12/87.39 tff(11133,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)), introduced(assumption)).
% 87.12/87.39 tff(11134,assumption,(node11(c_e_h_1, c_n, s10, s11)), introduced(assumption)).
% 87.12/87.39 tff(11135,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11136,plain,
% 87.12/87.39 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11137,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11))))),
% 87.12/87.39 inference(monotonicity,[status(thm)],[11136])).
% 87.12/87.39 tff(11138,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)))),
% 87.12/87.39 inference(transitivity,[status(thm)],[11137, 11135])).
% 87.12/87.39 tff(11139,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11140,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11))),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11139, 11138])).
% 87.12/87.39 tff(11141,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11140, 1161, 11133, 11036, 11134])).
% 87.12/87.39 tff(11142,plain,((~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11143,plain,
% 87.12/87.39 (~node11(c_e_h_1, c_n, s10, s11)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11142, 11036, 11133])).
% 87.12/87.39 tff(11144,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)), introduced(assumption)).
% 87.12/87.39 tff(11145,assumption,(node10(c_e_h_1, c_n, s10, s11)), introduced(assumption)).
% 87.12/87.39 tff(11146,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11147,plain,
% 87.12/87.39 (((~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11148,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10))))),
% 87.12/87.39 inference(monotonicity,[status(thm)],[11147])).
% 87.12/87.39 tff(11149,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)))),
% 87.12/87.39 inference(transitivity,[status(thm)],[11148, 11146])).
% 87.12/87.39 tff(11150,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11151,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10))),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11150, 11149])).
% 87.12/87.39 tff(11152,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11151, 1191, 11036, 11145, 11037, 11144])).
% 87.12/87.39 tff(11153,plain,((~node10(c_e_h_1, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11154,plain,
% 87.12/87.39 (~node10(c_e_h_1, c_n, s10, s11)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11153, 11036, 11037, 11144])).
% 87.12/87.39 tff(11155,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11156,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11157,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11156, 11155])).
% 87.12/87.39 tff(11158,plain,
% 87.12/87.39 (node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11157, 1092, 3778])).
% 87.12/87.39 tff(11159,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11158, 11154, 11143])).
% 87.12/87.39 tff(11160,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11161,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11160, 11132, 11039, 11037, 11036])).
% 87.12/87.39 tff(11162,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11163,plain,
% 87.12/87.39 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11162, 8327, 11036, 11035, 11034, 8303])).
% 87.12/87.39 tff(11164,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)), introduced(assumption)).
% 87.12/87.39 tff(11165,plain,
% 87.12/87.39 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11166,plain,
% 87.12/87.39 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11167,plain,
% 87.12/87.39 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11166, 11165])).
% 87.12/87.39 tff(11168,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11167, 1142, 8371, 11164])).
% 87.12/87.39 tff(11169,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11170,plain,
% 87.12/87.39 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11169, 11163])).
% 87.12/87.39 tff(11171,plain,
% 87.12/87.39 (node9(c_e_h_1, c_m, s9)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[7385, 11170, 7364])).
% 87.12/87.39 tff(11172,plain,
% 87.12/87.39 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[7357, 1048, 8327])).
% 87.12/87.39 tff(11173,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[7361, 1062, 11172, 11171])).
% 87.12/87.39 tff(11174,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11175,plain,
% 87.12/87.39 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11174, 7354, 6887])).
% 87.12/87.39 tff(11176,plain,
% 87.12/87.39 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11175, 8301])).
% 87.12/87.39 tff(11177,plain,
% 87.12/87.39 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11176, 11033])).
% 87.12/87.39 tff(11178,plain,
% 87.12/87.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11179,plain,
% 87.12/87.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11180,plain,
% 87.12/87.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11179, 11178])).
% 87.12/87.39 tff(11181,plain,
% 87.12/87.39 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11180, 1048, 11177])).
% 87.12/87.39 tff(11182,plain,
% 87.12/87.39 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11183,plain,
% 87.12/87.39 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11184,plain,
% 87.12/87.39 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11183, 11182])).
% 87.12/87.39 tff(11185,plain,
% 87.12/87.39 (~node9(c_e_h_1, c_m, s11)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11184, 1062, 11181])).
% 87.12/87.39 tff(11186,assumption,(~node9(c_e_h_1, c_m, s11)), introduced(assumption)).
% 87.12/87.39 tff(11187,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)), introduced(assumption)).
% 87.12/87.39 tff(11188,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)), introduced(assumption)).
% 87.12/87.39 tff(11189,assumption,(node11(c_e_h_1, c_m, s11, s12)), introduced(assumption)).
% 87.12/87.39 tff(11190,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11191,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11192,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11191, 11190])).
% 87.12/87.39 tff(11193,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11192, 1130, 11188, 11189, 11187])).
% 87.12/87.39 tff(11194,plain,((~node11(c_e_h_1, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11195,plain,
% 87.12/87.39 (~node11(c_e_h_1, c_m, s11, s12)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11194, 11188, 11187])).
% 87.12/87.39 tff(11196,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11197,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11198,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11197, 11196])).
% 87.12/87.39 tff(11199,plain,
% 87.12/87.39 (node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11198, 1092, 4461])).
% 87.12/87.39 tff(11200,plain,
% 87.12/87.39 (node10(c_e_h_1, c_m, s11, s12)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11199, 11195])).
% 87.12/87.39 tff(11201,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11202,plain,
% 87.12/87.39 ((node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11203,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11)))),
% 87.12/87.39 inference(monotonicity,[status(thm)],[11202])).
% 87.12/87.39 tff(11204,plain,
% 87.12/87.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11))),
% 87.12/87.39 inference(transitivity,[status(thm)],[11203, 11201])).
% 87.12/87.39 tff(11205,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11206,plain,
% 87.12/87.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11205, 11204])).
% 87.12/87.39 tff(11207,plain,
% 87.12/87.39 ($false),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11206, 1076, 11188, 11200, 11186])).
% 87.12/87.39 tff(11208,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | node9(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.39 tff(11209,plain,
% 87.12/87.39 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | node9(c_e_h_1, c_m, s11)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11208, 8378])).
% 87.12/87.39 tff(11210,plain,
% 87.12/87.39 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11209, 11185])).
% 87.12/87.39 tff(11211,plain,
% 87.12/87.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11212,plain,
% 87.12/87.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11213,plain,
% 87.12/87.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11212, 11211])).
% 87.12/87.39 tff(11214,plain,
% 87.12/87.39 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11213, 1521])).
% 87.12/87.39 tff(11215,plain,
% 87.12/87.39 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s12)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11214, 11210])).
% 87.12/87.39 tff(11216,plain,
% 87.12/87.39 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s12)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s12)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s12))),
% 87.12/87.39 inference(rewrite,[status(thm)],[])).
% 87.12/87.39 tff(11217,plain,
% 87.12/87.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s12)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s12))),
% 87.12/87.39 inference(quant_inst,[status(thm)],[])).
% 87.12/87.39 tff(11218,plain,
% 87.12/87.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s12)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s12)),
% 87.12/87.39 inference(modus_ponens,[status(thm)],[11217, 11216])).
% 87.12/87.39 tff(11219,plain,
% 87.12/87.39 (~node20(c_e_h_1, c_r, s12)),
% 87.12/87.39 inference(unit_resolution,[status(thm)],[11218, 1535, 11215])).
% 87.12/87.40 tff(11220,assumption,(node21(c_e_h_1, c_r, s12, s13)), introduced(assumption)).
% 87.12/87.40 tff(11221,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13)))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11222,plain,
% 87.12/87.40 ((node20(c_e_h_1, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node21(c_e_h_1, c_r, s12, s13))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13)))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11223,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node21(c_e_h_1, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13))))),
% 87.12/87.40 inference(monotonicity,[status(thm)],[11222])).
% 87.12/87.40 tff(11224,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node21(c_e_h_1, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13)))),
% 87.12/87.40 inference(transitivity,[status(thm)],[11223, 11221])).
% 87.12/87.40 tff(11225,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node21(c_e_h_1, c_r, s12, s13)))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11226,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13))),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11225, 11224])).
% 87.12/87.40 tff(11227,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11226, 51, 10521, 11220, 11219])).
% 87.12/87.40 tff(11228,plain,((~node21(c_e_h_1, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11229,plain,
% 87.12/87.40 (~node21(c_e_h_1, c_r, s12, s13)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11228, 10521])).
% 87.12/87.40 tff(11230,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11231,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11232,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11231, 11230])).
% 87.12/87.40 tff(11233,plain,
% 87.12/87.40 (node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11232, 81, 9599])).
% 87.12/87.40 tff(11234,plain,
% 87.12/87.40 (node22(c_e_h_1, c_r, s12, s13)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11233, 11229])).
% 87.12/87.40 tff(11235,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node22(c_e_h_1, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node22(c_e_h_1, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11236,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node22(c_e_h_1, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11237,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node22(c_e_h_1, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11236, 11235])).
% 87.12/87.40 tff(11238,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11237, 107, 10521, 8396, 11234])).
% 87.12/87.40 tff(11239,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11240,plain,
% 87.12/87.40 ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11123, 8301])).
% 87.12/87.40 tff(11241,plain,
% 87.12/87.40 (~m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11240, 11033])).
% 87.12/87.40 tff(11242,assumption,(m_and_h_gate_v_in2(c_e_h_3, c_q, s6)), introduced(assumption)).
% 87.12/87.40 tff(11243,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)), introduced(assumption)).
% 87.12/87.40 tff(11244,plain,
% 87.12/87.40 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11245,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11246,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11245, 11244])).
% 87.12/87.40 tff(11247,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11246, 6389, 11243, 10750])).
% 87.12/87.40 tff(11248,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s4) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11249,plain,
% 87.12/87.40 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11248, 7998])).
% 87.12/87.40 tff(11250,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)), introduced(assumption)).
% 87.12/87.40 tff(11251,plain,
% 87.12/87.40 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11252,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11253,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11252, 11251])).
% 87.12/87.40 tff(11254,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11253, 6389, 7925, 11250])).
% 87.12/87.40 tff(11255,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11256,plain,
% 87.12/87.40 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11255, 7923])).
% 87.12/87.40 tff(11257,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)), introduced(assumption)).
% 87.12/87.40 tff(11258,plain,
% 87.12/87.40 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11259,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11260,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11259, 11258])).
% 87.12/87.40 tff(11261,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11260, 6389, 7838, 11257])).
% 87.12/87.40 tff(11262,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11263,plain,
% 87.12/87.40 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11262, 7836])).
% 87.12/87.40 tff(11264,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)), introduced(assumption)).
% 87.12/87.40 tff(11265,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)), introduced(assumption)).
% 87.12/87.40 tff(11266,plain,
% 87.12/87.40 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11267,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11268,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11267, 11266])).
% 87.12/87.40 tff(11269,plain,
% 87.12/87.40 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11268, 6378, 6506])).
% 87.12/87.40 tff(11270,assumption,(node11(c_e_h_3, c_m, s2, s3)), introduced(assumption)).
% 87.12/87.40 tff(11271,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)), introduced(assumption)).
% 87.12/87.40 tff(11272,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11273,plain,
% 87.12/87.40 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11274,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3))))),
% 87.12/87.40 inference(monotonicity,[status(thm)],[11273])).
% 87.12/87.40 tff(11275,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)))),
% 87.12/87.40 inference(transitivity,[status(thm)],[11274, 11272])).
% 87.12/87.40 tff(11276,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11277,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3))),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11276, 11275])).
% 87.12/87.40 tff(11278,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11277, 1161, 11271, 11270, 11265])).
% 87.12/87.40 tff(11279,plain,((~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11280,plain,
% 87.12/87.40 ((~node11(c_e_h_3, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11279, 6980])).
% 87.12/87.40 tff(11281,plain,
% 87.12/87.40 (~node11(c_e_h_3, c_m, s2, s3)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11280, 11265])).
% 87.12/87.40 tff(11282,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11283,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11284,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11283, 11282])).
% 87.12/87.40 tff(11285,plain,
% 87.12/87.40 (node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11284, 1092, 582])).
% 87.12/87.40 tff(11286,plain,
% 87.12/87.40 (node10(c_e_h_3, c_m, s2, s3)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11285, 11281])).
% 87.12/87.40 tff(11287,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11288,plain,
% 87.12/87.40 (((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) <=> ((~node10(c_e_h_3, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11289,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2))))),
% 87.12/87.40 inference(monotonicity,[status(thm)],[11288])).
% 87.12/87.40 tff(11290,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)))),
% 87.12/87.40 inference(transitivity,[status(thm)],[11289, 11287])).
% 87.12/87.40 tff(11291,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11292,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2))),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11291, 11290])).
% 87.12/87.40 tff(11293,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11292, 1191, 11286, 11269, 11265, 11264])).
% 87.12/87.40 tff(11294,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11295,plain,
% 87.12/87.40 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11294, 11263])).
% 87.12/87.40 tff(11296,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)), introduced(assumption)).
% 87.12/87.40 tff(11297,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)), introduced(assumption)).
% 87.12/87.40 tff(11298,plain,
% 87.12/87.40 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11299,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11300,plain,
% 87.12/87.40 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11299, 11298])).
% 87.12/87.40 tff(11301,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11300, 6378, 11297, 11296])).
% 87.12/87.40 tff(11302,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11303,plain,
% 87.12/87.40 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11302, 7006])).
% 87.12/87.40 tff(11304,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)), introduced(assumption)).
% 87.12/87.40 tff(11305,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)), introduced(assumption)).
% 87.12/87.40 tff(11306,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)), introduced(assumption)).
% 87.12/87.40 tff(11307,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)), introduced(assumption)).
% 87.12/87.40 tff(11308,assumption,(node10(c_e_h_3, c_m, s3, s4)), introduced(assumption)).
% 87.12/87.40 tff(11309,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~node10(c_e_h_3, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~node10(c_e_h_3, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11310,plain,
% 87.12/87.40 (((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~node10(c_e_h_3, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11311,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~node10(c_e_h_3, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))),
% 87.12/87.40 inference(monotonicity,[status(thm)],[11310])).
% 87.12/87.40 tff(11312,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~node10(c_e_h_3, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 87.12/87.40 inference(transitivity,[status(thm)],[11311, 11309])).
% 87.12/87.40 tff(11313,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11314,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~node10(c_e_h_3, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11313, 11312])).
% 87.12/87.40 tff(11315,plain,
% 87.12/87.40 ($false),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11314, 1191, 11306, 11307, 11308, 11305])).
% 87.12/87.40 tff(11316,plain,((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.40 tff(11317,plain,
% 87.12/87.40 (~node10(c_e_h_3, c_m, s3, s4)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11316, 11305, 11307, 11306])).
% 87.12/87.40 tff(11318,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4))),
% 87.12/87.40 inference(rewrite,[status(thm)],[])).
% 87.12/87.40 tff(11319,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4))),
% 87.12/87.40 inference(quant_inst,[status(thm)],[])).
% 87.12/87.40 tff(11320,plain,
% 87.12/87.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4)),
% 87.12/87.40 inference(modus_ponens,[status(thm)],[11319, 11318])).
% 87.12/87.40 tff(11321,plain,
% 87.12/87.40 (node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11320, 1092, 679])).
% 87.12/87.40 tff(11322,plain,
% 87.12/87.40 (node11(c_e_h_3, c_m, s3, s4)),
% 87.12/87.40 inference(unit_resolution,[status(thm)],[11321, 11317])).
% 87.12/87.40 tff(11323,plain,
% 87.12/87.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)))),
% 87.12/87.41 inference(rewrite,[status(thm)],[])).
% 87.12/87.41 tff(11324,plain,
% 87.12/87.41 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)))),
% 87.12/87.41 inference(rewrite,[status(thm)],[])).
% 87.12/87.41 tff(11325,plain,
% 87.12/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4))))),
% 87.12/87.41 inference(monotonicity,[status(thm)],[11324])).
% 87.12/87.41 tff(11326,plain,
% 87.12/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)))),
% 87.12/87.41 inference(transitivity,[status(thm)],[11325, 11323])).
% 87.12/87.41 tff(11327,plain,
% 87.12/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))),
% 87.12/87.41 inference(quant_inst,[status(thm)],[])).
% 87.12/87.41 tff(11328,plain,
% 87.12/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4))),
% 87.12/87.41 inference(modus_ponens,[status(thm)],[11327, 11326])).
% 87.12/87.41 tff(11329,plain,
% 87.12/87.41 ($false),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11328, 1161, 11322, 11305, 11304])).
% 87.12/87.41 tff(11330,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.41 tff(11331,plain,
% 87.12/87.41 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3))),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11330, 11303])).
% 87.12/87.41 tff(11332,plain,
% 87.12/87.41 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3))),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11331, 11295])).
% 87.12/87.41 tff(11333,plain,
% 87.12/87.41 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11332, 11256])).
% 87.12/87.41 tff(11334,assumption,(node9(c_e_h_3, c_n, s3)), introduced(assumption)).
% 87.12/87.41 tff(11335,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)), introduced(assumption)).
% 87.12/87.41 tff(11336,plain,
% 87.12/87.41 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))),
% 87.12/87.41 inference(rewrite,[status(thm)],[])).
% 87.12/87.41 tff(11337,plain,
% 87.12/87.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))),
% 87.12/87.41 inference(quant_inst,[status(thm)],[])).
% 87.12/87.41 tff(11338,plain,
% 87.12/87.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))),
% 87.12/87.41 inference(modus_ponens,[status(thm)],[11337, 11336])).
% 87.12/87.41 tff(11339,plain,
% 87.12/87.41 ($false),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11338, 6442, 11335, 11304])).
% 87.12/87.41 tff(11340,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.41 tff(11341,plain,
% 87.12/87.41 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11340, 11295])).
% 87.12/87.41 tff(11342,plain,
% 87.12/87.41 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3))),
% 87.12/87.41 inference(rewrite,[status(thm)],[])).
% 87.12/87.41 tff(11343,plain,
% 87.12/87.41 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3))),
% 87.12/87.41 inference(quant_inst,[status(thm)],[])).
% 87.12/87.41 tff(11344,plain,
% 87.12/87.41 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)),
% 87.12/87.41 inference(modus_ponens,[status(thm)],[11343, 11342])).
% 87.12/87.41 tff(11345,plain,
% 87.12/87.41 ($false),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11344, 1062, 11341, 11334])).
% 87.12/87.41 tff(11346,plain,(~node9(c_e_h_3, c_n, s3)), inference(lemma,lemma(discharge,[]))).
% 87.12/87.41 tff(11347,assumption,(~node9(c_e_h_3, c_n, s3)), introduced(assumption)).
% 87.12/87.41 tff(11348,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)), introduced(assumption)).
% 87.12/87.41 tff(11349,assumption,(node11(c_e_h_3, c_n, s3, s4)), introduced(assumption)).
% 87.12/87.41 tff(11350,plain,
% 87.12/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 87.12/87.41 inference(rewrite,[status(thm)],[])).
% 87.12/87.41 tff(11351,plain,
% 87.12/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 87.12/87.41 inference(quant_inst,[status(thm)],[])).
% 87.12/87.41 tff(11352,plain,
% 87.12/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)),
% 87.12/87.41 inference(modus_ponens,[status(thm)],[11351, 11350])).
% 87.12/87.41 tff(11353,plain,
% 87.12/87.41 ($false),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11352, 1130, 11297, 11348, 11349])).
% 87.12/87.41 tff(11354,plain,((~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 87.12/87.41 tff(11355,plain,
% 87.12/87.41 (~node11(c_e_h_3, c_n, s3, s4)),
% 87.12/87.41 inference(unit_resolution,[status(thm)],[11354, 11348, 7006])).
% 87.12/87.41 tff(11356,plain,
% 87.12/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11357,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11358,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4)),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11357, 11356])).
% 87.22/87.41 tff(11359,plain,
% 87.22/87.41 (node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11358, 1092, 679])).
% 87.22/87.41 tff(11360,plain,
% 87.22/87.41 (node10(c_e_h_3, c_n, s3, s4)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11359, 11355])).
% 87.22/87.41 tff(11361,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11362,plain,
% 87.22/87.41 ((node9(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node10(c_e_h_3, c_n, s3, s4))) <=> (node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11363,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node10(c_e_h_3, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))))),
% 87.22/87.41 inference(monotonicity,[status(thm)],[11362])).
% 87.22/87.41 tff(11364,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node10(c_e_h_3, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)))),
% 87.22/87.41 inference(transitivity,[status(thm)],[11363, 11361])).
% 87.22/87.41 tff(11365,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node10(c_e_h_3, c_n, s3, s4)))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11366,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11365, 11364])).
% 87.22/87.41 tff(11367,plain,
% 87.22/87.41 ($false),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11366, 1076, 11348, 11360, 11347])).
% 87.22/87.41 tff(11368,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | node9(c_e_h_3, c_n, s3)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.41 tff(11369,plain,
% 87.22/87.41 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11368, 11346])).
% 87.22/87.41 tff(11370,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)), introduced(assumption)).
% 87.22/87.41 tff(11371,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)), introduced(assumption)).
% 87.22/87.41 tff(11372,plain,
% 87.22/87.41 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11373,plain,
% 87.22/87.41 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11374,plain,
% 87.22/87.41 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11373, 11372])).
% 87.22/87.41 tff(11375,plain,
% 87.22/87.41 ($false),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11374, 6378, 11371, 11370])).
% 87.22/87.41 tff(11376,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.41 tff(11377,plain,
% 87.22/87.41 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11376, 11369])).
% 87.22/87.41 tff(11378,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)), introduced(assumption)).
% 87.22/87.41 tff(11379,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)), introduced(assumption)).
% 87.22/87.41 tff(11380,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)), introduced(assumption)).
% 87.22/87.41 tff(11381,assumption,(node10(c_e_h_3, c_m, s4, s5)), introduced(assumption)).
% 87.22/87.41 tff(11382,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11383,plain,
% 87.22/87.41 (((~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11384,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5))))),
% 87.22/87.41 inference(monotonicity,[status(thm)],[11383])).
% 87.22/87.41 tff(11385,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)))),
% 87.22/87.41 inference(transitivity,[status(thm)],[11384, 11382])).
% 87.22/87.41 tff(11386,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11387,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5))),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11386, 11385])).
% 87.22/87.41 tff(11388,plain,
% 87.22/87.41 ($false),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11387, 1191, 11380, 11378, 11379, 11381])).
% 87.22/87.41 tff(11389,plain,((~node10(c_e_h_3, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.41 tff(11390,plain,
% 87.22/87.41 (~node10(c_e_h_3, c_m, s4, s5)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11389, 11380, 11379, 11378])).
% 87.22/87.41 tff(11391,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)), introduced(assumption)).
% 87.22/87.41 tff(11392,assumption,(node11(c_e_h_3, c_m, s4, s5)), introduced(assumption)).
% 87.22/87.41 tff(11393,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11394,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11395,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11394, 11393])).
% 87.22/87.41 tff(11396,plain,
% 87.22/87.41 ($false),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11395, 1161, 11380, 11392, 11391])).
% 87.22/87.41 tff(11397,plain,((~node11(c_e_h_3, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.41 tff(11398,plain,
% 87.22/87.41 (~node11(c_e_h_3, c_m, s4, s5)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11397, 11380, 11391])).
% 87.22/87.41 tff(11399,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11400,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11401,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5)),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11400, 11399])).
% 87.22/87.41 tff(11402,plain,
% 87.22/87.41 (node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11401, 1092, 1432])).
% 87.22/87.41 tff(11403,plain,
% 87.22/87.41 ($false),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11402, 11398, 11390])).
% 87.22/87.41 tff(11404,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.41 tff(11405,plain,
% 87.22/87.41 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4))),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11404, 11377])).
% 87.22/87.41 tff(11406,plain,
% 87.22/87.41 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4))),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11405, 11333])).
% 87.22/87.41 tff(11407,plain,
% 87.22/87.41 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11406, 11249])).
% 87.22/87.41 tff(11408,plain,
% 87.22/87.41 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11409,plain,
% 87.22/87.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11410,plain,
% 87.22/87.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11409, 11408])).
% 87.22/87.41 tff(11411,plain,
% 87.22/87.41 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11410, 6442, 11407])).
% 87.22/87.41 tff(11412,plain,
% 87.22/87.41 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11413,plain,
% 87.22/87.41 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11414,plain,
% 87.22/87.41 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11413, 11412])).
% 87.22/87.41 tff(11415,plain,
% 87.22/87.41 (~node9(c_e_h_3, c_n, s5)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11414, 1062, 11411])).
% 87.22/87.41 tff(11416,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)), introduced(assumption)).
% 87.22/87.41 tff(11417,plain,
% 87.22/87.41 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11418,plain,
% 87.22/87.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11419,plain,
% 87.22/87.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11418, 11417])).
% 87.22/87.41 tff(11420,plain,
% 87.22/87.41 ($false),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11419, 6442, 11391, 11416])).
% 87.22/87.41 tff(11421,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.41 tff(11422,plain,
% 87.22/87.41 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11421, 11333])).
% 87.22/87.41 tff(11423,assumption,(node9(c_e_h_3, c_n, s4)), introduced(assumption)).
% 87.22/87.41 tff(11424,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)), introduced(assumption)).
% 87.22/87.41 tff(11425,plain,
% 87.22/87.41 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11426,plain,
% 87.22/87.41 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11427,plain,
% 87.22/87.41 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)),
% 87.22/87.41 inference(modus_ponens,[status(thm)],[11426, 11425])).
% 87.22/87.41 tff(11428,plain,
% 87.22/87.41 ($false),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11427, 1062, 11424, 11423])).
% 87.22/87.41 tff(11429,plain,((~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.41 tff(11430,plain,
% 87.22/87.41 (~node9(c_e_h_3, c_n, s4)),
% 87.22/87.41 inference(unit_resolution,[status(thm)],[11429, 11422])).
% 87.22/87.41 tff(11431,assumption,(~node9(c_e_h_3, c_n, s4)), introduced(assumption)).
% 87.22/87.41 tff(11432,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)), introduced(assumption)).
% 87.22/87.41 tff(11433,assumption,(node11(c_e_h_3, c_n, s4, s5)), introduced(assumption)).
% 87.22/87.41 tff(11434,plain,
% 87.22/87.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 87.22/87.41 inference(rewrite,[status(thm)],[])).
% 87.22/87.41 tff(11435,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 87.22/87.41 inference(quant_inst,[status(thm)],[])).
% 87.22/87.41 tff(11436,plain,
% 87.22/87.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11435, 11434])).
% 87.22/87.42 tff(11437,plain,
% 87.22/87.42 ($false),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11436, 1130, 11370, 11433, 11432])).
% 87.22/87.42 tff(11438,plain,((~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.42 tff(11439,plain,
% 87.22/87.42 (~node11(c_e_h_3, c_n, s4, s5)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11438, 11432, 11370])).
% 87.22/87.42 tff(11440,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11441,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11442,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11441, 11440])).
% 87.22/87.42 tff(11443,plain,
% 87.22/87.42 (node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11442, 1092, 1432])).
% 87.22/87.42 tff(11444,plain,
% 87.22/87.42 (node10(c_e_h_3, c_n, s4, s5)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11443, 11439])).
% 87.22/87.42 tff(11445,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | node9(c_e_h_3, c_n, s4) | (~node10(c_e_h_3, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | node9(c_e_h_3, c_n, s4) | (~node10(c_e_h_3, c_n, s4, s5)))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11446,plain,
% 87.22/87.42 ((node9(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node10(c_e_h_3, c_n, s4, s5))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | node9(c_e_h_3, c_n, s4) | (~node10(c_e_h_3, c_n, s4, s5)))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11447,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node10(c_e_h_3, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | node9(c_e_h_3, c_n, s4) | (~node10(c_e_h_3, c_n, s4, s5))))),
% 87.22/87.42 inference(monotonicity,[status(thm)],[11446])).
% 87.22/87.42 tff(11448,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node10(c_e_h_3, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | node9(c_e_h_3, c_n, s4) | (~node10(c_e_h_3, c_n, s4, s5)))),
% 87.22/87.42 inference(transitivity,[status(thm)],[11447, 11445])).
% 87.22/87.42 tff(11449,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node10(c_e_h_3, c_n, s4, s5)))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11450,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | node9(c_e_h_3, c_n, s4) | (~node10(c_e_h_3, c_n, s4, s5))),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11449, 11448])).
% 87.22/87.42 tff(11451,plain,
% 87.22/87.42 ($false),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11450, 1076, 11444, 11432, 11431])).
% 87.22/87.42 tff(11452,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | node9(c_e_h_3, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.42 tff(11453,plain,
% 87.22/87.42 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | node9(c_e_h_3, c_n, s4)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11452, 11369])).
% 87.22/87.42 tff(11454,plain,
% 87.22/87.42 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11453, 11430])).
% 87.22/87.42 tff(11455,assumption,(~node9(c_e_h_3, c_n, s5)), introduced(assumption)).
% 87.22/87.42 tff(11456,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), introduced(assumption)).
% 87.22/87.42 tff(11457,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)), introduced(assumption)).
% 87.22/87.42 tff(11458,assumption,(node11(c_e_h_3, c_n, s5, s6)), introduced(assumption)).
% 87.22/87.42 tff(11459,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node11(c_e_h_3, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node11(c_e_h_3, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11460,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node11(c_e_h_3, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11461,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node11(c_e_h_3, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11460, 11459])).
% 87.22/87.42 tff(11462,plain,
% 87.22/87.42 ($false),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11461, 1130, 11458, 11456, 11457])).
% 87.22/87.42 tff(11463,plain,((~node11(c_e_h_3, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.42 tff(11464,plain,
% 87.22/87.42 (~node11(c_e_h_3, c_n, s5, s6)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11463, 11456, 11457])).
% 87.22/87.42 tff(11465,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11466,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11467,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11466, 11465])).
% 87.22/87.42 tff(11468,plain,
% 87.22/87.42 (node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11467, 1092, 1499])).
% 87.22/87.42 tff(11469,plain,
% 87.22/87.42 (node10(c_e_h_3, c_n, s5, s6)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11468, 11464])).
% 87.22/87.42 tff(11470,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)) | node9(c_e_h_3, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)) | node9(c_e_h_3, c_n, s5))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11471,plain,
% 87.22/87.42 ((node9(c_e_h_3, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)) | node9(c_e_h_3, c_n, s5))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11472,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)) | node9(c_e_h_3, c_n, s5)))),
% 87.22/87.42 inference(monotonicity,[status(thm)],[11471])).
% 87.22/87.42 tff(11473,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)) | node9(c_e_h_3, c_n, s5))),
% 87.22/87.42 inference(transitivity,[status(thm)],[11472, 11470])).
% 87.22/87.42 tff(11474,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11475,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)) | node9(c_e_h_3, c_n, s5)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11474, 11473])).
% 87.22/87.42 tff(11476,plain,
% 87.22/87.42 ($false),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11475, 1076, 11469, 11456, 11455])).
% 87.22/87.42 tff(11477,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | node9(c_e_h_3, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.42 tff(11478,plain,
% 87.22/87.42 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | node9(c_e_h_3, c_n, s5)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11477, 11454])).
% 87.22/87.42 tff(11479,plain,
% 87.22/87.42 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11478, 11415])).
% 87.22/87.42 tff(11480,plain,
% 87.22/87.42 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11481,plain,
% 87.22/87.42 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11482,plain,
% 87.22/87.42 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11481, 11480])).
% 87.22/87.42 tff(11483,plain,
% 87.22/87.42 ($false),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11482, 6513, 11479, 11242])).
% 87.22/87.42 tff(11484,plain,(~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.42 tff(11485,plain,
% 87.22/87.42 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s6))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11486,plain,
% 87.22/87.42 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s6))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11487,plain,
% 87.22/87.42 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s6)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11486, 11485])).
% 87.22/87.42 tff(11488,plain,
% 87.22/87.42 (~node20(c_e_h_3, c_q, s6)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11487, 1535, 11484])).
% 87.22/87.42 tff(11489,assumption,(~node20(c_e_h_3, c_q, s6)), introduced(assumption)).
% 87.22/87.42 tff(11490,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s7)), introduced(assumption)).
% 87.22/87.42 tff(11491,assumption,(node21(c_e_h_3, c_q, s6, s7)), introduced(assumption)).
% 87.22/87.42 tff(11492,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node21(c_e_h_3, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node21(c_e_h_3, c_q, s6, s7)))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11493,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node21(c_e_h_3, c_q, s6, s7)))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11494,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node21(c_e_h_3, c_q, s6, s7))),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11493, 11492])).
% 87.22/87.42 tff(11495,plain,
% 87.22/87.42 ($false),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11494, 51, 11490, 11491, 11489])).
% 87.22/87.42 tff(11496,plain,((~node21(c_e_h_3, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | node20(c_e_h_3, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.42 tff(11497,plain,
% 87.22/87.42 (~node21(c_e_h_3, c_q, s6, s7)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11496, 11490, 11489])).
% 87.22/87.42 tff(11498,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11499,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11500,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11499, 11498])).
% 87.22/87.42 tff(11501,plain,
% 87.22/87.42 (node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11500, 81, 1552])).
% 87.22/87.42 tff(11502,plain,
% 87.22/87.42 (node22(c_e_h_3, c_q, s6, s7)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11501, 11497])).
% 87.22/87.42 tff(11503,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s6)), introduced(assumption)).
% 87.22/87.42 tff(11504,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node22(c_e_h_3, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node22(c_e_h_3, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11505,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node22(c_e_h_3, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11506,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node22(c_e_h_3, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11505, 11504])).
% 87.22/87.42 tff(11507,plain,
% 87.22/87.42 ($false),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11506, 107, 11490, 11503, 11502])).
% 87.22/87.42 tff(11508,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6) | node20(c_e_h_3, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.42 tff(11509,plain,
% 87.22/87.42 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | node20(c_e_h_3, c_q, s6)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11508, 10839])).
% 87.22/87.42 tff(11510,plain,
% 87.22/87.42 (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11509, 11488])).
% 87.22/87.42 tff(11511,plain,
% 87.22/87.42 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s7))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11512,plain,
% 87.22/87.42 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s7))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11513,plain,
% 87.22/87.42 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s7)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11512, 11511])).
% 87.22/87.42 tff(11514,plain,
% 87.22/87.42 (node3(c_e_h_3, c_e_h_1, s7)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11513, 3860, 814])).
% 87.22/87.42 tff(11515,plain,
% 87.22/87.42 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s7)) | (~node3(c_e_h_3, c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s7)) | (~node3(c_e_h_3, c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11516,plain,
% 87.22/87.42 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s7)) | (~node3(c_e_h_3, c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11517,plain,
% 87.22/87.42 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s7)) | (~node3(c_e_h_3, c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11516, 11515])).
% 87.22/87.42 tff(11518,plain,
% 87.22/87.42 ((~m_cell_v_ack(c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11517, 836, 11514])).
% 87.22/87.42 tff(11519,plain,
% 87.22/87.42 (~m_cell_v_ack(c_e_h_1, s7)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11518, 11510])).
% 87.22/87.42 tff(11520,plain,
% 87.22/87.42 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)) | m_cell_v_ack(c_e_h_1, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)) | m_cell_v_ack(c_e_h_1, s7))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11521,plain,
% 87.22/87.42 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)) | m_cell_v_ack(c_e_h_1, s7))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11522,plain,
% 87.22/87.42 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)) | m_cell_v_ack(c_e_h_1, s7)),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11521, 11520])).
% 87.22/87.42 tff(11523,plain,
% 87.22/87.42 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)),
% 87.22/87.42 inference(unit_resolution,[status(thm)],[11522, 848, 11519])).
% 87.22/87.42 tff(11524,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s8)), introduced(assumption)).
% 87.22/87.42 tff(11525,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s7)), introduced(assumption)).
% 87.22/87.42 tff(11526,assumption,(node6(c_e_h_1, c_j, s7, s8)), introduced(assumption)).
% 87.22/87.42 tff(11527,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~node6(c_e_h_1, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~node6(c_e_h_1, c_j, s7, s8)))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11528,plain,
% 87.22/87.42 (((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~node6(c_e_h_1, c_j, s7, s8)))),
% 87.22/87.42 inference(rewrite,[status(thm)],[])).
% 87.22/87.42 tff(11529,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~node6(c_e_h_1, c_j, s7, s8))))),
% 87.22/87.42 inference(monotonicity,[status(thm)],[11528])).
% 87.22/87.42 tff(11530,plain,
% 87.22/87.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~node6(c_e_h_1, c_j, s7, s8)))),
% 87.22/87.42 inference(transitivity,[status(thm)],[11529, 11527])).
% 87.22/87.42 tff(11531,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))),
% 87.22/87.42 inference(quant_inst,[status(thm)],[])).
% 87.22/87.42 tff(11532,plain,
% 87.22/87.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~node6(c_e_h_1, c_j, s7, s8))),
% 87.22/87.42 inference(modus_ponens,[status(thm)],[11531, 11530])).
% 87.22/87.42 tff(11533,plain,
% 87.22/87.42 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11532, 899, 11524, 11526, 11525])).
% 87.22/87.43 tff(11534,plain,((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11535,plain,
% 87.22/87.43 ((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8))),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11534, 10922])).
% 87.22/87.43 tff(11536,plain,
% 87.22/87.43 (~node6(c_e_h_1, c_j, s7, s8)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11535, 11524])).
% 87.22/87.43 tff(11537,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)), introduced(assumption)).
% 87.22/87.43 tff(11538,plain,
% 87.22/87.43 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11539,plain,
% 87.22/87.43 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11540,plain,
% 87.22/87.43 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11539, 11538])).
% 87.22/87.43 tff(11541,plain,
% 87.22/87.43 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11540, 1638, 5377])).
% 87.22/87.43 tff(11542,plain,
% 87.22/87.43 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s6))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11543,plain,
% 87.22/87.43 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s6))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11544,plain,
% 87.22/87.43 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s6)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11543, 11542])).
% 87.22/87.43 tff(11545,plain,
% 87.22/87.43 (~node20(c_e_h_1, c_l, s6)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11544, 1535, 11541])).
% 87.22/87.43 tff(11546,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s7)), introduced(assumption)).
% 87.22/87.43 tff(11547,assumption,(~node20(c_e_h_1, c_l, s6)), introduced(assumption)).
% 87.22/87.43 tff(11548,assumption,(node21(c_e_h_1, c_l, s6, s7)), introduced(assumption)).
% 87.22/87.43 tff(11549,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node21(c_e_h_1, c_l, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node21(c_e_h_1, c_l, s6, s7)))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11550,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node21(c_e_h_1, c_l, s6, s7)))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11551,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node21(c_e_h_1, c_l, s6, s7))),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11550, 11549])).
% 87.22/87.43 tff(11552,plain,
% 87.22/87.43 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11551, 51, 11548, 11546, 11547])).
% 87.22/87.43 tff(11553,plain,((~node21(c_e_h_1, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | node20(c_e_h_1, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11554,plain,
% 87.22/87.43 (~node21(c_e_h_1, c_l, s6, s7)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11553, 11546, 11547])).
% 87.22/87.43 tff(11555,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11556,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11557,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11556, 11555])).
% 87.22/87.43 tff(11558,plain,
% 87.22/87.43 (node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11557, 81, 1552])).
% 87.22/87.43 tff(11559,plain,
% 87.22/87.43 (node22(c_e_h_1, c_l, s6, s7)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11558, 11554])).
% 87.22/87.43 tff(11560,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node22(c_e_h_1, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node22(c_e_h_1, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11561,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node22(c_e_h_1, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11562,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node22(c_e_h_1, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11561, 11560])).
% 87.22/87.43 tff(11563,plain,
% 87.22/87.43 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11562, 107, 11559, 11546, 10893])).
% 87.22/87.43 tff(11564,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6) | node20(c_e_h_1, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11565,plain,
% 87.22/87.43 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11564, 11545])).
% 87.22/87.43 tff(11566,plain,
% 87.22/87.43 (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11565, 10891])).
% 87.22/87.43 tff(11567,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s7)), introduced(assumption)).
% 87.22/87.43 tff(11568,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s7)), introduced(assumption)).
% 87.22/87.43 tff(11569,plain,
% 87.22/87.43 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11570,plain,
% 87.22/87.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11571,plain,
% 87.22/87.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11570, 11569])).
% 87.22/87.43 tff(11572,plain,
% 87.22/87.43 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11571, 801, 11568, 11567])).
% 87.22/87.43 tff(11573,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11574,plain,
% 87.22/87.43 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11573, 11566])).
% 87.22/87.43 tff(11575,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)), introduced(assumption)).
% 87.22/87.43 tff(11576,assumption,(node5(c_e_h_1, c_j, s7, s8)), introduced(assumption)).
% 87.22/87.43 tff(11577,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11578,plain,
% 87.22/87.43 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11579,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8))))),
% 87.22/87.43 inference(monotonicity,[status(thm)],[11578])).
% 87.22/87.43 tff(11580,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)))),
% 87.22/87.43 inference(transitivity,[status(thm)],[11579, 11577])).
% 87.22/87.43 tff(11581,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11582,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8))),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11581, 11580])).
% 87.22/87.43 tff(11583,plain,
% 87.22/87.43 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11582, 862, 11524, 11576, 11575, 11537])).
% 87.22/87.43 tff(11584,plain,((~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11585,plain,
% 87.22/87.43 ((~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11584, 11574])).
% 87.22/87.43 tff(11586,plain,
% 87.22/87.43 (~node5(c_e_h_1, c_j, s7, s8)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11585, 11524, 11537])).
% 87.22/87.43 tff(11587,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11588,plain,
% 87.22/87.43 ((node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8) | (~trans(s7, s8))) <=> ((~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11589,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8)))),
% 87.22/87.43 inference(monotonicity,[status(thm)],[11588])).
% 87.22/87.43 tff(11590,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8))),
% 87.22/87.43 inference(transitivity,[status(thm)],[11589, 11587])).
% 87.22/87.43 tff(11591,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8) | (~trans(s7, s8)))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11592,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11591, 11590])).
% 87.22/87.43 tff(11593,plain,
% 87.22/87.43 (node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11592, 881, 2152])).
% 87.22/87.43 tff(11594,plain,
% 87.22/87.43 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11593, 11586, 11536])).
% 87.22/87.43 tff(11595,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11596,plain,
% 87.22/87.43 (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11595, 11523])).
% 87.22/87.43 tff(11597,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s8)), introduced(assumption)).
% 87.22/87.43 tff(11598,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s8)), introduced(assumption)).
% 87.22/87.43 tff(11599,plain,
% 87.22/87.43 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11600,plain,
% 87.22/87.43 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11601,plain,
% 87.22/87.43 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11600, 11599])).
% 87.22/87.43 tff(11602,plain,
% 87.22/87.43 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11601, 309, 11598, 11597])).
% 87.22/87.43 tff(11603,plain,((~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11604,plain,
% 87.22/87.43 (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11603, 11596])).
% 87.22/87.43 tff(11605,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s9)), introduced(assumption)).
% 87.22/87.43 tff(11606,assumption,(node18(c_e_h_1, c_h, s8, s9)), introduced(assumption)).
% 87.22/87.43 tff(11607,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s8)), introduced(assumption)).
% 87.22/87.43 tff(11608,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~node18(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~node18(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11609,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~node18(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11610,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~node18(c_e_h_1, c_h, s8, s9))),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11609, 11608])).
% 87.22/87.43 tff(11611,plain,
% 87.22/87.43 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11610, 124, 11605, 11607, 11606])).
% 87.22/87.43 tff(11612,plain,((~node18(c_e_h_1, c_h, s8, s9)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11613,plain,
% 87.22/87.43 (~node18(c_e_h_1, c_h, s8, s9)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11612, 11605, 11003])).
% 87.22/87.43 tff(11614,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s8)), introduced(assumption)).
% 87.22/87.43 tff(11615,plain,
% 87.22/87.43 (~node18(c_e_h_1, c_h, s8, s9)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11612, 11605, 11607])).
% 87.22/87.43 tff(11616,assumption,(~node19(c_e_h_1, c_h, s8, s9)), introduced(assumption)).
% 87.22/87.43 tff(11617,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_h, s8, s9))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11618,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_h, s8, s9))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11619,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_h, s8, s9)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11618, 11617])).
% 87.22/87.43 tff(11620,plain,
% 87.22/87.43 ($false),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11619, 141, 2636, 11616])).
% 87.22/87.43 tff(11621,plain,(node19(c_e_h_1, c_h, s8, s9)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.43 tff(11622,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11623,plain,
% 87.22/87.43 ((node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9))) <=> (node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11624,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.43 inference(monotonicity,[status(thm)],[11623])).
% 87.22/87.43 tff(11625,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9))),
% 87.22/87.43 inference(transitivity,[status(thm)],[11624, 11622])).
% 87.22/87.43 tff(11626,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11627,plain,
% 87.22/87.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11626, 11625])).
% 87.22/87.43 tff(11628,plain,
% 87.22/87.43 (node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11627, 156, 11621])).
% 87.22/87.43 tff(11629,plain,
% 87.22/87.43 (node17(c_e_h_1, c_h, s8)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11628, 11615])).
% 87.22/87.43 tff(11630,assumption,(~node15(c_e_h_1, c_h, s8, s9)), introduced(assumption)).
% 87.22/87.43 tff(11631,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s8)), introduced(assumption)).
% 87.22/87.43 tff(11632,plain,
% 87.22/87.43 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))),
% 87.22/87.43 inference(rewrite,[status(thm)],[])).
% 87.22/87.43 tff(11633,plain,
% 87.22/87.43 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))),
% 87.22/87.43 inference(quant_inst,[status(thm)],[])).
% 87.22/87.43 tff(11634,plain,
% 87.22/87.43 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s8)),
% 87.22/87.43 inference(modus_ponens,[status(thm)],[11633, 11632])).
% 87.22/87.43 tff(11635,plain,
% 87.22/87.43 ((~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11634, 228, 11631])).
% 87.22/87.43 tff(11636,plain,
% 87.22/87.43 (~node16(c_e_h_1, c_h, s8)),
% 87.22/87.43 inference(unit_resolution,[status(thm)],[11635, 11614])).
% 87.22/87.43 tff(11637,plain,
% 87.22/87.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)) | node15(c_e_h_1, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)) | node15(c_e_h_1, c_h, s8, s9))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11638,plain,
% 87.22/87.44 ((node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9))) <=> (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)) | node15(c_e_h_1, c_h, s8, s9))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11639,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)) | node15(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.44 inference(monotonicity,[status(thm)],[11638])).
% 87.22/87.44 tff(11640,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)) | node15(c_e_h_1, c_h, s8, s9))),
% 87.22/87.44 inference(transitivity,[status(thm)],[11639, 11637])).
% 87.22/87.44 tff(11641,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11642,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)) | node15(c_e_h_1, c_h, s8, s9)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11641, 11640])).
% 87.22/87.44 tff(11643,plain,
% 87.22/87.44 (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11642, 189, 11621])).
% 87.22/87.44 tff(11644,plain,
% 87.22/87.44 (node14(c_e_h_1, c_h, s8, s9)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11643, 11636, 11630])).
% 87.22/87.44 tff(11645,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11646,plain,
% 87.22/87.44 (((~node14(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11647,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9))))),
% 87.22/87.44 inference(monotonicity,[status(thm)],[11646])).
% 87.22/87.44 tff(11648,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9)))),
% 87.22/87.44 inference(transitivity,[status(thm)],[11647, 11645])).
% 87.22/87.44 tff(11649,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11650,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9))),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11649, 11648])).
% 87.22/87.44 tff(11651,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11650, 283, 11605, 11614, 11644])).
% 87.22/87.44 tff(11652,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | node15(c_e_h_1, c_h, s8, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11653,plain,
% 87.22/87.44 (m_c_h_element_v_in2(c_e_h_1, c_h, s8)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11652, 11614, 11630, 11605])).
% 87.22/87.44 tff(11654,assumption,(node17(c_e_h_1, c_h, s8)), introduced(assumption)).
% 87.22/87.44 tff(11655,plain,
% 87.22/87.44 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11656,plain,
% 87.22/87.44 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11657,plain,
% 87.22/87.44 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8))),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11656, 11655])).
% 87.22/87.44 tff(11658,plain,
% 87.22/87.44 (m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8))),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11657, 245, 11654])).
% 87.22/87.44 tff(11659,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11658, 11653, 11614])).
% 87.22/87.44 tff(11660,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8)) | node15(c_e_h_1, c_h, s8, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11661,plain,
% 87.22/87.44 (node15(c_e_h_1, c_h, s8, s9)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11660, 11629, 11605, 11614])).
% 87.22/87.44 tff(11662,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11663,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11664,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11663, 11662])).
% 87.22/87.44 tff(11665,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11664, 173, 11605, 11607, 11661])).
% 87.22/87.44 tff(11666,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | m_c_h_element_v_in1(c_e_h_1, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11667,plain,
% 87.22/87.44 (m_c_h_element_v_in1(c_e_h_1, c_h, s8)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11666, 11605, 11003])).
% 87.22/87.44 tff(11668,plain,
% 87.22/87.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11669,plain,
% 87.22/87.44 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11670,plain,
% 87.22/87.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8)))),
% 87.22/87.44 inference(monotonicity,[status(thm)],[11669])).
% 87.22/87.44 tff(11671,plain,
% 87.22/87.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))),
% 87.22/87.44 inference(transitivity,[status(thm)],[11670, 11668])).
% 87.22/87.44 tff(11672,plain,
% 87.22/87.44 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8)))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11673,plain,
% 87.22/87.44 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11672, 11671])).
% 87.22/87.44 tff(11674,plain,
% 87.22/87.44 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8))),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11673, 209, 11631])).
% 87.22/87.44 tff(11675,plain,
% 87.22/87.44 (~node17(c_e_h_1, c_h, s8)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11674, 11667])).
% 87.22/87.44 tff(11676,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11628, 11675, 11613])).
% 87.22/87.44 tff(11677,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11678,plain,
% 87.22/87.44 (~m_c_h_element_v_out(c_e_h_1, c_h, s9)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11677, 11604])).
% 87.22/87.44 tff(11679,plain,
% 87.22/87.44 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11680,plain,
% 87.22/87.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11681,plain,
% 87.22/87.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s9)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11680, 11679])).
% 87.22/87.44 tff(11682,plain,
% 87.22/87.44 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11681, 23, 11678])).
% 87.22/87.44 tff(11683,plain,
% 87.22/87.44 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s9))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11684,plain,
% 87.22/87.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s9))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11685,plain,
% 87.22/87.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s9)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11684, 11683])).
% 87.22/87.44 tff(11686,plain,
% 87.22/87.44 (~node20(c_e_h_1, c_i, s9)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11685, 37, 11682])).
% 87.22/87.44 tff(11687,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s9)), introduced(assumption)).
% 87.22/87.44 tff(11688,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s10)), introduced(assumption)).
% 87.22/87.44 tff(11689,assumption,(node22(c_e_h_1, c_i, s9, s10)), introduced(assumption)).
% 87.22/87.44 tff(11690,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node22(c_e_h_1, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node22(c_e_h_1, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11691,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node22(c_e_h_1, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11692,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node22(c_e_h_1, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11691, 11690])).
% 87.22/87.44 tff(11693,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11692, 107, 11688, 11687, 11689])).
% 87.22/87.44 tff(11694,plain,((~node22(c_e_h_1, c_i, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11695,plain,
% 87.22/87.44 (~node22(c_e_h_1, c_i, s9, s10)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11694, 11688, 11687])).
% 87.22/87.44 tff(11696,assumption,(~node20(c_e_h_1, c_i, s9)), introduced(assumption)).
% 87.22/87.44 tff(11697,assumption,(node21(c_e_h_1, c_i, s9, s10)), introduced(assumption)).
% 87.22/87.44 tff(11698,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node21(c_e_h_1, c_i, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node21(c_e_h_1, c_i, s9, s10)))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11699,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node21(c_e_h_1, c_i, s9, s10)))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11700,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node21(c_e_h_1, c_i, s9, s10))),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11699, 11698])).
% 87.22/87.44 tff(11701,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11700, 51, 11688, 11696, 11697])).
% 87.22/87.44 tff(11702,plain,((~node21(c_e_h_1, c_i, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | node20(c_e_h_1, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11703,plain,
% 87.22/87.44 (~node21(c_e_h_1, c_i, s9, s10)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11702, 11688, 11696])).
% 87.22/87.44 tff(11704,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11705,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11706,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11705, 11704])).
% 87.22/87.44 tff(11707,plain,
% 87.22/87.44 (node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11706, 81, 3175])).
% 87.22/87.44 tff(11708,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11707, 11703, 11695])).
% 87.22/87.44 tff(11709,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | node20(c_e_h_1, c_i, s9) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11710,plain,
% 87.22/87.44 (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11709, 11686, 11029])).
% 87.22/87.44 tff(11711,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s10)), introduced(assumption)).
% 87.22/87.44 tff(11712,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s10)), introduced(assumption)).
% 87.22/87.44 tff(11713,plain,
% 87.22/87.44 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11714,plain,
% 87.22/87.44 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11715,plain,
% 87.22/87.44 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11714, 11713])).
% 87.22/87.44 tff(11716,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11715, 365, 11712, 11711])).
% 87.22/87.44 tff(11717,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11718,plain,
% 87.22/87.44 (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11717, 11710])).
% 87.22/87.44 tff(11719,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s11)), introduced(assumption)).
% 87.22/87.44 tff(11720,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s10)), introduced(assumption)).
% 87.22/87.44 tff(11721,assumption,(node15(c_e_h_1, c_e, s10, s11)), introduced(assumption)).
% 87.22/87.44 tff(11722,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11723,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11724,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11723, 11722])).
% 87.22/87.44 tff(11725,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11724, 173, 11719, 11721, 11126])).
% 87.22/87.44 tff(11726,plain,((~node15(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11727,plain,
% 87.22/87.44 (~node15(c_e_h_1, c_e, s10, s11)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11726, 11719, 11126])).
% 87.22/87.44 tff(11728,assumption,(node18(c_e_h_1, c_e, s10, s11)), introduced(assumption)).
% 87.22/87.44 tff(11729,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node18(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node18(c_e_h_1, c_e, s10, s11)))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11730,plain,
% 87.22/87.44 (((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~node18(c_e_h_1, c_e, s10, s11))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node18(c_e_h_1, c_e, s10, s11)))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11731,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~node18(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node18(c_e_h_1, c_e, s10, s11))))),
% 87.22/87.44 inference(monotonicity,[status(thm)],[11730])).
% 87.22/87.44 tff(11732,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~node18(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node18(c_e_h_1, c_e, s10, s11)))),
% 87.22/87.44 inference(transitivity,[status(thm)],[11731, 11729])).
% 87.22/87.44 tff(11733,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~node18(c_e_h_1, c_e, s10, s11)))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11734,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node18(c_e_h_1, c_e, s10, s11))),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11733, 11732])).
% 87.22/87.44 tff(11735,plain,
% 87.22/87.44 ($false),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11734, 124, 11719, 11728, 11126])).
% 87.22/87.44 tff(11736,plain,((~node18(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.44 tff(11737,plain,
% 87.22/87.44 (~node18(c_e_h_1, c_e, s10, s11)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11736, 11719, 11126])).
% 87.22/87.44 tff(11738,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_e, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_e, s10, s11))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11739,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_e, s10, s11))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11740,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_e, s10, s11)),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11739, 11738])).
% 87.22/87.44 tff(11741,plain,
% 87.22/87.44 (node19(c_e_h_1, c_e, s10, s11)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11740, 141, 3778])).
% 87.22/87.44 tff(11742,plain,
% 87.22/87.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))),
% 87.22/87.44 inference(rewrite,[status(thm)],[])).
% 87.22/87.44 tff(11743,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))),
% 87.22/87.44 inference(quant_inst,[status(thm)],[])).
% 87.22/87.44 tff(11744,plain,
% 87.22/87.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11))),
% 87.22/87.44 inference(modus_ponens,[status(thm)],[11743, 11742])).
% 87.22/87.44 tff(11745,plain,
% 87.22/87.44 (node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11744, 156, 11741])).
% 87.22/87.44 tff(11746,plain,
% 87.22/87.44 (node17(c_e_h_1, c_e, s10)),
% 87.22/87.44 inference(unit_resolution,[status(thm)],[11745, 11737])).
% 87.22/87.44 tff(11747,assumption,(node17(c_e_h_1, c_e, s10)), introduced(assumption)).
% 87.22/87.44 tff(11748,plain,
% 87.22/87.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~node17(c_e_h_1, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~node17(c_e_h_1, c_e, s10)))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11749,plain,
% 87.22/87.45 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~node17(c_e_h_1, c_e, s10)))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11750,plain,
% 87.22/87.45 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~node17(c_e_h_1, c_e, s10))),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11749, 11748])).
% 87.22/87.45 tff(11751,plain,
% 87.22/87.45 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11750, 209, 11747])).
% 87.22/87.45 tff(11752,plain,
% 87.22/87.45 (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11751, 11720])).
% 87.22/87.45 tff(11753,assumption,(~node15(c_e_h_1, c_e, s10, s11)), introduced(assumption)).
% 87.22/87.45 tff(11754,plain,
% 87.22/87.45 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s10))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11755,plain,
% 87.22/87.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s10))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11756,plain,
% 87.22/87.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11755, 11754])).
% 87.22/87.45 tff(11757,plain,
% 87.22/87.45 (~node16(c_e_h_1, c_e, s10)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11756, 228, 11752, 11720])).
% 87.22/87.45 tff(11758,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node15(c_e_h_1, c_e, s10, s11) | node16(c_e_h_1, c_e, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node15(c_e_h_1, c_e, s10, s11) | node16(c_e_h_1, c_e, s10))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11759,plain,
% 87.22/87.45 ((node16(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11))) <=> (node14(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node15(c_e_h_1, c_e, s10, s11) | node16(c_e_h_1, c_e, s10))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11760,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node15(c_e_h_1, c_e, s10, s11) | node16(c_e_h_1, c_e, s10)))),
% 87.22/87.45 inference(monotonicity,[status(thm)],[11759])).
% 87.22/87.45 tff(11761,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node15(c_e_h_1, c_e, s10, s11) | node16(c_e_h_1, c_e, s10))),
% 87.22/87.45 inference(transitivity,[status(thm)],[11760, 11758])).
% 87.22/87.45 tff(11762,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11763,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node15(c_e_h_1, c_e, s10, s11) | node16(c_e_h_1, c_e, s10)),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11762, 11761])).
% 87.22/87.45 tff(11764,plain,
% 87.22/87.45 (node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | node16(c_e_h_1, c_e, s10)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11763, 189, 11741])).
% 87.22/87.45 tff(11765,plain,
% 87.22/87.45 (node14(c_e_h_1, c_e, s10, s11)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11764, 11757, 11753])).
% 87.22/87.45 tff(11766,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11767,plain,
% 87.22/87.45 (((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11768,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11))))),
% 87.22/87.45 inference(monotonicity,[status(thm)],[11767])).
% 87.22/87.45 tff(11769,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))),
% 87.22/87.45 inference(transitivity,[status(thm)],[11768, 11766])).
% 87.22/87.45 tff(11770,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11771,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11770, 11769])).
% 87.22/87.45 tff(11772,plain,
% 87.22/87.45 ($false),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11771, 283, 11719, 11765, 11752])).
% 87.22/87.45 tff(11773,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | node15(c_e_h_1, c_e, s10, s11) | (~node17(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.45 tff(11774,plain,
% 87.22/87.45 ($false),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11773, 11746, 11727, 11720, 11719])).
% 87.22/87.45 tff(11775,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.45 tff(11776,plain,
% 87.22/87.45 (~m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11775, 11718, 11241])).
% 87.22/87.45 tff(11777,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)), introduced(assumption)).
% 87.22/87.45 tff(11778,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s11)), introduced(assumption)).
% 87.22/87.45 tff(11779,plain,
% 87.22/87.45 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11780,plain,
% 87.22/87.45 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11781,plain,
% 87.22/87.45 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11780, 11779])).
% 87.22/87.45 tff(11782,plain,
% 87.22/87.45 ($false),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11781, 976, 11778, 11777])).
% 87.22/87.45 tff(11783,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.45 tff(11784,plain,
% 87.22/87.45 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11783, 11776])).
% 87.22/87.45 tff(11785,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)), introduced(assumption)).
% 87.22/87.45 tff(11786,plain,
% 87.22/87.45 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11180, 1048, 11785])).
% 87.22/87.45 tff(11787,plain,
% 87.22/87.45 (~node9(c_e_h_1, c_m, s11)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11184, 1062, 11786])).
% 87.22/87.45 tff(11788,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), introduced(assumption)).
% 87.22/87.45 tff(11789,plain,
% 87.22/87.45 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11790,plain,
% 87.22/87.45 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11791,plain,
% 87.22/87.45 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11790, 11789])).
% 87.22/87.45 tff(11792,plain,
% 87.22/87.45 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11791, 1142, 11187])).
% 87.22/87.45 tff(11793,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)), introduced(assumption)).
% 87.22/87.45 tff(11794,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)), introduced(assumption)).
% 87.22/87.45 tff(11795,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)), introduced(assumption)).
% 87.22/87.45 tff(11796,assumption,(node10(c_e_h_1, c_n, s11, s12)), introduced(assumption)).
% 87.22/87.45 tff(11797,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11798,plain,
% 87.22/87.45 (((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11799,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11))))),
% 87.22/87.45 inference(monotonicity,[status(thm)],[11798])).
% 87.22/87.45 tff(11800,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)))),
% 87.22/87.45 inference(transitivity,[status(thm)],[11799, 11797])).
% 87.22/87.45 tff(11801,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11802,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11))),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11801, 11800])).
% 87.22/87.45 tff(11803,plain,
% 87.22/87.45 ($false),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11802, 1191, 11795, 11796, 11793, 11794])).
% 87.22/87.45 tff(11804,plain,((~node10(c_e_h_1, c_n, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.45 tff(11805,plain,
% 87.22/87.45 (~node10(c_e_h_1, c_n, s11, s12)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11804, 11795, 11794, 11793])).
% 87.22/87.45 tff(11806,assumption,(node11(c_e_h_1, c_n, s11, s12)), introduced(assumption)).
% 87.22/87.45 tff(11807,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12)))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11808,plain,
% 87.22/87.45 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12)))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11809,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12))))),
% 87.22/87.45 inference(monotonicity,[status(thm)],[11808])).
% 87.22/87.45 tff(11810,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12)))),
% 87.22/87.45 inference(transitivity,[status(thm)],[11809, 11807])).
% 87.22/87.45 tff(11811,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11812,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12))),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11811, 11810])).
% 87.22/87.45 tff(11813,plain,
% 87.22/87.45 ($false),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11812, 1161, 11785, 11795, 11806])).
% 87.22/87.45 tff(11814,plain,((~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.45 tff(11815,plain,
% 87.22/87.45 (~node11(c_e_h_1, c_n, s11, s12)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11814, 11795, 11785])).
% 87.22/87.45 tff(11816,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11817,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11818,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12)),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11817, 11816])).
% 87.22/87.45 tff(11819,plain,
% 87.22/87.45 (node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11818, 1092, 4461])).
% 87.22/87.45 tff(11820,plain,
% 87.22/87.45 ($false),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11819, 11815, 11805])).
% 87.22/87.45 tff(11821,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.45 tff(11822,plain,
% 87.22/87.45 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11821, 11785, 11793, 11792])).
% 87.22/87.45 tff(11823,plain,
% 87.22/87.45 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11824,plain,
% 87.22/87.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11825,plain,
% 87.22/87.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11824, 11823])).
% 87.22/87.45 tff(11826,plain,
% 87.22/87.45 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11825, 1048, 11822])).
% 87.22/87.45 tff(11827,plain,
% 87.22/87.45 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11828,plain,
% 87.22/87.45 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11829,plain,
% 87.22/87.45 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11828, 11827])).
% 87.22/87.45 tff(11830,plain,
% 87.22/87.45 (~node9(c_e_h_1, c_m, s12)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11829, 1062, 11826])).
% 87.22/87.45 tff(11831,assumption,(~node9(c_e_h_1, c_m, s12)), introduced(assumption)).
% 87.22/87.45 tff(11832,assumption,(node10(c_e_h_1, c_m, s12, s13)), introduced(assumption)).
% 87.22/87.45 tff(11833,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | node9(c_e_h_1, c_m, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | node9(c_e_h_1, c_m, s12))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11834,plain,
% 87.22/87.45 ((node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node10(c_e_h_1, c_m, s12, s13))) <=> ((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | node9(c_e_h_1, c_m, s12))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11835,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node10(c_e_h_1, c_m, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | node9(c_e_h_1, c_m, s12)))),
% 87.22/87.45 inference(monotonicity,[status(thm)],[11834])).
% 87.22/87.45 tff(11836,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node10(c_e_h_1, c_m, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | node9(c_e_h_1, c_m, s12))),
% 87.22/87.45 inference(transitivity,[status(thm)],[11835, 11833])).
% 87.22/87.45 tff(11837,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node10(c_e_h_1, c_m, s12, s13)))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11838,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | node9(c_e_h_1, c_m, s12)),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11837, 11836])).
% 87.22/87.45 tff(11839,plain,
% 87.22/87.45 ($false),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11838, 1076, 11788, 11832, 11831])).
% 87.22/87.45 tff(11840,plain,((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | node9(c_e_h_1, c_m, s12)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.45 tff(11841,plain,
% 87.22/87.45 (~node10(c_e_h_1, c_m, s12, s13)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11840, 11830, 11788])).
% 87.22/87.45 tff(11842,plain,
% 87.22/87.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13))),
% 87.22/87.45 inference(rewrite,[status(thm)],[])).
% 87.22/87.45 tff(11843,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13))),
% 87.22/87.45 inference(quant_inst,[status(thm)],[])).
% 87.22/87.45 tff(11844,plain,
% 87.22/87.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13)),
% 87.22/87.45 inference(modus_ponens,[status(thm)],[11843, 11842])).
% 87.22/87.45 tff(11845,plain,
% 87.22/87.45 (node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13)),
% 87.22/87.45 inference(unit_resolution,[status(thm)],[11844, 1092, 9599])).
% 87.22/87.45 tff(11846,plain,
% 87.22/87.45 (node11(c_e_h_1, c_m, s12, s13)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11845, 11841])).
% 87.22/87.46 tff(11847,assumption,(node11(c_e_h_1, c_m, s12, s13)), introduced(assumption)).
% 87.22/87.46 tff(11848,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)), introduced(assumption)).
% 87.22/87.46 tff(11849,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11850,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11851,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11850, 11849])).
% 87.22/87.46 tff(11852,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11851, 1130, 11788, 11848, 11847])).
% 87.22/87.46 tff(11853,plain,((~node11(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11854,plain,
% 87.22/87.46 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11853, 11846, 11788])).
% 87.22/87.46 tff(11855,plain,
% 87.22/87.46 (~node11(c_e_h_1, c_m, s11, s12)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11194, 11854, 11187])).
% 87.22/87.46 tff(11856,plain,
% 87.22/87.46 (node10(c_e_h_1, c_m, s11, s12)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11199, 11855])).
% 87.22/87.46 tff(11857,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11206, 1076, 11854, 11856, 11787])).
% 87.22/87.46 tff(11858,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11859,plain,
% 87.22/87.46 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11858, 8378])).
% 87.22/87.46 tff(11860,plain,
% 87.22/87.46 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11859, 11784, 11177])).
% 87.22/87.46 tff(11861,plain,
% 87.22/87.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11862,plain,
% 87.22/87.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11863,plain,
% 87.22/87.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11862, 11861])).
% 87.22/87.46 tff(11864,plain,
% 87.22/87.46 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11863, 1521])).
% 87.22/87.46 tff(11865,plain,
% 87.22/87.46 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11864, 11860])).
% 87.22/87.46 tff(11866,plain,
% 87.22/87.46 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11867,plain,
% 87.22/87.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11868,plain,
% 87.22/87.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11867, 11866])).
% 87.22/87.46 tff(11869,plain,
% 87.22/87.46 (~node20(c_e_h_1, c_r, s13)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11868, 1535, 11865])).
% 87.22/87.46 tff(11870,assumption,(~node20(c_e_h_1, c_r, s13)), introduced(assumption)).
% 87.22/87.46 tff(11871,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s14)), introduced(assumption)).
% 87.22/87.46 tff(11872,assumption,(node21(c_e_h_1, c_r, s13, s14)), introduced(assumption)).
% 87.22/87.46 tff(11873,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14)))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11874,plain,
% 87.22/87.46 ((node20(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node21(c_e_h_1, c_r, s13, s14))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14)))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11875,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node21(c_e_h_1, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14))))),
% 87.22/87.46 inference(monotonicity,[status(thm)],[11874])).
% 87.22/87.46 tff(11876,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node21(c_e_h_1, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14)))),
% 87.22/87.46 inference(transitivity,[status(thm)],[11875, 11873])).
% 87.22/87.46 tff(11877,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node21(c_e_h_1, c_r, s13, s14)))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11878,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14))),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11877, 11876])).
% 87.22/87.46 tff(11879,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11878, 51, 11871, 11872, 11870])).
% 87.22/87.46 tff(11880,plain,((~node21(c_e_h_1, c_r, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11881,plain,
% 87.22/87.46 (~node21(c_e_h_1, c_r, s13, s14)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11880, 11871, 11870])).
% 87.22/87.46 tff(11882,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11883,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11884,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11883, 11882])).
% 87.22/87.46 tff(11885,plain,
% 87.22/87.46 (node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11884, 81, 10040])).
% 87.22/87.46 tff(11886,plain,
% 87.22/87.46 (node22(c_e_h_1, c_r, s13, s14)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11885, 11881])).
% 87.22/87.46 tff(11887,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s13)), introduced(assumption)).
% 87.22/87.46 tff(11888,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11889,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11890,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11889, 11888])).
% 87.22/87.46 tff(11891,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11890, 107, 11887, 11871, 11886])).
% 87.22/87.46 tff(11892,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13) | node20(c_e_h_1, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11893,plain,
% 87.22/87.46 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11892, 11869])).
% 87.22/87.46 tff(11894,plain,
% 87.22/87.46 (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11893, 11239])).
% 87.22/87.46 tff(11895,plain,
% 87.22/87.46 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11131, 11241])).
% 87.22/87.46 tff(11896,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)), introduced(assumption)).
% 87.22/87.46 tff(11897,plain,
% 87.22/87.46 (~m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[7495, 309, 10586])).
% 87.22/87.46 tff(11898,plain,
% 87.22/87.46 (~m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[7620, 11897])).
% 87.22/87.46 tff(11899,plain,
% 87.22/87.46 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[7624, 23, 11898])).
% 87.22/87.46 tff(11900,plain,
% 87.22/87.46 (~node20(c_e_h_3, c_i, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[7628, 37, 11899])).
% 87.22/87.46 tff(11901,plain,
% 87.22/87.46 (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[7722, 11900])).
% 87.22/87.46 tff(11902,plain,
% 87.22/87.46 (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[7726, 2218, 11901])).
% 87.22/87.46 tff(11903,plain,
% 87.22/87.46 (~m_c_h_element_v_out(c_e_h_3, c_f, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[7997, 11902])).
% 87.22/87.46 tff(11904,plain,
% 87.22/87.46 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11248, 11903])).
% 87.22/87.46 tff(11905,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)), introduced(assumption)).
% 87.22/87.46 tff(11906,plain,
% 87.22/87.46 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11405, 11391, 11378])).
% 87.22/87.46 tff(11907,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)), introduced(assumption)).
% 87.22/87.46 tff(11908,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)), introduced(assumption)).
% 87.22/87.46 tff(11909,assumption,(node11(c_e_h_3, c_m, s5, s6)), introduced(assumption)).
% 87.22/87.46 tff(11910,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11911,plain,
% 87.22/87.46 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11912,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6))))),
% 87.22/87.46 inference(monotonicity,[status(thm)],[11911])).
% 87.22/87.46 tff(11913,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)))),
% 87.22/87.46 inference(transitivity,[status(thm)],[11912, 11910])).
% 87.22/87.46 tff(11914,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11915,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6))),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11914, 11913])).
% 87.22/87.46 tff(11916,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11915, 1161, 11908, 11909, 11896])).
% 87.22/87.46 tff(11917,plain,((~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11918,plain,
% 87.22/87.46 (~node11(c_e_h_3, c_m, s5, s6)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11917, 11896, 11908])).
% 87.22/87.46 tff(11919,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11920,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11921,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11920, 11919])).
% 87.22/87.46 tff(11922,plain,
% 87.22/87.46 (node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11921, 1092, 1499])).
% 87.22/87.46 tff(11923,plain,
% 87.22/87.46 (node10(c_e_h_3, c_m, s5, s6)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11922, 11918])).
% 87.22/87.46 tff(11924,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~node10(c_e_h_3, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~node10(c_e_h_3, c_m, s5, s6)))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11925,plain,
% 87.22/87.46 (((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~node10(c_e_h_3, c_m, s5, s6)))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11926,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~node10(c_e_h_3, c_m, s5, s6))))),
% 87.22/87.46 inference(monotonicity,[status(thm)],[11925])).
% 87.22/87.46 tff(11927,plain,
% 87.22/87.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~node10(c_e_h_3, c_m, s5, s6)))),
% 87.22/87.46 inference(transitivity,[status(thm)],[11926, 11924])).
% 87.22/87.46 tff(11928,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11929,plain,
% 87.22/87.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~node10(c_e_h_3, c_m, s5, s6))),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11928, 11927])).
% 87.22/87.46 tff(11930,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11929, 1191, 11923, 11896, 11905, 11907])).
% 87.22/87.46 tff(11931,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11932,plain,
% 87.22/87.46 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11931, 11906, 11905, 11896])).
% 87.22/87.46 tff(11933,plain,
% 87.22/87.46 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11421, 11391])).
% 87.22/87.46 tff(11934,plain,
% 87.22/87.46 (~node9(c_e_h_3, c_n, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11429, 11933])).
% 87.22/87.46 tff(11935,plain,
% 87.22/87.46 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11453, 11934])).
% 87.22/87.46 tff(11936,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)), introduced(assumption)).
% 87.22/87.46 tff(11937,plain,
% 87.22/87.46 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11938,plain,
% 87.22/87.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11939,plain,
% 87.22/87.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11938, 11937])).
% 87.22/87.46 tff(11940,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11939, 6378, 11457, 11936])).
% 87.22/87.46 tff(11941,plain,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11942,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11941, 11935, 11932])).
% 87.22/87.46 tff(11943,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11944,plain,
% 87.22/87.46 ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4))),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11943, 11333])).
% 87.22/87.46 tff(11945,plain,
% 87.22/87.46 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11944, 11904, 11896])).
% 87.22/87.46 tff(11946,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)), introduced(assumption)).
% 87.22/87.46 tff(11947,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s5)), introduced(assumption)).
% 87.22/87.46 tff(11948,plain,
% 87.22/87.46 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11949,plain,
% 87.22/87.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11950,plain,
% 87.22/87.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11949, 11948])).
% 87.22/87.46 tff(11951,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11950, 6389, 11947, 11946])).
% 87.22/87.46 tff(11952,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11953,plain,
% 87.22/87.46 (m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11952, 11945])).
% 87.22/87.46 tff(11954,plain,
% 87.22/87.46 (m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10811, 11953, 11903])).
% 87.22/87.46 tff(11955,plain,
% 87.22/87.46 (m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10746, 2218, 11954])).
% 87.22/87.46 tff(11956,plain,
% 87.22/87.46 (~node22(c_e_h_3, c_i, s3, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10532, 11955, 11901])).
% 87.22/87.46 tff(11957,plain,
% 87.22/87.46 (node21(c_e_h_3, c_i, s3, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10739, 11956])).
% 87.22/87.46 tff(11958,plain,
% 87.22/87.46 (node20(c_e_h_3, c_i, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10733, 11957, 11955])).
% 87.22/87.46 tff(11959,plain,
% 87.22/87.46 (m_and_h_gate_v_in1(c_e_h_3, c_i, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10725, 37, 11958])).
% 87.22/87.46 tff(11960,plain,
% 87.22/87.46 (m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10721, 23, 11959])).
% 87.22/87.46 tff(11961,plain,
% 87.22/87.46 (~node14(c_e_h_3, c_h, s2, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10679, 11960, 10543])).
% 87.22/87.46 tff(11962,plain,
% 87.22/87.46 (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10660, 10586, 10606])).
% 87.22/87.46 tff(11963,plain,
% 87.22/87.46 (~m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10664, 309, 11962])).
% 87.22/87.46 tff(11964,plain,
% 87.22/87.46 ((~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10668, 228, 10543])).
% 87.22/87.46 tff(11965,plain,
% 87.22/87.46 (~node16(c_e_h_3, c_h, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11964, 11963])).
% 87.22/87.46 tff(11966,plain,
% 87.22/87.46 (node15(c_e_h_3, c_h, s2, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10691, 11965, 11961])).
% 87.22/87.46 tff(11967,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10539, 173, 11898, 11960, 11966])).
% 87.22/87.46 tff(11968,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s1) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11969,plain,
% 87.22/87.46 (m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11968, 7492, 10585])).
% 87.22/87.46 tff(11970,plain,
% 87.22/87.46 (m_c_h_element_v_in1(c_e_h_3, c_h, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11969, 11896])).
% 87.22/87.46 tff(11971,plain,
% 87.22/87.46 (~node17(c_e_h_3, c_h, s2)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10701, 11970])).
% 87.22/87.46 tff(11972,plain,
% 87.22/87.46 (node18(c_e_h_3, c_h, s2, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10709, 11971])).
% 87.22/87.46 tff(11973,plain,
% 87.22/87.46 (~m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10716, 124, 7621, 11972])).
% 87.22/87.46 tff(11974,plain,
% 87.22/87.46 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10721, 23, 11973])).
% 87.22/87.46 tff(11975,plain,
% 87.22/87.46 ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11944, 11249])).
% 87.22/87.46 tff(11976,plain,
% 87.22/87.46 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11975, 11896])).
% 87.22/87.46 tff(11977,plain,
% 87.22/87.46 (m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11952, 11976])).
% 87.22/87.46 tff(11978,plain,
% 87.22/87.46 (m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10812, 11977])).
% 87.22/87.46 tff(11979,plain,
% 87.22/87.46 (m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10746, 2218, 11978])).
% 87.22/87.46 tff(11980,plain,
% 87.22/87.46 (~node22(c_e_h_3, c_i, s3, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10533, 11979])).
% 87.22/87.46 tff(11981,plain,
% 87.22/87.46 (node21(c_e_h_3, c_i, s3, s4)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10739, 11980])).
% 87.22/87.46 tff(11982,plain,
% 87.22/87.46 (node20(c_e_h_3, c_i, s3)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10733, 11981, 11979])).
% 87.22/87.46 tff(11983,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[10725, 37, 11982, 11974])).
% 87.22/87.46 tff(11984,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11985,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)), introduced(assumption)).
% 87.22/87.46 tff(11986,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)), introduced(assumption)).
% 87.22/87.46 tff(11987,plain,
% 87.22/87.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11988,plain,
% 87.22/87.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11989,plain,
% 87.22/87.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11988, 11987])).
% 87.22/87.46 tff(11990,plain,
% 87.22/87.46 ($false),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11989, 6442, 11986, 11985])).
% 87.22/87.46 tff(11991,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.46 tff(11992,plain,
% 87.22/87.46 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)),
% 87.22/87.46 inference(unit_resolution,[status(thm)],[11991, 11984])).
% 87.22/87.46 tff(11993,assumption,(node9(c_e_h_3, c_n, s6)), introduced(assumption)).
% 87.22/87.46 tff(11994,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)), introduced(assumption)).
% 87.22/87.46 tff(11995,plain,
% 87.22/87.46 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6))),
% 87.22/87.46 inference(rewrite,[status(thm)],[])).
% 87.22/87.46 tff(11996,plain,
% 87.22/87.46 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6))),
% 87.22/87.46 inference(quant_inst,[status(thm)],[])).
% 87.22/87.46 tff(11997,plain,
% 87.22/87.46 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)),
% 87.22/87.46 inference(modus_ponens,[status(thm)],[11996, 11995])).
% 87.22/87.46 tff(11998,plain,
% 87.22/87.46 ($false),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11997, 1062, 11994, 11993])).
% 87.22/87.47 tff(11999,plain,((~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.47 tff(12000,plain,
% 87.22/87.47 (~node9(c_e_h_3, c_n, s6)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11999, 11992])).
% 87.22/87.47 tff(12001,assumption,(~node9(c_e_h_3, c_n, s6)), introduced(assumption)).
% 87.22/87.47 tff(12002,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), introduced(assumption)).
% 87.22/87.47 tff(12003,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)), introduced(assumption)).
% 87.22/87.47 tff(12004,assumption,(node11(c_e_h_3, c_n, s6, s7)), introduced(assumption)).
% 87.22/87.47 tff(12005,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node11(c_e_h_3, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node11(c_e_h_3, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12006,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node11(c_e_h_3, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12007,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node11(c_e_h_3, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12006, 12005])).
% 87.22/87.47 tff(12008,plain,
% 87.22/87.47 ($false),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12007, 1130, 12003, 12002, 12004])).
% 87.22/87.47 tff(12009,plain,((~node11(c_e_h_3, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.47 tff(12010,plain,
% 87.22/87.47 (~node11(c_e_h_3, c_n, s6, s7)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12009, 12003, 12002])).
% 87.22/87.47 tff(12011,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12012,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12013,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12012, 12011])).
% 87.22/87.47 tff(12014,plain,
% 87.22/87.47 (node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12013, 1092, 1552])).
% 87.22/87.47 tff(12015,plain,
% 87.22/87.47 (node10(c_e_h_3, c_n, s6, s7)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12014, 12010])).
% 87.22/87.47 tff(12016,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7)))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12017,plain,
% 87.22/87.47 ((node9(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node10(c_e_h_3, c_n, s6, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7)))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12018,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node10(c_e_h_3, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7))))),
% 87.22/87.47 inference(monotonicity,[status(thm)],[12017])).
% 87.22/87.47 tff(12019,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node10(c_e_h_3, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7)))),
% 87.22/87.47 inference(transitivity,[status(thm)],[12018, 12016])).
% 87.22/87.47 tff(12020,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node10(c_e_h_3, c_n, s6, s7)))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12021,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7))),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12020, 12019])).
% 87.22/87.47 tff(12022,plain,
% 87.22/87.47 ($false),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12021, 1076, 12003, 12015, 12001])).
% 87.22/87.47 tff(12023,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.47 tff(12024,plain,
% 87.22/87.47 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12023, 11479])).
% 87.22/87.47 tff(12025,plain,
% 87.22/87.47 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12024, 12000])).
% 87.22/87.47 tff(12026,plain,
% 87.22/87.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12027,plain,
% 87.22/87.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12028,plain,
% 87.22/87.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12027, 12026])).
% 87.22/87.47 tff(12029,plain,
% 87.22/87.47 ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12028, 6513])).
% 87.22/87.47 tff(12030,plain,
% 87.22/87.47 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12029, 12025])).
% 87.22/87.47 tff(12031,plain,
% 87.22/87.47 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s7))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12032,plain,
% 87.22/87.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s7))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12033,plain,
% 87.22/87.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s7)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12032, 12031])).
% 87.22/87.47 tff(12034,plain,
% 87.22/87.47 (~node20(c_e_h_3, c_q, s7)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12033, 1535, 12030])).
% 87.22/87.47 tff(12035,assumption,(~node20(c_e_h_3, c_q, s7)), introduced(assumption)).
% 87.22/87.47 tff(12036,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s7)), introduced(assumption)).
% 87.22/87.47 tff(12037,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s8)), introduced(assumption)).
% 87.22/87.47 tff(12038,assumption,(node22(c_e_h_3, c_q, s7, s8)), introduced(assumption)).
% 87.22/87.47 tff(12039,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node22(c_e_h_3, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node22(c_e_h_3, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12040,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node22(c_e_h_3, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12041,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node22(c_e_h_3, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12040, 12039])).
% 87.22/87.47 tff(12042,plain,
% 87.22/87.47 ($false),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12041, 107, 12037, 12036, 12038])).
% 87.22/87.47 tff(12043,plain,((~node22(c_e_h_3, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.47 tff(12044,plain,
% 87.22/87.47 (~node22(c_e_h_3, c_q, s7, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12043, 12037, 12036])).
% 87.22/87.47 tff(12045,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12046,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12047,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12046, 12045])).
% 87.22/87.47 tff(12048,plain,
% 87.22/87.47 (node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12047, 81, 2152])).
% 87.22/87.47 tff(12049,plain,
% 87.22/87.47 (node21(c_e_h_3, c_q, s7, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12048, 12044])).
% 87.22/87.47 tff(12050,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7) | (~node21(c_e_h_3, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7) | (~node21(c_e_h_3, c_q, s7, s8)))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12051,plain,
% 87.22/87.47 ((node20(c_e_h_3, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node21(c_e_h_3, c_q, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7) | (~node21(c_e_h_3, c_q, s7, s8)))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12052,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node21(c_e_h_3, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7) | (~node21(c_e_h_3, c_q, s7, s8))))),
% 87.22/87.47 inference(monotonicity,[status(thm)],[12051])).
% 87.22/87.47 tff(12053,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node21(c_e_h_3, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7) | (~node21(c_e_h_3, c_q, s7, s8)))),
% 87.22/87.47 inference(transitivity,[status(thm)],[12052, 12050])).
% 87.22/87.47 tff(12054,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node21(c_e_h_3, c_q, s7, s8)))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12055,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7) | (~node21(c_e_h_3, c_q, s7, s8))),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12054, 12053])).
% 87.22/87.47 tff(12056,plain,
% 87.22/87.47 ($false),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12055, 51, 12037, 12049, 12035])).
% 87.22/87.47 tff(12057,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.47 tff(12058,plain,
% 87.22/87.47 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12057, 12034])).
% 87.22/87.47 tff(12059,plain,
% 87.22/87.47 (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12058, 11510])).
% 87.22/87.47 tff(12060,assumption,(~node3(c_e_h_3, c_e_h_1, s8)), introduced(assumption)).
% 87.22/87.47 tff(12061,plain,
% 87.22/87.47 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s8))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12062,plain,
% 87.22/87.47 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s8))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12063,plain,
% 87.22/87.47 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s8)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12062, 12061])).
% 87.22/87.47 tff(12064,plain,
% 87.22/87.47 ($false),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12063, 3860, 814, 12060])).
% 87.22/87.47 tff(12065,plain,(node3(c_e_h_3, c_e_h_1, s8)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.47 tff(12066,plain,
% 87.22/87.47 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12067,plain,
% 87.22/87.47 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12068,plain,
% 87.22/87.47 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12067, 12066])).
% 87.22/87.47 tff(12069,plain,
% 87.22/87.47 ((~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12068, 836])).
% 87.22/87.47 tff(12070,plain,
% 87.22/87.47 ((~m_cell_v_ack(c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12069, 12065])).
% 87.22/87.47 tff(12071,plain,
% 87.22/87.47 (~m_cell_v_ack(c_e_h_1, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12070, 12059])).
% 87.22/87.47 tff(12072,plain,
% 87.22/87.47 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)) | m_cell_v_ack(c_e_h_1, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)) | m_cell_v_ack(c_e_h_1, s8))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12073,plain,
% 87.22/87.47 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)) | m_cell_v_ack(c_e_h_1, s8))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12074,plain,
% 87.22/87.47 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)) | m_cell_v_ack(c_e_h_1, s8)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12073, 12072])).
% 87.22/87.47 tff(12075,plain,
% 87.22/87.47 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12074, 848, 12071])).
% 87.22/87.47 tff(12076,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)), introduced(assumption)).
% 87.22/87.47 tff(12077,plain,
% 87.22/87.47 (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11603, 11598])).
% 87.22/87.47 tff(12078,plain,
% 87.22/87.47 (~m_c_h_element_v_out(c_e_h_1, c_h, s9)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11677, 12077])).
% 87.22/87.47 tff(12079,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s12)), introduced(assumption)).
% 87.22/87.47 tff(12080,plain,
% 87.22/87.47 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11681, 23, 12078])).
% 87.22/87.47 tff(12081,plain,
% 87.22/87.47 (~node20(c_e_h_1, c_i, s9)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11685, 37, 12080])).
% 87.22/87.47 tff(12082,plain,
% 87.22/87.47 (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11709, 12081, 11029])).
% 87.22/87.47 tff(12083,plain,
% 87.22/87.47 (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11717, 11712])).
% 87.22/87.47 tff(12084,plain,
% 87.22/87.47 (~m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[11775, 12083, 11241])).
% 87.22/87.47 tff(12085,assumption,(~node20(c_e_h_1, c_i, s10)), introduced(assumption)).
% 87.22/87.47 tff(12086,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s11)), introduced(assumption)).
% 87.22/87.47 tff(12087,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12088,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12089,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12088, 12087])).
% 87.22/87.47 tff(12090,plain,
% 87.22/87.47 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12089, 107])).
% 87.22/87.47 tff(12091,plain,
% 87.22/87.47 (~node22(c_e_h_1, c_i, s10, s11)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12090, 12086, 11712])).
% 87.22/87.47 tff(12092,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12093,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12094,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12093, 12092])).
% 87.22/87.47 tff(12095,plain,
% 87.22/87.47 (node21(c_e_h_1, c_i, s10, s11)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12094, 81, 3778, 12091])).
% 87.22/87.47 tff(12096,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node21(c_e_h_1, c_i, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node21(c_e_h_1, c_i, s10, s11)))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12097,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node21(c_e_h_1, c_i, s10, s11)))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12098,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node21(c_e_h_1, c_i, s10, s11))),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12097, 12096])).
% 87.22/87.47 tff(12099,plain,
% 87.22/87.47 ($false),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12098, 51, 12085, 12086, 12095])).
% 87.22/87.47 tff(12100,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | node20(c_e_h_1, c_i, s10) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.47 tff(12101,plain,
% 87.22/87.47 (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12100, 11712, 12085])).
% 87.22/87.47 tff(12102,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s11)), introduced(assumption)).
% 87.22/87.47 tff(12103,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s11)), introduced(assumption)).
% 87.22/87.47 tff(12104,plain,
% 87.22/87.47 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12105,plain,
% 87.22/87.47 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 87.22/87.47 inference(quant_inst,[status(thm)],[])).
% 87.22/87.47 tff(12106,plain,
% 87.22/87.47 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 87.22/87.47 inference(modus_ponens,[status(thm)],[12105, 12104])).
% 87.22/87.47 tff(12107,plain,
% 87.22/87.47 ($false),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12106, 365, 12103, 12102])).
% 87.22/87.47 tff(12108,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.47 tff(12109,plain,
% 87.22/87.47 (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 87.22/87.47 inference(unit_resolution,[status(thm)],[12108, 12101])).
% 87.22/87.47 tff(12110,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s11)), introduced(assumption)).
% 87.22/87.47 tff(12111,assumption,(node15(c_e_h_1, c_e, s11, s12)), introduced(assumption)).
% 87.22/87.47 tff(12112,plain,
% 87.22/87.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 87.22/87.47 inference(rewrite,[status(thm)],[])).
% 87.22/87.47 tff(12113,plain,
% 87.22/87.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12114,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12113, 12112])).
% 87.22/87.48 tff(12115,plain,
% 87.22/87.48 ($false),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12114, 173, 12079, 11778, 12111])).
% 87.22/87.48 tff(12116,plain,((~node15(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.48 tff(12117,plain,
% 87.22/87.48 (~node15(c_e_h_1, c_e, s11, s12)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12116, 12079, 11778])).
% 87.22/87.48 tff(12118,assumption,(~node15(c_e_h_1, c_e, s11, s12)), introduced(assumption)).
% 87.22/87.48 tff(12119,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s11)), introduced(assumption)).
% 87.22/87.48 tff(12120,plain,
% 87.22/87.48 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12121,plain,
% 87.22/87.48 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12122,plain,
% 87.22/87.48 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12121, 12120])).
% 87.22/87.48 tff(12123,plain,
% 87.22/87.48 ((~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12122, 228, 12110])).
% 87.22/87.48 tff(12124,plain,
% 87.22/87.48 (~node16(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12123, 12119])).
% 87.22/87.48 tff(12125,assumption,(node14(c_e_h_1, c_e, s11, s12)), introduced(assumption)).
% 87.22/87.48 tff(12126,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12127,plain,
% 87.22/87.48 (((~node14(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12))) <=> ((~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12128,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11)))),
% 87.22/87.48 inference(monotonicity,[status(thm)],[12127])).
% 87.22/87.48 tff(12129,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(transitivity,[status(thm)],[12128, 12126])).
% 87.22/87.48 tff(12130,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12131,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12130, 12129])).
% 87.22/87.48 tff(12132,plain,
% 87.22/87.48 ($false),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12131, 283, 12079, 12125, 12119])).
% 87.22/87.48 tff(12133,plain,((~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.48 tff(12134,plain,
% 87.22/87.48 (~node14(c_e_h_1, c_e, s11, s12)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12133, 12119, 12079])).
% 87.22/87.48 tff(12135,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_e, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_e, s11, s12))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12136,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_e, s11, s12))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12137,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_e, s11, s12)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12136, 12135])).
% 87.22/87.48 tff(12138,plain,
% 87.22/87.48 (node19(c_e_h_1, c_e, s11, s12)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12137, 141, 4461])).
% 87.22/87.48 tff(12139,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s11) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s11) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12140,plain,
% 87.22/87.48 ((node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12))) <=> (node16(c_e_h_1, c_e, s11) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12141,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s11) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12)))),
% 87.22/87.48 inference(monotonicity,[status(thm)],[12140])).
% 87.22/87.48 tff(12142,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s11) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12))),
% 87.22/87.48 inference(transitivity,[status(thm)],[12141, 12139])).
% 87.22/87.48 tff(12143,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12144,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s11) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12143, 12142])).
% 87.22/87.48 tff(12145,plain,
% 87.22/87.48 (node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12144, 189, 12138])).
% 87.22/87.48 tff(12146,plain,
% 87.22/87.48 ($false),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12145, 12134, 12124, 12118])).
% 87.22/87.48 tff(12147,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s11) | node15(c_e_h_1, c_e, s11, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.48 tff(12148,plain,
% 87.22/87.48 (m_c_h_element_v_in1(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12147, 12117, 12079, 12110])).
% 87.22/87.48 tff(12149,plain,
% 87.22/87.48 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12150,plain,
% 87.22/87.48 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12151,plain,
% 87.22/87.48 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11))))),
% 87.22/87.48 inference(monotonicity,[status(thm)],[12150])).
% 87.22/87.48 tff(12152,plain,
% 87.22/87.48 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)))),
% 87.22/87.48 inference(transitivity,[status(thm)],[12151, 12149])).
% 87.22/87.48 tff(12153,plain,
% 87.22/87.48 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12154,plain,
% 87.22/87.48 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12153, 12152])).
% 87.22/87.48 tff(12155,plain,
% 87.22/87.48 ((~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12154, 209, 12110])).
% 87.22/87.48 tff(12156,plain,
% 87.22/87.48 (~node17(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12155, 12148])).
% 87.22/87.48 tff(12157,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s11, s12)) | node18(c_e_h_1, c_e, s11, s12) | node17(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s11, s12)) | node18(c_e_h_1, c_e, s11, s12) | node17(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12158,plain,
% 87.22/87.48 ((node17(c_e_h_1, c_e, s11) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12))) <=> ((~node19(c_e_h_1, c_e, s11, s12)) | node18(c_e_h_1, c_e, s11, s12) | node17(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12159,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s11) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s11, s12)) | node18(c_e_h_1, c_e, s11, s12) | node17(c_e_h_1, c_e, s11)))),
% 87.22/87.48 inference(monotonicity,[status(thm)],[12158])).
% 87.22/87.48 tff(12160,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s11) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s11, s12)) | node18(c_e_h_1, c_e, s11, s12) | node17(c_e_h_1, c_e, s11))),
% 87.22/87.48 inference(transitivity,[status(thm)],[12159, 12157])).
% 87.22/87.48 tff(12161,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s11) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12162,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s11, s12)) | node18(c_e_h_1, c_e, s11, s12) | node17(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12161, 12160])).
% 87.22/87.48 tff(12163,plain,
% 87.22/87.48 (node18(c_e_h_1, c_e, s11, s12) | node17(c_e_h_1, c_e, s11)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12162, 156, 12138])).
% 87.22/87.48 tff(12164,plain,
% 87.22/87.48 (node18(c_e_h_1, c_e, s11, s12)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12163, 12156])).
% 87.22/87.48 tff(12165,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12)))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12166,plain,
% 87.22/87.48 (((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node18(c_e_h_1, c_e, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12)))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12167,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node18(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12))))),
% 87.22/87.48 inference(monotonicity,[status(thm)],[12166])).
% 87.22/87.48 tff(12168,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node18(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12)))),
% 87.22/87.48 inference(transitivity,[status(thm)],[12167, 12165])).
% 87.22/87.48 tff(12169,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node18(c_e_h_1, c_e, s11, s12)))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12170,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12))),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12169, 12168])).
% 87.22/87.48 tff(12171,plain,
% 87.22/87.48 ($false),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12170, 124, 12079, 11778, 12164])).
% 87.22/87.48 tff(12172,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.48 tff(12173,plain,
% 87.22/87.48 ($false),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12172, 12109, 12084, 12079])).
% 87.22/87.48 tff(12174,plain,(m_and_h_gate_v_out(c_e_h_1, c_i, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | node20(c_e_h_1, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.48 tff(12175,plain,
% 87.22/87.48 (node20(c_e_h_1, c_i, s10)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12174, 12082, 12079])).
% 87.22/87.48 tff(12176,plain,
% 87.22/87.48 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s10))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12177,plain,
% 87.22/87.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s10))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12178,plain,
% 87.22/87.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s10)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12177, 12176])).
% 87.22/87.48 tff(12179,plain,
% 87.22/87.48 (m_and_h_gate_v_in1(c_e_h_1, c_i, s10)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12178, 37, 12175])).
% 87.22/87.48 tff(12180,plain,
% 87.22/87.48 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12181,plain,
% 87.22/87.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12182,plain,
% 87.22/87.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s10)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12181, 12180])).
% 87.22/87.48 tff(12183,plain,
% 87.22/87.48 (m_c_h_element_v_out(c_e_h_1, c_h, s10)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12182, 23, 12179])).
% 87.22/87.48 tff(12184,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s10)), introduced(assumption)).
% 87.22/87.48 tff(12185,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s9)), introduced(assumption)).
% 87.22/87.48 tff(12186,assumption,(node18(c_e_h_1, c_h, s9, s10)), introduced(assumption)).
% 87.22/87.48 tff(12187,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12188,plain,
% 87.22/87.48 (((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~node18(c_e_h_1, c_h, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12189,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~node18(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10))))),
% 87.22/87.48 inference(monotonicity,[status(thm)],[12188])).
% 87.22/87.48 tff(12190,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~node18(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.48 inference(transitivity,[status(thm)],[12189, 12187])).
% 87.22/87.48 tff(12191,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~node18(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12192,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10))),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12191, 12190])).
% 87.22/87.48 tff(12193,plain,
% 87.22/87.48 ($false),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12192, 124, 12184, 12185, 12186])).
% 87.22/87.48 tff(12194,plain,((~node18(c_e_h_1, c_h, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.48 tff(12195,plain,
% 87.22/87.48 (~node18(c_e_h_1, c_h, s9, s10)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12194, 12185, 12184])).
% 87.22/87.48 tff(12196,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s9)), introduced(assumption)).
% 87.22/87.48 tff(12197,assumption,(node15(c_e_h_1, c_h, s9, s10)), introduced(assumption)).
% 87.22/87.48 tff(12198,plain,
% 87.22/87.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))),
% 87.22/87.48 inference(rewrite,[status(thm)],[])).
% 87.22/87.48 tff(12199,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))),
% 87.22/87.48 inference(quant_inst,[status(thm)],[])).
% 87.22/87.48 tff(12200,plain,
% 87.22/87.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9)),
% 87.22/87.48 inference(modus_ponens,[status(thm)],[12199, 12198])).
% 87.22/87.48 tff(12201,plain,
% 87.22/87.48 ($false),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12200, 173, 12184, 12185, 12197])).
% 87.22/87.48 tff(12202,plain,((~node15(c_e_h_1, c_h, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.48 tff(12203,plain,
% 87.22/87.48 (~node15(c_e_h_1, c_h, s9, s10)),
% 87.22/87.48 inference(unit_resolution,[status(thm)],[12202, 12185, 12184])).
% 87.22/87.48 tff(12204,assumption,(~node15(c_e_h_1, c_h, s9, s10)), introduced(assumption)).
% 87.22/87.48 tff(12205,assumption,(node17(c_e_h_1, c_h, s9)), introduced(assumption)).
% 87.22/87.48 tff(12206,plain,
% 87.22/87.48 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12207,plain,
% 87.22/87.49 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node17(c_e_h_1, c_h, s9))) <=> ((~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12208,plain,
% 87.22/87.49 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node17(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))))),
% 87.22/87.49 inference(monotonicity,[status(thm)],[12207])).
% 87.22/87.49 tff(12209,plain,
% 87.22/87.49 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node17(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 87.22/87.49 inference(transitivity,[status(thm)],[12208, 12206])).
% 87.22/87.49 tff(12210,plain,
% 87.22/87.49 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node17(c_e_h_1, c_h, s9)))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12211,plain,
% 87.22/87.49 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12210, 12209])).
% 87.22/87.49 tff(12212,plain,
% 87.22/87.49 (m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12211, 209, 12205])).
% 87.22/87.49 tff(12213,plain,
% 87.22/87.49 (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12212, 12196])).
% 87.22/87.49 tff(12214,plain,
% 87.22/87.49 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12215,plain,
% 87.22/87.49 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12216,plain,
% 87.22/87.49 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12215, 12214])).
% 87.22/87.49 tff(12217,plain,
% 87.22/87.49 (~node16(c_e_h_1, c_h, s9)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12216, 228, 12213, 12196])).
% 87.22/87.49 tff(12218,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_h, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_h, s9, s10))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12219,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_h, s9, s10))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12220,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_h, s9, s10)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12219, 12218])).
% 87.22/87.49 tff(12221,plain,
% 87.22/87.49 (node19(c_e_h_1, c_h, s9, s10)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12220, 141, 3175])).
% 87.22/87.49 tff(12222,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s9) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)) | node14(c_e_h_1, c_h, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s9) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)) | node14(c_e_h_1, c_h, s9, s10))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12223,plain,
% 87.22/87.49 ((node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10))) <=> (node16(c_e_h_1, c_h, s9) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)) | node14(c_e_h_1, c_h, s9, s10))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12224,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s9) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)) | node14(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.49 inference(monotonicity,[status(thm)],[12223])).
% 87.22/87.49 tff(12225,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s9) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)) | node14(c_e_h_1, c_h, s9, s10))),
% 87.22/87.49 inference(transitivity,[status(thm)],[12224, 12222])).
% 87.22/87.49 tff(12226,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12227,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s9) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)) | node14(c_e_h_1, c_h, s9, s10)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12226, 12225])).
% 87.22/87.49 tff(12228,plain,
% 87.22/87.49 (node16(c_e_h_1, c_h, s9) | node15(c_e_h_1, c_h, s9, s10) | node14(c_e_h_1, c_h, s9, s10)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12227, 189, 12221])).
% 87.22/87.49 tff(12229,plain,
% 87.22/87.49 (node14(c_e_h_1, c_h, s9, s10)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12228, 12217, 12204])).
% 87.22/87.49 tff(12230,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12231,plain,
% 87.22/87.49 (((~node14(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12232,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10))))),
% 87.22/87.49 inference(monotonicity,[status(thm)],[12231])).
% 87.22/87.49 tff(12233,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.49 inference(transitivity,[status(thm)],[12232, 12230])).
% 87.22/87.49 tff(12234,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12235,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10))),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12234, 12233])).
% 87.22/87.49 tff(12236,plain,
% 87.22/87.49 ($false),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12235, 283, 12184, 12213, 12229])).
% 87.22/87.49 tff(12237,plain,(m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | node15(c_e_h_1, c_h, s9, s10) | (~node17(c_e_h_1, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.49 tff(12238,plain,
% 87.22/87.49 (~node17(c_e_h_1, c_h, s9)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12237, 12203, 12196, 12184])).
% 87.22/87.49 tff(12239,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12240,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12241,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10))),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12240, 12239])).
% 87.22/87.49 tff(12242,plain,
% 87.22/87.49 (node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12241, 156, 12221])).
% 87.22/87.49 tff(12243,plain,
% 87.22/87.49 ($false),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12242, 12238, 12195])).
% 87.22/87.49 tff(12244,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.49 tff(12245,plain,
% 87.22/87.49 (m_c_h_element_v_in2(c_e_h_1, c_h, s9)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12244, 12183, 12078])).
% 87.22/87.49 tff(12246,plain,
% 87.22/87.49 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12247,plain,
% 87.22/87.49 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12248,plain,
% 87.22/87.49 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12247, 12246])).
% 87.22/87.49 tff(12249,plain,
% 87.22/87.49 (m_or_h_gate_v_out(c_e_h_1, c_j, s9)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12248, 309, 12245])).
% 87.22/87.49 tff(12250,plain,
% 87.22/87.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12251,plain,
% 87.22/87.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12252,plain,
% 87.22/87.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12251, 12250])).
% 87.22/87.49 tff(12253,plain,
% 87.22/87.49 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12252, 1638, 5776])).
% 87.22/87.49 tff(12254,plain,
% 87.22/87.49 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s7))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12255,plain,
% 87.22/87.49 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s7))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12256,plain,
% 87.22/87.49 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s7)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12255, 12254])).
% 87.22/87.49 tff(12257,plain,
% 87.22/87.49 (~node20(c_e_h_1, c_l, s7)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12256, 1535, 12253])).
% 87.22/87.49 tff(12258,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s8)), introduced(assumption)).
% 87.22/87.49 tff(12259,assumption,(~node20(c_e_h_1, c_l, s7)), introduced(assumption)).
% 87.22/87.49 tff(12260,assumption,(node21(c_e_h_1, c_l, s7, s8)), introduced(assumption)).
% 87.22/87.49 tff(12261,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node21(c_e_h_1, c_l, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node21(c_e_h_1, c_l, s7, s8)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12262,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node21(c_e_h_1, c_l, s7, s8)))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12263,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node21(c_e_h_1, c_l, s7, s8))),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12262, 12261])).
% 87.22/87.49 tff(12264,plain,
% 87.22/87.49 ($false),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12263, 51, 12260, 12259, 12258])).
% 87.22/87.49 tff(12265,plain,((~node21(c_e_h_1, c_l, s7, s8)) | node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8))), inference(lemma,lemma(discharge,[]))).
% 87.22/87.49 tff(12266,plain,
% 87.22/87.49 (~node21(c_e_h_1, c_l, s7, s8)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12265, 12258, 12259])).
% 87.22/87.49 tff(12267,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12268,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12269,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12268, 12267])).
% 87.22/87.49 tff(12270,plain,
% 87.22/87.49 (node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12269, 81, 2152])).
% 87.22/87.49 tff(12271,plain,
% 87.22/87.49 (node22(c_e_h_1, c_l, s7, s8)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12270, 12266])).
% 87.22/87.49 tff(12272,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12273,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12274,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12273, 12272])).
% 87.22/87.49 tff(12275,plain,
% 87.22/87.49 ($false),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12274, 107, 12271, 11568, 12258])).
% 87.22/87.49 tff(12276,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7) | node20(c_e_h_1, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.49 tff(12277,plain,
% 87.22/87.49 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12276, 12257])).
% 87.22/87.49 tff(12278,plain,
% 87.22/87.49 (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12277, 11566])).
% 87.22/87.49 tff(12279,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s8)), introduced(assumption)).
% 87.22/87.49 tff(12280,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s8)), introduced(assumption)).
% 87.22/87.49 tff(12281,plain,
% 87.22/87.49 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12282,plain,
% 87.22/87.49 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12283,plain,
% 87.22/87.49 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8)),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12282, 12281])).
% 87.22/87.49 tff(12284,plain,
% 87.22/87.49 ($false),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12283, 801, 12280, 12279])).
% 87.22/87.49 tff(12285,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.49 tff(12286,plain,
% 87.22/87.49 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12285, 12278])).
% 87.22/87.49 tff(12287,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)), introduced(assumption)).
% 87.22/87.49 tff(12288,assumption,(node5(c_e_h_1, c_j, s8, s9)), introduced(assumption)).
% 87.22/87.49 tff(12289,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s9)), introduced(assumption)).
% 87.22/87.49 tff(12290,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12291,plain,
% 87.22/87.49 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12292,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9))))),
% 87.22/87.49 inference(monotonicity,[status(thm)],[12291])).
% 87.22/87.49 tff(12293,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)))),
% 87.22/87.49 inference(transitivity,[status(thm)],[12292, 12290])).
% 87.22/87.49 tff(12294,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12295,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9))),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12294, 12293])).
% 87.22/87.49 tff(12296,plain,
% 87.22/87.49 ($false),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12295, 862, 12289, 12288, 12287, 12076])).
% 87.22/87.49 tff(12297,plain,((~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 87.22/87.49 tff(12298,plain,
% 87.22/87.49 ((~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12297, 12286])).
% 87.22/87.49 tff(12299,plain,
% 87.22/87.49 (~node5(c_e_h_1, c_j, s8, s9)),
% 87.22/87.49 inference(unit_resolution,[status(thm)],[12298, 12249, 12076])).
% 87.22/87.49 tff(12300,assumption,(node6(c_e_h_1, c_j, s8, s9)), introduced(assumption)).
% 87.22/87.49 tff(12301,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | (~node6(c_e_h_1, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | (~node6(c_e_h_1, c_j, s8, s9)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12302,plain,
% 87.22/87.49 (((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | (~node6(c_e_h_1, c_j, s8, s9)))),
% 87.22/87.49 inference(rewrite,[status(thm)],[])).
% 87.22/87.49 tff(12303,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | (~node6(c_e_h_1, c_j, s8, s9))))),
% 87.22/87.49 inference(monotonicity,[status(thm)],[12302])).
% 87.22/87.49 tff(12304,plain,
% 87.22/87.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | (~node6(c_e_h_1, c_j, s8, s9)))),
% 87.22/87.49 inference(transitivity,[status(thm)],[12303, 12301])).
% 87.22/87.49 tff(12305,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))),
% 87.22/87.49 inference(quant_inst,[status(thm)],[])).
% 87.22/87.49 tff(12306,plain,
% 87.22/87.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | (~node6(c_e_h_1, c_j, s8, s9))),
% 87.22/87.49 inference(modus_ponens,[status(thm)],[12305, 12304])).
% 87.22/87.49 tff(12307,plain,
% 87.32/87.50 ($false),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12306, 899, 11598, 12289, 12300])).
% 87.32/87.50 tff(12308,plain,((~node6(c_e_h_1, c_j, s8, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.50 tff(12309,plain,
% 87.32/87.50 (~node6(c_e_h_1, c_j, s8, s9)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12308, 12249, 11598])).
% 87.32/87.50 tff(12310,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node5(c_e_h_1, c_j, s8, s9) | node6(c_e_h_1, c_j, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_1, c_j, s8, s9) | node6(c_e_h_1, c_j, s8, s9))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12311,plain,
% 87.32/87.50 ((node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9) | (~trans(s8, s9))) <=> ((~trans(s8, s9)) | node5(c_e_h_1, c_j, s8, s9) | node6(c_e_h_1, c_j, s8, s9))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12312,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node5(c_e_h_1, c_j, s8, s9) | node6(c_e_h_1, c_j, s8, s9)))),
% 87.32/87.50 inference(monotonicity,[status(thm)],[12311])).
% 87.32/87.50 tff(12313,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_1, c_j, s8, s9) | node6(c_e_h_1, c_j, s8, s9))),
% 87.32/87.50 inference(transitivity,[status(thm)],[12312, 12310])).
% 87.32/87.50 tff(12314,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9) | (~trans(s8, s9)))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12315,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_1, c_j, s8, s9) | node6(c_e_h_1, c_j, s8, s9)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12314, 12313])).
% 87.32/87.50 tff(12316,plain,
% 87.32/87.50 (node5(c_e_h_1, c_j, s8, s9) | node6(c_e_h_1, c_j, s8, s9)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12315, 881, 2636])).
% 87.32/87.50 tff(12317,plain,
% 87.32/87.50 ($false),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12316, 12309, 12299])).
% 87.32/87.50 tff(12318,plain,(m_or_h_gate_v_out(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.50 tff(12319,plain,
% 87.32/87.50 (~m_c_h_element_v_out(c_e_h_1, c_e, s12)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12318, 12075, 11596])).
% 87.32/87.50 tff(12320,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)), introduced(assumption)).
% 87.32/87.50 tff(12321,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s12)), introduced(assumption)).
% 87.32/87.50 tff(12322,plain,
% 87.32/87.50 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12323,plain,
% 87.32/87.50 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12324,plain,
% 87.32/87.50 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12323, 12322])).
% 87.32/87.50 tff(12325,plain,
% 87.32/87.50 ($false),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12324, 976, 12321, 12320])).
% 87.32/87.50 tff(12326,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s12) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.50 tff(12327,plain,
% 87.32/87.50 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12326, 12319])).
% 87.32/87.50 tff(12328,plain,
% 87.32/87.50 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11169, 8371])).
% 87.32/87.50 tff(12329,plain,
% 87.32/87.50 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11160, 11133, 12328, 11144])).
% 87.32/87.50 tff(12330,plain,
% 87.32/87.50 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11180, 1048, 12329])).
% 87.32/87.50 tff(12331,plain,
% 87.32/87.50 (~node9(c_e_h_1, c_m, s11)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11184, 1062, 12330])).
% 87.32/87.50 tff(12332,plain,
% 87.32/87.50 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[8348, 1048, 11133])).
% 87.32/87.50 tff(12333,plain,
% 87.32/87.50 (~node9(c_e_h_1, c_m, s10)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[8352, 1062, 12332])).
% 87.32/87.50 tff(12334,plain,
% 87.32/87.50 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[8376, 12333, 8371])).
% 87.32/87.50 tff(12335,plain,
% 87.32/87.50 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11791, 1142, 12334])).
% 87.32/87.50 tff(12336,plain,
% 87.32/87.50 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11821, 12335, 11793, 12329])).
% 87.32/87.50 tff(12337,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)), introduced(assumption)).
% 87.32/87.50 tff(12338,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)), introduced(assumption)).
% 87.32/87.50 tff(12339,plain,
% 87.32/87.50 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11858, 12334, 12329, 11793])).
% 87.32/87.50 tff(12340,assumption,(node11(c_e_h_1, c_m, s13, s14)), introduced(assumption)).
% 87.32/87.50 tff(12341,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), introduced(assumption)).
% 87.32/87.50 tff(12342,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node11(c_e_h_1, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node11(c_e_h_1, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12343,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node11(c_e_h_1, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12344,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node11(c_e_h_1, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12343, 12342])).
% 87.32/87.50 tff(12345,plain,
% 87.32/87.50 ($false),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12344, 1130, 12338, 12341, 12340])).
% 87.32/87.50 tff(12346,plain,((~node11(c_e_h_1, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.50 tff(12347,plain,
% 87.32/87.50 (~node11(c_e_h_1, c_m, s13, s14)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12346, 12339, 12338])).
% 87.32/87.50 tff(12348,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12349,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12350,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12349, 12348])).
% 87.32/87.50 tff(12351,plain,
% 87.32/87.50 (node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12350, 1092, 10040])).
% 87.32/87.50 tff(12352,plain,
% 87.32/87.50 (node10(c_e_h_1, c_m, s13, s14)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12351, 12347])).
% 87.32/87.50 tff(12353,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14)))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12354,plain,
% 87.32/87.50 ((node9(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node10(c_e_h_1, c_m, s13, s14))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14)))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12355,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node10(c_e_h_1, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14))))),
% 87.32/87.50 inference(monotonicity,[status(thm)],[12354])).
% 87.32/87.50 tff(12356,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node10(c_e_h_1, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14)))),
% 87.32/87.50 inference(transitivity,[status(thm)],[12355, 12353])).
% 87.32/87.50 tff(12357,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node10(c_e_h_1, c_m, s13, s14)))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12358,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14))),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12357, 12356])).
% 87.32/87.50 tff(12359,plain,
% 87.32/87.50 (node9(c_e_h_1, c_m, s13)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12358, 1076, 12338, 12352])).
% 87.32/87.50 tff(12360,plain,
% 87.32/87.50 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12361,plain,
% 87.32/87.50 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12362,plain,
% 87.32/87.50 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12361, 12360])).
% 87.32/87.50 tff(12363,plain,
% 87.32/87.50 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12362, 1062, 12359])).
% 87.32/87.50 tff(12364,plain,
% 87.32/87.50 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12365,plain,
% 87.32/87.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12366,plain,
% 87.32/87.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12365, 12364])).
% 87.32/87.50 tff(12367,plain,
% 87.32/87.50 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12366, 1048, 12363])).
% 87.32/87.50 tff(12368,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)), introduced(assumption)).
% 87.32/87.50 tff(12369,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)), introduced(assumption)).
% 87.32/87.50 tff(12370,assumption,(node10(c_e_h_1, c_n, s12, s13)), introduced(assumption)).
% 87.32/87.50 tff(12371,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12372,plain,
% 87.32/87.50 (((~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12373,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12))))),
% 87.32/87.50 inference(monotonicity,[status(thm)],[12372])).
% 87.32/87.50 tff(12374,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)))),
% 87.32/87.50 inference(transitivity,[status(thm)],[12373, 12371])).
% 87.32/87.50 tff(12375,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12376,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12))),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12375, 12374])).
% 87.32/87.50 tff(12377,plain,
% 87.32/87.50 ($false),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12376, 1191, 12369, 12370, 12337, 12368])).
% 87.32/87.50 tff(12378,plain,((~node10(c_e_h_1, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.50 tff(12379,plain,
% 87.32/87.50 (~node10(c_e_h_1, c_n, s12, s13)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12378, 12369, 12337, 12368])).
% 87.32/87.50 tff(12380,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12381,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12382,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12381, 12380])).
% 87.32/87.50 tff(12383,plain,
% 87.32/87.50 (node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12382, 1092, 9599])).
% 87.32/87.50 tff(12384,plain,
% 87.32/87.50 (node11(c_e_h_1, c_n, s12, s13)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12383, 12379])).
% 87.32/87.50 tff(12385,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)), introduced(assumption)).
% 87.32/87.50 tff(12386,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13)))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12387,plain,
% 87.32/87.50 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~node11(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13)))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12388,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~node11(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13))))),
% 87.32/87.50 inference(monotonicity,[status(thm)],[12387])).
% 87.32/87.50 tff(12389,plain,
% 87.32/87.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~node11(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13)))),
% 87.32/87.50 inference(transitivity,[status(thm)],[12388, 12386])).
% 87.32/87.50 tff(12390,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~node11(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12391,plain,
% 87.32/87.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13))),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12390, 12389])).
% 87.32/87.50 tff(12392,plain,
% 87.32/87.50 ($false),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12391, 1161, 12369, 12385, 12384])).
% 87.32/87.50 tff(12393,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.50 tff(12394,plain,
% 87.32/87.50 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12393, 12367, 12337, 12336])).
% 87.32/87.50 tff(12395,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)), introduced(assumption)).
% 87.32/87.50 tff(12396,plain,
% 87.32/87.50 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12397,plain,
% 87.32/87.50 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12398,plain,
% 87.32/87.50 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12397, 12396])).
% 87.32/87.50 tff(12399,plain,
% 87.32/87.50 ($false),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12398, 1142, 11848, 12395])).
% 87.32/87.50 tff(12400,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.50 tff(12401,plain,
% 87.32/87.50 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12400, 12394])).
% 87.32/87.50 tff(12402,plain,
% 87.32/87.50 (~node11(c_e_h_1, c_m, s11, s12)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11194, 12401, 12334])).
% 87.32/87.50 tff(12403,plain,
% 87.32/87.50 (node10(c_e_h_1, c_m, s11, s12)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11199, 12402])).
% 87.32/87.50 tff(12404,plain,
% 87.32/87.50 ($false),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[11206, 1076, 12401, 12403, 12331])).
% 87.32/87.50 tff(12405,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.50 tff(12406,plain,
% 87.32/87.50 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10))),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12405, 7386])).
% 87.32/87.50 tff(12407,plain,
% 87.32/87.50 ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10))),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12406, 8345])).
% 87.32/87.50 tff(12408,plain,
% 87.32/87.50 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12407, 11784, 12327, 11895])).
% 87.32/87.50 tff(12409,plain,
% 87.32/87.50 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12410,plain,
% 87.32/87.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12411,plain,
% 87.32/87.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12410, 12409])).
% 87.32/87.50 tff(12412,plain,
% 87.32/87.50 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12411, 1521])).
% 87.32/87.50 tff(12413,plain,
% 87.32/87.50 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)),
% 87.32/87.50 inference(unit_resolution,[status(thm)],[12412, 12408])).
% 87.32/87.50 tff(12414,plain,
% 87.32/87.50 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14))),
% 87.32/87.50 inference(rewrite,[status(thm)],[])).
% 87.32/87.50 tff(12415,plain,
% 87.32/87.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14))),
% 87.32/87.50 inference(quant_inst,[status(thm)],[])).
% 87.32/87.50 tff(12416,plain,
% 87.32/87.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14)),
% 87.32/87.50 inference(modus_ponens,[status(thm)],[12415, 12414])).
% 87.32/87.51 tff(12417,plain,
% 87.32/87.51 (~node20(c_e_h_1, c_r, s14)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12416, 1535, 12413])).
% 87.32/87.51 tff(12418,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s14)), introduced(assumption)).
% 87.32/87.51 tff(12419,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s15)), introduced(assumption)).
% 87.32/87.51 tff(12420,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12421,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12422,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12421, 12420])).
% 87.32/87.51 tff(12423,plain,
% 87.32/87.51 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12422, 107])).
% 87.32/87.51 tff(12424,plain,
% 87.32/87.51 (~node22(c_e_h_1, c_r, s14, s15)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12423, 12419, 12418])).
% 87.32/87.51 tff(12425,assumption,(~node20(c_e_h_1, c_r, s14)), introduced(assumption)).
% 87.32/87.51 tff(12426,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12427,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15)))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12428,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12427, 12426])).
% 87.32/87.51 tff(12429,plain,
% 87.32/87.51 (node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15))),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12428, 51])).
% 87.32/87.51 tff(12430,plain,
% 87.32/87.51 (~node21(c_e_h_1, c_r, s14, s15)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12429, 12419, 12425])).
% 87.32/87.51 tff(12431,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12432,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12433,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12432, 12431])).
% 87.32/87.51 tff(12434,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12433, 81, 10504, 12430, 12424])).
% 87.32/87.51 tff(12435,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14) | node20(c_e_h_1, c_r, s14)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12436,plain,
% 87.32/87.51 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12435, 12417])).
% 87.32/87.51 tff(12437,plain,
% 87.32/87.51 (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12436, 11894])).
% 87.32/87.51 tff(12438,plain,
% 87.32/87.51 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12439,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12440,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12439, 12438])).
% 87.32/87.51 tff(12441,plain,
% 87.32/87.51 (~m_user_v_ack(c_e_h_1, c_u, s15)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12440, 4481, 12437])).
% 87.32/87.51 tff(12442,plain,
% 87.32/87.51 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s15) | (~node24(s15)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s15) | (~node24(s15)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12443,plain,
% 87.32/87.51 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s15) | (~node24(s15)))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12444,plain,
% 87.32/87.51 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s15) | (~node24(s15))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12443, 12442])).
% 87.32/87.51 tff(12445,plain,
% 87.32/87.51 (~node24(s15)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12444, 8407, 12441])).
% 87.32/87.51 tff(12446,plain,
% 87.32/87.51 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s15) | (~node23(s15)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s15) | (~node23(s15)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12447,plain,
% 87.32/87.51 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s15) | (~node23(s15)))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12448,plain,
% 87.32/87.51 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s15) | (~node23(s15))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12447, 12446])).
% 87.32/87.51 tff(12449,plain,
% 87.32/87.51 (~node23(s15)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12448, 8418, 12441])).
% 87.32/87.51 tff(12450,plain,
% 87.32/87.51 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s15) | node24(s15) | node25(s15) | (~node26(s15)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s15) | node24(s15) | node25(s15) | (~node26(s15)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12451,plain,
% 87.32/87.51 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s15) | node24(s15) | node25(s15) | (~node26(s15)))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12452,plain,
% 87.32/87.51 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s15) | node24(s15) | node25(s15) | (~node26(s15))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12451, 12450])).
% 87.32/87.51 tff(12453,plain,
% 87.32/87.51 (node25(s15) | (~node26(s15))),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12452, 8435, 12449, 12445])).
% 87.32/87.51 tff(12454,plain,
% 87.32/87.51 (~node26(s15)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12453, 10520])).
% 87.32/87.51 tff(12455,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)), introduced(assumption)).
% 87.32/87.51 tff(12456,plain,
% 87.32/87.51 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12457,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12458,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12457, 12456])).
% 87.32/87.51 tff(12459,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12458, 1142, 4404, 12455])).
% 87.32/87.51 tff(12460,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12461,plain,
% 87.32/87.51 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12460, 3750])).
% 87.32/87.51 tff(12462,plain,
% 87.32/87.51 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[4395, 3668, 4270])).
% 87.32/87.51 tff(12463,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)), introduced(assumption)).
% 87.32/87.51 tff(12464,plain,
% 87.32/87.51 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13) | m_c_h_element_v_out(c_e_h_2, c_e, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13) | m_c_h_element_v_out(c_e_h_2, c_e, s13))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12465,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13) | m_c_h_element_v_out(c_e_h_2, c_e, s13))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12466,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13) | m_c_h_element_v_out(c_e_h_2, c_e, s13)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12465, 12464])).
% 87.32/87.51 tff(12467,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12466, 976, 10004, 12463])).
% 87.32/87.51 tff(12468,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13) | m_c_h_element_v_out(c_e_h_2, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12469,plain,
% 87.32/87.51 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12468, 10002])).
% 87.32/87.51 tff(12470,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)), introduced(assumption)).
% 87.32/87.51 tff(12471,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)), introduced(assumption)).
% 87.32/87.51 tff(12472,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)), introduced(assumption)).
% 87.32/87.51 tff(12473,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)), introduced(assumption)).
% 87.32/87.51 tff(12474,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)), introduced(assumption)).
% 87.32/87.51 tff(12475,plain,
% 87.32/87.51 (~m_c_h_element_v_out(c_e_h_2, c_e, s11)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[9211, 9152, 9153])).
% 87.32/87.51 tff(12476,plain,
% 87.32/87.51 (~m_c_h_element_v_out(c_e_h_2, c_e, s12)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[9573, 12475, 9537])).
% 87.32/87.51 tff(12477,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)), introduced(assumption)).
% 87.32/87.51 tff(12478,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)), introduced(assumption)).
% 87.32/87.51 tff(12479,plain,
% 87.32/87.51 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10) | m_c_h_element_v_out(c_e_h_2, c_e, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10) | m_c_h_element_v_out(c_e_h_2, c_e, s10))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12480,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10) | m_c_h_element_v_out(c_e_h_2, c_e, s10))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12481,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10) | m_c_h_element_v_out(c_e_h_2, c_e, s10)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12480, 12479])).
% 87.32/87.51 tff(12482,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12481, 976, 9153, 12478])).
% 87.32/87.51 tff(12483,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10) | m_c_h_element_v_out(c_e_h_2, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12484,plain,
% 87.32/87.51 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12483, 9153])).
% 87.32/87.51 tff(12485,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)), introduced(assumption)).
% 87.32/87.51 tff(12486,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)), introduced(assumption)).
% 87.32/87.51 tff(12487,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)), introduced(assumption)).
% 87.32/87.51 tff(12488,assumption,(node10(c_e_h_2, c_n, s10, s11)), introduced(assumption)).
% 87.32/87.51 tff(12489,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~node10(c_e_h_2, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~node10(c_e_h_2, c_n, s10, s11)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12490,plain,
% 87.32/87.51 (((~node10(c_e_h_2, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~node10(c_e_h_2, c_n, s10, s11)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12491,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~node10(c_e_h_2, c_n, s10, s11))))),
% 87.32/87.51 inference(monotonicity,[status(thm)],[12490])).
% 87.32/87.51 tff(12492,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~node10(c_e_h_2, c_n, s10, s11)))),
% 87.32/87.51 inference(transitivity,[status(thm)],[12491, 12489])).
% 87.32/87.51 tff(12493,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12494,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~node10(c_e_h_2, c_n, s10, s11))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12493, 12492])).
% 87.32/87.51 tff(12495,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12494, 1191, 12487, 12488, 12472, 12486])).
% 87.32/87.51 tff(12496,plain,((~node10(c_e_h_2, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12497,plain,
% 87.32/87.51 (~node10(c_e_h_2, c_n, s10, s11)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12496, 12487, 12472, 12486])).
% 87.32/87.51 tff(12498,assumption,(node11(c_e_h_2, c_n, s10, s11)), introduced(assumption)).
% 87.32/87.51 tff(12499,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~node11(c_e_h_2, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~node11(c_e_h_2, c_n, s10, s11)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12500,plain,
% 87.32/87.51 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~node11(c_e_h_2, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~node11(c_e_h_2, c_n, s10, s11)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12501,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~node11(c_e_h_2, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~node11(c_e_h_2, c_n, s10, s11))))),
% 87.32/87.51 inference(monotonicity,[status(thm)],[12500])).
% 87.32/87.51 tff(12502,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~node11(c_e_h_2, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~node11(c_e_h_2, c_n, s10, s11)))),
% 87.32/87.51 inference(transitivity,[status(thm)],[12501, 12499])).
% 87.32/87.51 tff(12503,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~node11(c_e_h_2, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12504,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~node11(c_e_h_2, c_n, s10, s11))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12503, 12502])).
% 87.32/87.51 tff(12505,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12504, 1161, 12487, 12473, 12498])).
% 87.32/87.51 tff(12506,plain,((~node11(c_e_h_2, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12507,plain,
% 87.32/87.51 (~node11(c_e_h_2, c_n, s10, s11)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12506, 12487, 12473])).
% 87.32/87.51 tff(12508,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_2, c_n, s10, s11) | node11(c_e_h_2, c_n, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_2, c_n, s10, s11) | node11(c_e_h_2, c_n, s10, s11))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12509,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_2, c_n, s10, s11) | node11(c_e_h_2, c_n, s10, s11))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12510,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_2, c_n, s10, s11) | node11(c_e_h_2, c_n, s10, s11)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12509, 12508])).
% 87.32/87.51 tff(12511,plain,
% 87.32/87.51 (node10(c_e_h_2, c_n, s10, s11) | node11(c_e_h_2, c_n, s10, s11)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12510, 1092, 3778])).
% 87.32/87.51 tff(12512,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12511, 12507, 12497])).
% 87.32/87.51 tff(12513,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12514,plain,
% 87.32/87.51 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12513, 12486, 12473, 12472])).
% 87.32/87.51 tff(12515,assumption,(node10(c_e_h_2, c_n, s11, s12)), introduced(assumption)).
% 87.32/87.51 tff(12516,plain,
% 87.32/87.51 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12517,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12518,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12517, 12516])).
% 87.32/87.51 tff(12519,plain,
% 87.32/87.51 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12518, 1142, 4433])).
% 87.32/87.51 tff(12520,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)), introduced(assumption)).
% 87.32/87.51 tff(12521,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)), introduced(assumption)).
% 87.32/87.51 tff(12522,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12523,plain,
% 87.32/87.51 (((~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12524,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11))))),
% 87.32/87.51 inference(monotonicity,[status(thm)],[12523])).
% 87.32/87.51 tff(12525,plain,
% 87.32/87.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)))),
% 87.32/87.51 inference(transitivity,[status(thm)],[12524, 12522])).
% 87.32/87.51 tff(12526,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12527,plain,
% 87.32/87.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~node10(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12526, 12525])).
% 87.32/87.51 tff(12528,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12527, 1191, 12485, 12515, 12521, 12520])).
% 87.32/87.51 tff(12529,plain,((~node10(c_e_h_2, c_n, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12530,plain,
% 87.32/87.51 (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12529, 12519, 12515, 12485])).
% 87.32/87.51 tff(12531,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11)), introduced(assumption)).
% 87.32/87.51 tff(12532,plain,
% 87.32/87.51 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11) | m_c_h_element_v_out(c_e_h_2, c_e, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11) | m_c_h_element_v_out(c_e_h_2, c_e, s11))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12533,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11) | m_c_h_element_v_out(c_e_h_2, c_e, s11))),
% 87.32/87.51 inference(quant_inst,[status(thm)],[])).
% 87.32/87.51 tff(12534,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11) | m_c_h_element_v_out(c_e_h_2, c_e, s11)),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12533, 12532])).
% 87.32/87.51 tff(12535,plain,
% 87.32/87.51 ($false),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12534, 976, 9514, 12531])).
% 87.32/87.51 tff(12536,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s11) | m_c_h_element_v_out(c_e_h_2, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.51 tff(12537,plain,
% 87.32/87.51 (m_c_h_element_v_out(c_e_h_2, c_e, s11)),
% 87.32/87.51 inference(unit_resolution,[status(thm)],[12536, 12530])).
% 87.32/87.51 tff(12538,plain,
% 87.32/87.51 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X))) <=> ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X))))),
% 87.32/87.51 inference(bind,[status(th)],[])).
% 87.32/87.51 tff(12539,plain,
% 87.32/87.51 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))),
% 87.32/87.51 inference(quant_intro,[status(thm)],[12538])).
% 87.32/87.51 tff(12540,plain,
% 87.32/87.51 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12541,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_58')).
% 87.32/87.51 tff(12542,plain,
% 87.32/87.51 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12541, 12540])).
% 87.32/87.51 tff(12543,plain,(
% 87.32/87.51 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))),
% 87.32/87.51 inference(skolemize,[status(sab)],[12542])).
% 87.32/87.51 tff(12544,plain,
% 87.32/87.51 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))),
% 87.32/87.51 inference(modus_ponens,[status(thm)],[12543, 12539])).
% 87.32/87.51 tff(12545,plain,
% 87.32/87.51 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)))),
% 87.32/87.51 inference(rewrite,[status(thm)],[])).
% 87.32/87.51 tff(12546,plain,
% 87.32/87.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10)))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12547,plain,
% 87.32/87.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in1(I0, c_n, X)) | (~m_c_h_element_v_out(I0, c_e, X)))) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s10))),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12546, 12545])).
% 87.32/87.52 tff(12548,plain,
% 87.32/87.52 (~m_c_h_element_v_out(c_e_h_2, c_e, s10)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12547, 12544, 12486])).
% 87.32/87.52 tff(12549,plain,
% 87.32/87.52 (~node15(c_e_h_2, c_e, s10, s11)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[9159, 12548, 12537])).
% 87.32/87.52 tff(12550,plain,
% 87.32/87.52 (~node18(c_e_h_2, c_e, s10, s11)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[9166, 12548, 12537])).
% 87.32/87.52 tff(12551,plain,
% 87.32/87.52 (node17(c_e_h_2, c_e, s10)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[9178, 12550])).
% 87.32/87.52 tff(12552,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[9209, 12551, 12549, 9152, 12537])).
% 87.32/87.52 tff(12553,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~node10(c_e_h_2, c_n, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12554,plain,
% 87.32/87.52 (~node10(c_e_h_2, c_n, s11, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12553, 12486, 12485, 4433, 9152])).
% 87.32/87.52 tff(12555,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_2, c_n, s11, s12) | node11(c_e_h_2, c_n, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_2, c_n, s11, s12) | node11(c_e_h_2, c_n, s11, s12))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12556,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_2, c_n, s11, s12) | node11(c_e_h_2, c_n, s11, s12))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12557,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_2, c_n, s11, s12) | node11(c_e_h_2, c_n, s11, s12)),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12556, 12555])).
% 87.32/87.52 tff(12558,plain,
% 87.32/87.52 (node10(c_e_h_2, c_n, s11, s12) | node11(c_e_h_2, c_n, s11, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12557, 1092, 4461])).
% 87.32/87.52 tff(12559,plain,
% 87.32/87.52 (node11(c_e_h_2, c_n, s11, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12558, 12554])).
% 87.32/87.52 tff(12560,assumption,(node11(c_e_h_2, c_n, s11, s12)), introduced(assumption)).
% 87.32/87.52 tff(12561,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)), introduced(assumption)).
% 87.32/87.52 tff(12562,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12563,plain,
% 87.32/87.52 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12564,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12))))),
% 87.32/87.52 inference(monotonicity,[status(thm)],[12563])).
% 87.32/87.52 tff(12565,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12)))),
% 87.32/87.52 inference(transitivity,[status(thm)],[12564, 12562])).
% 87.32/87.52 tff(12566,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12567,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~node11(c_e_h_2, c_n, s11, s12))),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12566, 12565])).
% 87.32/87.52 tff(12568,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12567, 1161, 12561, 12485, 12560])).
% 87.32/87.52 tff(12569,plain,((~node11(c_e_h_2, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12570,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12569, 12559, 12514, 12485])).
% 87.32/87.52 tff(12571,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | m_c_h_element_v_in2(c_e_h_2, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12572,plain,
% 87.32/87.52 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12571, 9152, 4433, 12484, 12473, 12472])).
% 87.32/87.52 tff(12573,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)), introduced(assumption)).
% 87.32/87.52 tff(12574,assumption,(node10(c_e_h_2, c_n, s12, s13)), introduced(assumption)).
% 87.32/87.52 tff(12575,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~node10(c_e_h_2, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~node10(c_e_h_2, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12576,plain,
% 87.32/87.52 (((~node10(c_e_h_2, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~node10(c_e_h_2, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12577,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~node10(c_e_h_2, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12))))),
% 87.32/87.52 inference(monotonicity,[status(thm)],[12576])).
% 87.32/87.52 tff(12578,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~node10(c_e_h_2, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)))),
% 87.32/87.52 inference(transitivity,[status(thm)],[12577, 12575])).
% 87.32/87.52 tff(12579,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12580,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~node10(c_e_h_2, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12))),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12579, 12578])).
% 87.32/87.52 tff(12581,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12580, 1191, 12474, 12574, 12477, 12573])).
% 87.32/87.52 tff(12582,plain,((~node10(c_e_h_2, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12583,plain,
% 87.32/87.52 (~node10(c_e_h_2, c_n, s12, s13)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12582, 12474, 12477, 12573])).
% 87.32/87.52 tff(12584,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)), introduced(assumption)).
% 87.32/87.52 tff(12585,assumption,(node11(c_e_h_2, c_n, s12, s13)), introduced(assumption)).
% 87.32/87.52 tff(12586,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)) | (~node11(c_e_h_2, c_n, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)) | (~node11(c_e_h_2, c_n, s12, s13)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12587,plain,
% 87.32/87.52 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~node11(c_e_h_2, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)) | (~node11(c_e_h_2, c_n, s12, s13)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12588,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~node11(c_e_h_2, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)) | (~node11(c_e_h_2, c_n, s12, s13))))),
% 87.32/87.52 inference(monotonicity,[status(thm)],[12587])).
% 87.32/87.52 tff(12589,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~node11(c_e_h_2, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)) | (~node11(c_e_h_2, c_n, s12, s13)))),
% 87.32/87.52 inference(transitivity,[status(thm)],[12588, 12586])).
% 87.32/87.52 tff(12590,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~node11(c_e_h_2, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12591,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)) | (~node11(c_e_h_2, c_n, s12, s13))),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12590, 12589])).
% 87.32/87.52 tff(12592,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12591, 1161, 12474, 12584, 12585])).
% 87.32/87.52 tff(12593,plain,((~node11(c_e_h_2, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12594,plain,
% 87.32/87.52 (~node11(c_e_h_2, c_n, s12, s13)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12593, 12474, 12584])).
% 87.32/87.52 tff(12595,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_2, c_n, s12, s13) | node11(c_e_h_2, c_n, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_2, c_n, s12, s13) | node11(c_e_h_2, c_n, s12, s13))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12596,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_2, c_n, s12, s13) | node11(c_e_h_2, c_n, s12, s13))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12597,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_2, c_n, s12, s13) | node11(c_e_h_2, c_n, s12, s13)),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12596, 12595])).
% 87.32/87.52 tff(12598,plain,
% 87.32/87.52 (node10(c_e_h_2, c_n, s12, s13) | node11(c_e_h_2, c_n, s12, s13)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12597, 1092, 9599])).
% 87.32/87.52 tff(12599,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12598, 12594, 12583])).
% 87.32/87.52 tff(12600,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12601,plain,
% 87.32/87.52 (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12600, 12572, 12474, 12477])).
% 87.32/87.52 tff(12602,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)), introduced(assumption)).
% 87.32/87.52 tff(12603,plain,
% 87.32/87.52 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12) | m_c_h_element_v_out(c_e_h_2, c_e, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12) | m_c_h_element_v_out(c_e_h_2, c_e, s12))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12604,plain,
% 87.32/87.52 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12) | m_c_h_element_v_out(c_e_h_2, c_e, s12))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12605,plain,
% 87.32/87.52 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12) | m_c_h_element_v_out(c_e_h_2, c_e, s12)),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12604, 12603])).
% 87.32/87.52 tff(12606,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12605, 976, 9932, 12602])).
% 87.32/87.52 tff(12607,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12) | m_c_h_element_v_out(c_e_h_2, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12608,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12607, 12601, 12476])).
% 87.32/87.52 tff(12609,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s10) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | m_c_h_element_v_out(c_e_h_2, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12610,plain,
% 87.32/87.52 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12609, 9153, 12472, 12473, 12474, 9537, 9152, 4433])).
% 87.32/87.52 tff(12611,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)), introduced(assumption)).
% 87.32/87.52 tff(12612,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)), introduced(assumption)).
% 87.32/87.52 tff(12613,plain,
% 87.32/87.52 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12614,plain,
% 87.32/87.52 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12615,plain,
% 87.32/87.52 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12614, 12613])).
% 87.32/87.52 tff(12616,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12615, 1142, 12612, 12611])).
% 87.32/87.52 tff(12617,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12618,plain,
% 87.32/87.52 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12617, 12610])).
% 87.32/87.52 tff(12619,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)), introduced(assumption)).
% 87.32/87.52 tff(12620,assumption,(node11(c_e_h_2, c_m, s11, s12)), introduced(assumption)).
% 87.32/87.52 tff(12621,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | (~node11(c_e_h_2, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | (~node11(c_e_h_2, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12622,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | (~node11(c_e_h_2, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12623,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | (~node11(c_e_h_2, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12622, 12621])).
% 87.32/87.52 tff(12624,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12623, 1130, 4433, 12620, 12619])).
% 87.32/87.52 tff(12625,plain,((~node11(c_e_h_2, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12626,plain,
% 87.32/87.52 (~node11(c_e_h_2, c_m, s11, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12625, 12619, 4433])).
% 87.32/87.52 tff(12627,assumption,(~node9(c_e_h_2, c_m, s11)), introduced(assumption)).
% 87.32/87.52 tff(12628,assumption,(node10(c_e_h_2, c_m, s11, s12)), introduced(assumption)).
% 87.32/87.52 tff(12629,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_2, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | node9(c_e_h_2, c_m, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_2, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | node9(c_e_h_2, c_m, s11))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12630,plain,
% 87.32/87.52 ((node9(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | (~node10(c_e_h_2, c_m, s11, s12))) <=> ((~node10(c_e_h_2, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | node9(c_e_h_2, c_m, s11))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12631,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | (~node10(c_e_h_2, c_m, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_2, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | node9(c_e_h_2, c_m, s11)))),
% 87.32/87.52 inference(monotonicity,[status(thm)],[12630])).
% 87.32/87.52 tff(12632,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | (~node10(c_e_h_2, c_m, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_2, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | node9(c_e_h_2, c_m, s11))),
% 87.32/87.52 inference(transitivity,[status(thm)],[12631, 12629])).
% 87.32/87.52 tff(12633,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | (~node10(c_e_h_2, c_m, s11, s12)))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12634,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_2, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | node9(c_e_h_2, c_m, s11)),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12633, 12632])).
% 87.32/87.52 tff(12635,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12634, 1076, 12628, 12619, 12627])).
% 87.32/87.52 tff(12636,plain,((~node10(c_e_h_2, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | node9(c_e_h_2, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12637,plain,
% 87.32/87.52 (~node10(c_e_h_2, c_m, s11, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12636, 12619, 12627])).
% 87.32/87.52 tff(12638,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_2, c_m, s11, s12) | node11(c_e_h_2, c_m, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_2, c_m, s11, s12) | node11(c_e_h_2, c_m, s11, s12))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12639,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_2, c_m, s11, s12) | node11(c_e_h_2, c_m, s11, s12))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12640,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_2, c_m, s11, s12) | node11(c_e_h_2, c_m, s11, s12)),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12639, 12638])).
% 87.32/87.52 tff(12641,plain,
% 87.32/87.52 (node10(c_e_h_2, c_m, s11, s12) | node11(c_e_h_2, c_m, s11, s12)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12640, 1092, 4461])).
% 87.32/87.52 tff(12642,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12641, 12637, 12626])).
% 87.32/87.52 tff(12643,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)) | node9(c_e_h_2, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12644,plain,
% 87.32/87.52 (node9(c_e_h_2, c_m, s11)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12643, 12618, 4433])).
% 87.32/87.52 tff(12645,plain,
% 87.32/87.52 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12513, 12484, 12472, 12473])).
% 87.32/87.52 tff(12646,plain,
% 87.32/87.52 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12647,plain,
% 87.32/87.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12648,plain,
% 87.32/87.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11))),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12647, 12646])).
% 87.32/87.52 tff(12649,plain,
% 87.32/87.52 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12648, 1048, 12645])).
% 87.32/87.52 tff(12650,plain,
% 87.32/87.52 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12651,plain,
% 87.32/87.52 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11))),
% 87.32/87.52 inference(quant_inst,[status(thm)],[])).
% 87.32/87.52 tff(12652,plain,
% 87.32/87.52 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)),
% 87.32/87.52 inference(modus_ponens,[status(thm)],[12651, 12650])).
% 87.32/87.52 tff(12653,plain,
% 87.32/87.52 ($false),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12652, 1062, 12649, 12644])).
% 87.32/87.52 tff(12654,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s10) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13) | m_c_h_element_v_in2(c_e_h_2, c_e, s11) | m_c_h_element_v_in2(c_e_h_2, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.52 tff(12655,plain,
% 87.32/87.52 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)),
% 87.32/87.52 inference(unit_resolution,[status(thm)],[12654, 9153, 9537, 12473, 4433, 9152, 12472])).
% 87.32/87.52 tff(12656,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)), introduced(assumption)).
% 87.32/87.52 tff(12657,assumption,(node10(c_e_h_2, c_n, s13, s14)), introduced(assumption)).
% 87.32/87.52 tff(12658,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12659,plain,
% 87.32/87.52 (((~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)))),
% 87.32/87.52 inference(rewrite,[status(thm)],[])).
% 87.32/87.52 tff(12660,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13))))),
% 87.32/87.52 inference(monotonicity,[status(thm)],[12659])).
% 87.32/87.52 tff(12661,plain,
% 87.32/87.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)))),
% 87.32/87.52 inference(transitivity,[status(thm)],[12660, 12658])).
% 87.32/87.52 tff(12662,plain,
% 87.32/87.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12663,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)) | (~node10(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13))),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12662, 12661])).
% 87.32/87.53 tff(12664,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12663, 1191, 12470, 12657, 12471, 12656])).
% 87.32/87.53 tff(12665,plain,((~node10(c_e_h_2, c_n, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12666,plain,
% 87.32/87.53 (~node10(c_e_h_2, c_n, s13, s14)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12665, 12470, 12471, 12656])).
% 87.32/87.53 tff(12667,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)), introduced(assumption)).
% 87.32/87.53 tff(12668,assumption,(node11(c_e_h_2, c_n, s13, s14)), introduced(assumption)).
% 87.32/87.53 tff(12669,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)) | (~node11(c_e_h_2, c_n, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)) | (~node11(c_e_h_2, c_n, s13, s14)))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12670,plain,
% 87.32/87.53 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~node11(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)) | (~node11(c_e_h_2, c_n, s13, s14)))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12671,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~node11(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)) | (~node11(c_e_h_2, c_n, s13, s14))))),
% 87.32/87.53 inference(monotonicity,[status(thm)],[12670])).
% 87.32/87.53 tff(12672,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~node11(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)) | (~node11(c_e_h_2, c_n, s13, s14)))),
% 87.32/87.53 inference(transitivity,[status(thm)],[12671, 12669])).
% 87.32/87.53 tff(12673,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~node11(c_e_h_2, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12674,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)) | (~node11(c_e_h_2, c_n, s13, s14))),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12673, 12672])).
% 87.32/87.53 tff(12675,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12674, 1161, 12470, 12668, 12667])).
% 87.32/87.53 tff(12676,plain,((~node11(c_e_h_2, c_n, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12677,plain,
% 87.32/87.53 (~node11(c_e_h_2, c_n, s13, s14)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12676, 12470, 12667])).
% 87.32/87.53 tff(12678,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_2, c_n, s13, s14) | node11(c_e_h_2, c_n, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_2, c_n, s13, s14) | node11(c_e_h_2, c_n, s13, s14))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12679,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_2, c_n, s13, s14) | node11(c_e_h_2, c_n, s13, s14))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12680,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_2, c_n, s13, s14) | node11(c_e_h_2, c_n, s13, s14)),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12679, 12678])).
% 87.32/87.53 tff(12681,plain,
% 87.32/87.53 (node10(c_e_h_2, c_n, s13, s14) | node11(c_e_h_2, c_n, s13, s14)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12680, 1092, 10040])).
% 87.32/87.53 tff(12682,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12681, 12677, 12666])).
% 87.32/87.53 tff(12683,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12684,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12683, 12655, 12471, 12470])).
% 87.32/87.53 tff(12685,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)), introduced(assumption)).
% 87.32/87.53 tff(12686,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)), introduced(assumption)).
% 87.32/87.53 tff(12687,plain,
% 87.32/87.53 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12688,plain,
% 87.32/87.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12689,plain,
% 87.32/87.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12688, 12687])).
% 87.32/87.53 tff(12690,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12689, 1142, 12686, 12685])).
% 87.32/87.53 tff(12691,plain,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12692,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12691, 12684])).
% 87.32/87.53 tff(12693,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12571, 12484, 9152, 4433, 12472, 12473])).
% 87.32/87.53 tff(12694,plain,
% 87.32/87.53 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12695,plain,
% 87.32/87.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12696,plain,
% 87.32/87.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12))),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12695, 12694])).
% 87.32/87.53 tff(12697,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12696, 1048, 12693])).
% 87.32/87.53 tff(12698,plain,
% 87.32/87.53 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12699,plain,
% 87.32/87.53 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12700,plain,
% 87.32/87.53 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12699, 12698])).
% 87.32/87.53 tff(12701,plain,
% 87.32/87.53 (~node9(c_e_h_2, c_m, s12)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12700, 1062, 12697])).
% 87.32/87.53 tff(12702,plain,
% 87.32/87.53 (~node9(c_e_h_2, c_m, s11)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12652, 1062, 12649])).
% 87.32/87.53 tff(12703,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12643, 12702, 4433])).
% 87.32/87.53 tff(12704,assumption,(~node9(c_e_h_2, c_m, s12)), introduced(assumption)).
% 87.32/87.53 tff(12705,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)), introduced(assumption)).
% 87.32/87.53 tff(12706,assumption,(node10(c_e_h_2, c_m, s12, s13)), introduced(assumption)).
% 87.32/87.53 tff(12707,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | (~node10(c_e_h_2, c_m, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | (~node10(c_e_h_2, c_m, s12, s13)))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12708,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | (~node10(c_e_h_2, c_m, s12, s13)))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12709,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | (~node10(c_e_h_2, c_m, s12, s13))),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12708, 12707])).
% 87.32/87.53 tff(12710,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12709, 1076, 12705, 12706, 12704])).
% 87.32/87.53 tff(12711,plain,((~node10(c_e_h_2, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | node9(c_e_h_2, c_m, s12)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12712,plain,
% 87.32/87.53 (~node10(c_e_h_2, c_m, s12, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12711, 12705, 12704])).
% 87.32/87.53 tff(12713,assumption,(node11(c_e_h_2, c_m, s12, s13)), introduced(assumption)).
% 87.32/87.53 tff(12714,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | (~node11(c_e_h_2, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | (~node11(c_e_h_2, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12715,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | (~node11(c_e_h_2, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12716,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | (~node11(c_e_h_2, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12715, 12714])).
% 87.32/87.53 tff(12717,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12716, 1130, 12705, 12612, 12713])).
% 87.32/87.53 tff(12718,plain,((~node11(c_e_h_2, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12719,plain,
% 87.32/87.53 (~node11(c_e_h_2, c_m, s12, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12718, 12705, 12612])).
% 87.32/87.53 tff(12720,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_2, c_m, s12, s13) | node11(c_e_h_2, c_m, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_2, c_m, s12, s13) | node11(c_e_h_2, c_m, s12, s13))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12721,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_2, c_m, s12, s13) | node11(c_e_h_2, c_m, s12, s13))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12722,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_2, c_m, s12, s13) | node11(c_e_h_2, c_m, s12, s13)),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12721, 12720])).
% 87.32/87.53 tff(12723,plain,
% 87.32/87.53 (node10(c_e_h_2, c_m, s12, s13) | node11(c_e_h_2, c_m, s12, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12722, 1092, 9599])).
% 87.32/87.53 tff(12724,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12723, 12719, 12712])).
% 87.32/87.53 tff(12725,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12) | node9(c_e_h_2, c_m, s12)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12726,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12725, 12703, 12701, 12692])).
% 87.32/87.53 tff(12727,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s10) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12728,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12727, 12469, 4431, 9150, 9512, 12462, 9075, 12461])).
% 87.32/87.53 tff(12729,plain,
% 87.32/87.53 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12730,plain,
% 87.32/87.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12731,plain,
% 87.32/87.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14))),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12730, 12729])).
% 87.32/87.53 tff(12732,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12731, 1048, 12728])).
% 87.32/87.53 tff(12733,assumption,(node9(c_e_h_2, c_m, s14)), introduced(assumption)).
% 87.32/87.53 tff(12734,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14)), introduced(assumption)).
% 87.32/87.53 tff(12735,plain,
% 87.32/87.53 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12736,plain,
% 87.32/87.53 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12737,plain,
% 87.32/87.53 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14)),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12736, 12735])).
% 87.32/87.53 tff(12738,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12737, 1062, 12734, 12733])).
% 87.32/87.53 tff(12739,plain,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14) | (~node9(c_e_h_2, c_m, s14))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12740,plain,
% 87.32/87.53 (~node9(c_e_h_2, c_m, s14)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12739, 12732])).
% 87.32/87.53 tff(12741,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12483, 9150])).
% 87.32/87.53 tff(12742,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12571, 12741, 9075, 12461, 12462, 4431])).
% 87.32/87.53 tff(12743,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12696, 1048, 12742])).
% 87.32/87.53 tff(12744,plain,
% 87.32/87.53 (~node9(c_e_h_2, c_m, s12)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12700, 1062, 12743])).
% 87.32/87.53 tff(12745,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[4391, 9083])).
% 87.32/87.53 tff(12746,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[1440, 1402, 1412])).
% 87.32/87.53 tff(12747,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[1445, 1048, 2065])).
% 87.32/87.53 tff(12748,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2063, 1484])).
% 87.32/87.53 tff(12749,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2091, 2065, 2074, 12748])).
% 87.32/87.53 tff(12750,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[3095, 12749, 3057, 2553, 3061])).
% 87.32/87.53 tff(12751,plain,
% 87.32/87.53 (node9(c_e_h_2, c_m, s5)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[1512, 12750, 1484])).
% 87.32/87.53 tff(12752,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[1449, 1062, 12751, 12747])).
% 87.32/87.53 tff(12753,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12754,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12753, 12746, 3061, 3057, 2074, 2553])).
% 87.32/87.53 tff(12755,plain,
% 87.32/87.53 (node9(c_e_h_2, c_m, s4)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[1481, 12754])).
% 87.32/87.53 tff(12756,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[1453, 1048, 1402])).
% 87.32/87.53 tff(12757,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[1457, 1062, 12756, 12755])).
% 87.32/87.53 tff(12758,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12759,plain,
% 87.32/87.53 ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4))),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12758, 1362])).
% 87.32/87.53 tff(12760,plain,
% 87.32/87.53 ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6))),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12759, 982])).
% 87.32/87.53 tff(12761,plain,
% 87.32/87.53 ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6))),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12760, 2057])).
% 87.32/87.53 tff(12762,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12761, 2553, 3061])).
% 87.32/87.53 tff(12763,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2579, 2553])).
% 87.32/87.53 tff(12764,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s7)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2583, 1048, 12763])).
% 87.32/87.53 tff(12765,plain,
% 87.32/87.53 (~node9(c_e_h_2, c_m, s7)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2587, 1062, 12764])).
% 87.32/87.53 tff(12766,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2612, 12765])).
% 87.32/87.53 tff(12767,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[3747, 12766, 3705, 12762])).
% 87.32/87.53 tff(12768,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[3090, 1142, 2590])).
% 87.32/87.53 tff(12769,plain,
% 87.32/87.53 (~node10(c_e_h_2, c_n, s7, s8)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[3086, 3057, 3077, 3061])).
% 87.32/87.53 tff(12770,plain,
% 87.32/87.53 (~node11(c_e_h_2, c_n, s7, s8)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[3070, 3057, 3065])).
% 87.32/87.53 tff(12771,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[3075, 12770, 12769])).
% 87.32/87.53 tff(12772,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12773,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s8)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12772, 12768, 3065, 3061])).
% 87.32/87.53 tff(12774,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s8)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[4374, 12773, 4333, 3705, 4335])).
% 87.32/87.53 tff(12775,plain,
% 87.32/87.53 (~node11(c_e_h_2, c_m, s7, s8)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2597, 12774, 2590])).
% 87.32/87.53 tff(12776,plain,
% 87.32/87.53 (node10(c_e_h_2, c_m, s7, s8)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2602, 12775])).
% 87.32/87.53 tff(12777,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[2609, 1076, 12774, 12776, 2589])).
% 87.32/87.53 tff(12778,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7) | node9(c_e_h_2, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12779,plain,
% 87.32/87.53 (node9(c_e_h_2, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12778, 2131])).
% 87.32/87.53 tff(12780,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12779, 12765, 4335, 3705, 3061, 12763])).
% 87.32/87.53 tff(12781,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12513, 12780, 12486, 12487])).
% 87.32/87.53 tff(12782,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12460, 12781, 12767])).
% 87.32/87.53 tff(12783,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12784,plain,
% 87.32/87.53 ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12783, 2547])).
% 87.32/87.53 tff(12785,plain,
% 87.32/87.53 ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9))),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12784, 4272])).
% 87.32/87.53 tff(12786,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12785, 12741, 3676, 12745])).
% 87.32/87.53 tff(12787,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12648, 1048, 12786])).
% 87.32/87.53 tff(12788,plain,
% 87.32/87.53 (~node9(c_e_h_2, c_m, s11)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12652, 1062, 12787])).
% 87.32/87.53 tff(12789,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12643, 12788, 4431])).
% 87.32/87.53 tff(12790,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12725, 12789, 12744])).
% 87.32/87.53 tff(12791,plain,
% 87.32/87.53 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12654, 9512, 12461, 9150, 9075, 4431, 12462])).
% 87.32/87.53 tff(12792,plain,
% 87.32/87.53 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12793,plain,
% 87.32/87.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12794,plain,
% 87.32/87.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13))),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12793, 12792])).
% 87.32/87.53 tff(12795,plain,
% 87.32/87.53 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12794, 1048, 12791])).
% 87.32/87.53 tff(12796,plain,
% 87.32/87.53 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12797,plain,
% 87.32/87.53 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12798,plain,
% 87.32/87.53 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13)),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12797, 12796])).
% 87.32/87.53 tff(12799,plain,
% 87.32/87.53 (~node9(c_e_h_2, c_m, s13)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12798, 1062, 12795])).
% 87.32/87.53 tff(12800,assumption,(~node9(c_e_h_2, c_m, s13)), introduced(assumption)).
% 87.32/87.53 tff(12801,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)), introduced(assumption)).
% 87.32/87.53 tff(12802,assumption,(node11(c_e_h_2, c_m, s13, s14)), introduced(assumption)).
% 87.32/87.53 tff(12803,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | (~node11(c_e_h_2, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | (~node11(c_e_h_2, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12804,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | (~node11(c_e_h_2, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12805,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | (~node11(c_e_h_2, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)),
% 87.32/87.53 inference(modus_ponens,[status(thm)],[12804, 12803])).
% 87.32/87.53 tff(12806,plain,
% 87.32/87.53 ($false),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12805, 1130, 12802, 12686, 12801])).
% 87.32/87.53 tff(12807,plain,((~node11(c_e_h_2, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.53 tff(12808,plain,
% 87.32/87.53 (~node11(c_e_h_2, c_m, s13, s14)),
% 87.32/87.53 inference(unit_resolution,[status(thm)],[12807, 12801, 12686])).
% 87.32/87.53 tff(12809,plain,
% 87.32/87.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_2, c_m, s13, s14) | node11(c_e_h_2, c_m, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_2, c_m, s13, s14) | node11(c_e_h_2, c_m, s13, s14))),
% 87.32/87.53 inference(rewrite,[status(thm)],[])).
% 87.32/87.53 tff(12810,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_2, c_m, s13, s14) | node11(c_e_h_2, c_m, s13, s14))),
% 87.32/87.53 inference(quant_inst,[status(thm)],[])).
% 87.32/87.53 tff(12811,plain,
% 87.32/87.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_2, c_m, s13, s14) | node11(c_e_h_2, c_m, s13, s14)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12810, 12809])).
% 87.32/87.54 tff(12812,plain,
% 87.32/87.54 (node10(c_e_h_2, c_m, s13, s14) | node11(c_e_h_2, c_m, s13, s14)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12811, 1092, 10040])).
% 87.32/87.54 tff(12813,plain,
% 87.32/87.54 (node10(c_e_h_2, c_m, s13, s14)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12812, 12808])).
% 87.32/87.54 tff(12814,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | node9(c_e_h_2, c_m, s13) | (~node10(c_e_h_2, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | node9(c_e_h_2, c_m, s13) | (~node10(c_e_h_2, c_m, s13, s14)))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12815,plain,
% 87.32/87.54 ((node9(c_e_h_2, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | (~node10(c_e_h_2, c_m, s13, s14))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | node9(c_e_h_2, c_m, s13) | (~node10(c_e_h_2, c_m, s13, s14)))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12816,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | (~node10(c_e_h_2, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | node9(c_e_h_2, c_m, s13) | (~node10(c_e_h_2, c_m, s13, s14))))),
% 87.32/87.54 inference(monotonicity,[status(thm)],[12815])).
% 87.32/87.54 tff(12817,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | (~node10(c_e_h_2, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | node9(c_e_h_2, c_m, s13) | (~node10(c_e_h_2, c_m, s13, s14)))),
% 87.32/87.54 inference(transitivity,[status(thm)],[12816, 12814])).
% 87.32/87.54 tff(12818,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | (~node10(c_e_h_2, c_m, s13, s14)))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12819,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | node9(c_e_h_2, c_m, s13) | (~node10(c_e_h_2, c_m, s13, s14))),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12818, 12817])).
% 87.32/87.54 tff(12820,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12819, 1076, 12813, 12801, 12800])).
% 87.32/87.54 tff(12821,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)) | node9(c_e_h_2, c_m, s13) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12822,plain,
% 87.32/87.54 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12821, 12799, 12790])).
% 87.32/87.54 tff(12823,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)), introduced(assumption)).
% 87.32/87.54 tff(12824,assumption,(~node9(c_e_h_2, c_m, s14)), introduced(assumption)).
% 87.32/87.54 tff(12825,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)), introduced(assumption)).
% 87.32/87.54 tff(12826,assumption,(node10(c_e_h_2, c_m, s14, s15)), introduced(assumption)).
% 87.32/87.54 tff(12827,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | (~node10(c_e_h_2, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | (~node10(c_e_h_2, c_m, s14, s15)))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12828,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | (~node10(c_e_h_2, c_m, s14, s15)))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12829,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | (~node10(c_e_h_2, c_m, s14, s15))),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12828, 12827])).
% 87.32/87.54 tff(12830,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12829, 1076, 12825, 12826, 12824])).
% 87.32/87.54 tff(12831,plain,((~node10(c_e_h_2, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | node9(c_e_h_2, c_m, s14)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12832,plain,
% 87.32/87.54 (~node10(c_e_h_2, c_m, s14, s15)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12831, 12825, 12824])).
% 87.32/87.54 tff(12833,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_2, c_m, s14, s15) | node11(c_e_h_2, c_m, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_2, c_m, s14, s15) | node11(c_e_h_2, c_m, s14, s15))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12834,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_2, c_m, s14, s15) | node11(c_e_h_2, c_m, s14, s15))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12835,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_2, c_m, s14, s15) | node11(c_e_h_2, c_m, s14, s15)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12834, 12833])).
% 87.32/87.54 tff(12836,plain,
% 87.32/87.54 (node10(c_e_h_2, c_m, s14, s15) | node11(c_e_h_2, c_m, s14, s15)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12835, 1092, 10504])).
% 87.32/87.54 tff(12837,plain,
% 87.32/87.54 (node11(c_e_h_2, c_m, s14, s15)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12836, 12832])).
% 87.32/87.54 tff(12838,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | (~node11(c_e_h_2, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | (~node11(c_e_h_2, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12839,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | (~node11(c_e_h_2, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12840,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | (~node11(c_e_h_2, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12839, 12838])).
% 87.32/87.54 tff(12841,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12840, 1130, 12825, 12837, 12823])).
% 87.32/87.54 tff(12842,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14) | node9(c_e_h_2, c_m, s14)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12843,plain,
% 87.32/87.54 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12842, 12822, 12740])).
% 87.32/87.54 tff(12844,plain,
% 87.32/87.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12845,plain,
% 87.32/87.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12846,plain,
% 87.32/87.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12845, 12844])).
% 87.32/87.54 tff(12847,plain,
% 87.32/87.54 ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12846, 1521])).
% 87.32/87.54 tff(12848,plain,
% 87.32/87.54 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s15)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12847, 12843])).
% 87.32/87.54 tff(12849,plain,
% 87.32/87.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s15))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12850,plain,
% 87.32/87.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s15))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12851,plain,
% 87.32/87.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s15)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12850, 12849])).
% 87.32/87.54 tff(12852,plain,
% 87.32/87.54 (~node20(c_e_h_2, c_r, s15)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12851, 1535, 12848])).
% 87.32/87.54 tff(12853,assumption,(~node20(c_e_h_2, c_r, s15)), introduced(assumption)).
% 87.32/87.54 tff(12854,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s16)), introduced(assumption)).
% 87.32/87.54 tff(12855,assumption,(node21(c_e_h_2, c_r, s15, s16)), introduced(assumption)).
% 87.32/87.54 tff(12856,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | node20(c_e_h_2, c_r, s15) | (~node21(c_e_h_2, c_r, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | node20(c_e_h_2, c_r, s15) | (~node21(c_e_h_2, c_r, s15, s16)))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12857,plain,
% 87.32/87.54 ((node20(c_e_h_2, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | (~node21(c_e_h_2, c_r, s15, s16))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | node20(c_e_h_2, c_r, s15) | (~node21(c_e_h_2, c_r, s15, s16)))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12858,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | (~node21(c_e_h_2, c_r, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | node20(c_e_h_2, c_r, s15) | (~node21(c_e_h_2, c_r, s15, s16))))),
% 87.32/87.54 inference(monotonicity,[status(thm)],[12857])).
% 87.32/87.54 tff(12859,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | (~node21(c_e_h_2, c_r, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | node20(c_e_h_2, c_r, s15) | (~node21(c_e_h_2, c_r, s15, s16)))),
% 87.32/87.54 inference(transitivity,[status(thm)],[12858, 12856])).
% 87.32/87.54 tff(12860,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | (~node21(c_e_h_2, c_r, s15, s16)))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12861,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | node20(c_e_h_2, c_r, s15) | (~node21(c_e_h_2, c_r, s15, s16))),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12860, 12859])).
% 87.32/87.54 tff(12862,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12861, 51, 12853, 12854, 12855])).
% 87.32/87.54 tff(12863,plain,((~node21(c_e_h_2, c_r, s15, s16)) | node20(c_e_h_2, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12864,plain,
% 87.32/87.54 (~node21(c_e_h_2, c_r, s15, s16)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12863, 12854, 12853])).
% 87.32/87.54 tff(12865,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s15)), introduced(assumption)).
% 87.32/87.54 tff(12866,assumption,(node22(c_e_h_2, c_r, s15, s16)), introduced(assumption)).
% 87.32/87.54 tff(12867,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | (~node22(c_e_h_2, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | (~node22(c_e_h_2, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12868,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | (~node22(c_e_h_2, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12869,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | (~node22(c_e_h_2, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12868, 12867])).
% 87.32/87.54 tff(12870,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12869, 107, 12865, 12854, 12866])).
% 87.32/87.54 tff(12871,plain,((~node22(c_e_h_2, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s16))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12872,plain,
% 87.32/87.54 (~node22(c_e_h_2, c_r, s15, s16)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12871, 12854, 12865])).
% 87.32/87.54 tff(12873,plain,
% 87.32/87.54 (succ(s15, s16) <=> succ(s15, s16)),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12874,axiom,(succ(s15, s16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound16')).
% 87.32/87.54 tff(12875,plain,
% 87.32/87.54 (succ(s15, s16)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12874, 12873])).
% 87.32/87.54 tff(12876,plain,
% 87.32/87.54 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12877,plain,
% 87.32/87.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12878,plain,
% 87.32/87.54 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12877, 12876])).
% 87.32/87.54 tff(12879,plain,
% 87.32/87.54 (trans(s15, s16)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12878, 12875, 64])).
% 87.32/87.54 tff(12880,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_2, c_r, s15, s16) | node22(c_e_h_2, c_r, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_2, c_r, s15, s16) | node22(c_e_h_2, c_r, s15, s16))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12881,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_2, c_r, s15, s16) | node22(c_e_h_2, c_r, s15, s16))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12882,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_2, c_r, s15, s16) | node22(c_e_h_2, c_r, s15, s16)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12881, 12880])).
% 87.32/87.54 tff(12883,plain,
% 87.32/87.54 (node21(c_e_h_2, c_r, s15, s16) | node22(c_e_h_2, c_r, s15, s16)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12882, 81, 12879])).
% 87.32/87.54 tff(12884,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12883, 12872, 12864])).
% 87.32/87.54 tff(12885,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15) | node20(c_e_h_2, c_r, s15)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12886,plain,
% 87.32/87.54 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s15)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12885, 12852])).
% 87.32/87.54 tff(12887,plain,
% 87.32/87.54 (~m_and_h_gate_v_out(c_e_h_2, c_r, s16)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12886, 10512])).
% 87.32/87.54 tff(12888,plain,
% 87.32/87.54 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12889,plain,
% 87.32/87.54 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12890,plain,
% 87.32/87.54 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s16)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12889, 12888])).
% 87.32/87.54 tff(12891,plain,
% 87.32/87.54 (~m_user_v_ack(c_e_h_2, c_u, s16)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12890, 4481, 12887])).
% 87.32/87.54 tff(12892,plain,
% 87.32/87.54 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s16) | (~node25(s16)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s16) | (~node25(s16)))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12893,plain,
% 87.32/87.54 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s16) | (~node25(s16)))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12894,plain,
% 87.32/87.54 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s16) | (~node25(s16))),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12893, 12892])).
% 87.32/87.54 tff(12895,plain,
% 87.32/87.54 (~node25(s16)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12894, 4492, 12891])).
% 87.32/87.54 tff(12896,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s15)), introduced(assumption)).
% 87.32/87.54 tff(12897,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s10)), introduced(assumption)).
% 87.32/87.54 tff(12898,plain,
% 87.32/87.54 ((~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9))),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12298, 12075])).
% 87.32/87.54 tff(12899,plain,
% 87.32/87.54 (~node5(c_e_h_1, c_j, s8, s9)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12898, 12289])).
% 87.32/87.54 tff(12900,plain,
% 87.32/87.54 ((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9))),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12308, 11596])).
% 87.32/87.54 tff(12901,plain,
% 87.32/87.54 (~node6(c_e_h_1, c_j, s8, s9)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12900, 12289])).
% 87.32/87.54 tff(12902,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12316, 12901, 12899])).
% 87.32/87.54 tff(12903,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12904,assumption,(node6(c_e_h_1, c_j, s9, s10)), introduced(assumption)).
% 87.32/87.54 tff(12905,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s9)), introduced(assumption)).
% 87.32/87.54 tff(12906,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10)))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12907,plain,
% 87.32/87.54 (((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10)))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12908,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10))))),
% 87.32/87.54 inference(monotonicity,[status(thm)],[12907])).
% 87.32/87.54 tff(12909,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10)))),
% 87.32/87.54 inference(transitivity,[status(thm)],[12908, 12906])).
% 87.32/87.54 tff(12910,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12911,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10))),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12910, 12909])).
% 87.32/87.54 tff(12912,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12911, 899, 12905, 12904, 12897])).
% 87.32/87.54 tff(12913,plain,((~node6(c_e_h_1, c_j, s9, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12914,plain,
% 87.32/87.54 ((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12913, 12903])).
% 87.32/87.54 tff(12915,plain,
% 87.32/87.54 (~node6(c_e_h_1, c_j, s9, s10)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12914, 12897])).
% 87.32/87.54 tff(12916,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node5(c_e_h_1, c_j, s9, s10) | node6(c_e_h_1, c_j, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_1, c_j, s9, s10) | node6(c_e_h_1, c_j, s9, s10))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12917,plain,
% 87.32/87.54 ((node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10) | (~trans(s9, s10))) <=> ((~trans(s9, s10)) | node5(c_e_h_1, c_j, s9, s10) | node6(c_e_h_1, c_j, s9, s10))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12918,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node5(c_e_h_1, c_j, s9, s10) | node6(c_e_h_1, c_j, s9, s10)))),
% 87.32/87.54 inference(monotonicity,[status(thm)],[12917])).
% 87.32/87.54 tff(12919,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_1, c_j, s9, s10) | node6(c_e_h_1, c_j, s9, s10))),
% 87.32/87.54 inference(transitivity,[status(thm)],[12918, 12916])).
% 87.32/87.54 tff(12920,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10) | (~trans(s9, s10)))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12921,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_1, c_j, s9, s10) | node6(c_e_h_1, c_j, s9, s10)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12920, 12919])).
% 87.32/87.54 tff(12922,plain,
% 87.32/87.54 (node5(c_e_h_1, c_j, s9, s10) | node6(c_e_h_1, c_j, s9, s10)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12921, 881, 3175])).
% 87.32/87.54 tff(12923,plain,
% 87.32/87.54 (node5(c_e_h_1, c_j, s9, s10)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12922, 12915])).
% 87.32/87.54 tff(12924,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s9)), introduced(assumption)).
% 87.32/87.54 tff(12925,assumption,(node22(c_e_h_1, c_l, s8, s9)), introduced(assumption)).
% 87.32/87.54 tff(12926,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node22(c_e_h_1, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node22(c_e_h_1, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))),
% 87.32/87.54 inference(rewrite,[status(thm)],[])).
% 87.32/87.54 tff(12927,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node22(c_e_h_1, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))),
% 87.32/87.54 inference(quant_inst,[status(thm)],[])).
% 87.32/87.54 tff(12928,plain,
% 87.32/87.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node22(c_e_h_1, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8)),
% 87.32/87.54 inference(modus_ponens,[status(thm)],[12927, 12926])).
% 87.32/87.54 tff(12929,plain,
% 87.32/87.54 ($false),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12928, 107, 12278, 12924, 12925])).
% 87.32/87.54 tff(12930,plain,((~node22(c_e_h_1, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.54 tff(12931,plain,
% 87.32/87.54 (~node22(c_e_h_1, c_l, s8, s9)),
% 87.32/87.54 inference(unit_resolution,[status(thm)],[12930, 12924])).
% 87.32/87.54 tff(12932,plain,
% 87.32/87.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12933,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12934,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9)),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12933, 12932])).
% 87.32/87.55 tff(12935,plain,
% 87.32/87.55 (node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12934, 81, 2636])).
% 87.32/87.55 tff(12936,plain,
% 87.32/87.55 (node21(c_e_h_1, c_l, s8, s9)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12935, 12931])).
% 87.32/87.55 tff(12937,plain,
% 87.32/87.55 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12938,plain,
% 87.32/87.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12939,plain,
% 87.32/87.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12938, 12937])).
% 87.32/87.55 tff(12940,plain,
% 87.32/87.55 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12939, 1638, 6286])).
% 87.32/87.55 tff(12941,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s8))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12942,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s8))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12943,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s8)),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12942, 12941])).
% 87.32/87.55 tff(12944,plain,
% 87.32/87.55 (~node20(c_e_h_1, c_l, s8)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12943, 1535, 12940])).
% 87.32/87.55 tff(12945,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | node20(c_e_h_1, c_l, s8) | (~node21(c_e_h_1, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | node20(c_e_h_1, c_l, s8) | (~node21(c_e_h_1, c_l, s8, s9)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12946,plain,
% 87.32/87.55 ((node20(c_e_h_1, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node21(c_e_h_1, c_l, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | node20(c_e_h_1, c_l, s8) | (~node21(c_e_h_1, c_l, s8, s9)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12947,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node21(c_e_h_1, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | node20(c_e_h_1, c_l, s8) | (~node21(c_e_h_1, c_l, s8, s9))))),
% 87.32/87.55 inference(monotonicity,[status(thm)],[12946])).
% 87.32/87.55 tff(12948,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node21(c_e_h_1, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | node20(c_e_h_1, c_l, s8) | (~node21(c_e_h_1, c_l, s8, s9)))),
% 87.32/87.55 inference(transitivity,[status(thm)],[12947, 12945])).
% 87.32/87.55 tff(12949,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node21(c_e_h_1, c_l, s8, s9)))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12950,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | node20(c_e_h_1, c_l, s8) | (~node21(c_e_h_1, c_l, s8, s9))),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12949, 12948])).
% 87.32/87.55 tff(12951,plain,
% 87.32/87.55 ($false),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12950, 51, 12944, 12924, 12936])).
% 87.32/87.55 tff(12952,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.55 tff(12953,plain,
% 87.32/87.55 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12954,plain,
% 87.32/87.55 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12955,plain,
% 87.32/87.55 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9)),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12954, 12953])).
% 87.32/87.55 tff(12956,plain,
% 87.32/87.55 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12955, 801, 12952])).
% 87.32/87.55 tff(12957,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s1)), introduced(assumption)).
% 87.32/87.55 tff(12958,assumption,(node18(c_e_h_2, c_f, s0, s1)), introduced(assumption)).
% 87.32/87.55 tff(12959,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12960,plain,
% 87.32/87.55 (((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12961,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))))),
% 87.32/87.55 inference(monotonicity,[status(thm)],[12960])).
% 87.32/87.55 tff(12962,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))),
% 87.32/87.55 inference(transitivity,[status(thm)],[12961, 12959])).
% 87.32/87.55 tff(12963,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12964,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s0) | (~node18(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12963, 12962])).
% 87.32/87.55 tff(12965,plain,
% 87.32/87.55 ($false),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12964, 124, 10611, 12958, 12957])).
% 87.32/87.55 tff(12966,plain,((~node18(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.55 tff(12967,plain,
% 87.32/87.55 (~node18(c_e_h_2, c_f, s0, s1)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12966, 12957])).
% 87.32/87.55 tff(12968,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_f, s0, s1))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12969,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_f, s0, s1))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12970,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_f, s0, s1)),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12969, 12968])).
% 87.32/87.55 tff(12971,plain,
% 87.32/87.55 (node19(c_e_h_2, c_f, s0, s1)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12970, 141, 71])).
% 87.32/87.55 tff(12972,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_f, s0, s1) | node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s0, s1) | node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12973,plain,
% 87.32/87.55 ((node17(c_e_h_2, c_f, s0) | node18(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1))) <=> (node18(c_e_h_2, c_f, s0, s1) | node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12974,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s0) | node18(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_f, s0, s1) | node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1))))),
% 87.32/87.55 inference(monotonicity,[status(thm)],[12973])).
% 87.32/87.55 tff(12975,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s0) | node18(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s0, s1) | node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1)))),
% 87.32/87.55 inference(transitivity,[status(thm)],[12974, 12972])).
% 87.32/87.55 tff(12976,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s0) | node18(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12977,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s0, s1) | node17(c_e_h_2, c_f, s0) | (~node19(c_e_h_2, c_f, s0, s1))),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12976, 12975])).
% 87.32/87.55 tff(12978,plain,
% 87.32/87.55 (node18(c_e_h_2, c_f, s0, s1) | node17(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12977, 156, 12971])).
% 87.32/87.55 tff(12979,plain,
% 87.32/87.55 (node17(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12978, 12967])).
% 87.32/87.55 tff(12980,assumption,(node17(c_e_h_2, c_f, s0)), introduced(assumption)).
% 87.32/87.55 tff(12981,assumption,(node16(c_e_h_2, c_f, s0)), introduced(assumption)).
% 87.32/87.55 tff(12982,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s0)), introduced(assumption)).
% 87.32/87.55 tff(12983,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12984,plain,
% 87.32/87.55 ((m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~node17(c_e_h_2, c_f, s0))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12985,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~node17(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0))))),
% 87.32/87.55 inference(monotonicity,[status(thm)],[12984])).
% 87.32/87.55 tff(12986,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~node17(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(transitivity,[status(thm)],[12985, 12983])).
% 87.32/87.55 tff(12987,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~node17(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12988,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12987, 12986])).
% 87.32/87.55 tff(12989,plain,
% 87.32/87.55 (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12988, 245, 12980])).
% 87.32/87.55 tff(12990,plain,
% 87.32/87.55 (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12989, 12982])).
% 87.32/87.55 tff(12991,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12992,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(12993,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[12992, 12991])).
% 87.32/87.55 tff(12994,plain,
% 87.32/87.55 (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12993, 228, 12981])).
% 87.32/87.55 tff(12995,plain,
% 87.32/87.55 ($false),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12994, 12990, 12982])).
% 87.32/87.55 tff(12996,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node16(c_e_h_2, c_f, s0)) | (~node17(c_e_h_2, c_f, s0))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.55 tff(12997,plain,
% 87.32/87.55 (m_c_h_element_v_in1(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[12996, 12981, 12980])).
% 87.32/87.55 tff(12998,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(12999,plain,
% 87.32/87.55 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0))) <=> ((~node17(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(13000,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0))))),
% 87.32/87.55 inference(monotonicity,[status(thm)],[12999])).
% 87.32/87.55 tff(13001,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(transitivity,[status(thm)],[13000, 12998])).
% 87.32/87.55 tff(13002,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~node17(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(13003,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[13002, 13001])).
% 87.32/87.55 tff(13004,plain,
% 87.32/87.55 (m_c_h_element_v_in2(c_e_h_2, c_f, s0) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13003, 209, 12980])).
% 87.32/87.55 tff(13005,plain,
% 87.32/87.55 (m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13004, 12997])).
% 87.32/87.55 tff(13006,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~node16(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~node16(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(13007,plain,
% 87.32/87.55 (((~node16(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~node16(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(13008,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~node16(c_e_h_2, c_f, s0))))),
% 87.32/87.55 inference(monotonicity,[status(thm)],[13007])).
% 87.32/87.55 tff(13009,plain,
% 87.32/87.55 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~node16(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(transitivity,[status(thm)],[13008, 13006])).
% 87.32/87.55 tff(13010,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(13011,plain,
% 87.32/87.55 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | (~node16(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[13010, 13009])).
% 87.32/87.55 tff(13012,plain,
% 87.32/87.55 ((~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13011, 263, 12981])).
% 87.32/87.55 tff(13013,plain,
% 87.32/87.55 ($false),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13012, 13005, 12997])).
% 87.32/87.55 tff(13014,plain,((~node16(c_e_h_2, c_f, s0)) | (~node17(c_e_h_2, c_f, s0))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.55 tff(13015,plain,
% 87.32/87.55 (~node16(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13014, 12979])).
% 87.32/87.55 tff(13016,plain,
% 87.32/87.55 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(13017,plain,
% 87.32/87.55 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(13018,plain,
% 87.32/87.55 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0)),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[13017, 13016])).
% 87.32/87.55 tff(13019,plain,
% 87.32/87.55 (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13018, 2218, 97])).
% 87.32/87.55 tff(13020,plain,
% 87.32/87.55 ((~node17(c_e_h_2, c_f, s0)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0))),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13003, 209, 13019])).
% 87.32/87.55 tff(13021,plain,
% 87.32/87.55 (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13020, 12979])).
% 87.32/87.55 tff(13022,assumption,(node14(c_e_h_2, c_f, s0, s1)), introduced(assumption)).
% 87.32/87.55 tff(13023,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(13024,plain,
% 87.32/87.55 (((~node14(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))),
% 87.32/87.55 inference(rewrite,[status(thm)],[])).
% 87.32/87.55 tff(13025,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))))),
% 87.32/87.55 inference(monotonicity,[status(thm)],[13024])).
% 87.32/87.55 tff(13026,plain,
% 87.32/87.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))),
% 87.32/87.55 inference(transitivity,[status(thm)],[13025, 13023])).
% 87.32/87.55 tff(13027,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))),
% 87.32/87.55 inference(quant_inst,[status(thm)],[])).
% 87.32/87.55 tff(13028,plain,
% 87.32/87.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 87.32/87.55 inference(modus_ponens,[status(thm)],[13027, 13026])).
% 87.32/87.55 tff(13029,plain,
% 87.32/87.55 ($false),
% 87.32/87.55 inference(unit_resolution,[status(thm)],[13028, 283, 13022, 13021, 12957])).
% 87.32/87.55 tff(13030,plain,((~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.55 tff(13031,plain,
% 87.32/87.55 (~node14(c_e_h_2, c_f, s0, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13030, 12957])).
% 87.32/87.56 tff(13032,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s0, s1)) | node16(c_e_h_2, c_f, s0) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s0, s1)) | node16(c_e_h_2, c_f, s0) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13033,plain,
% 87.32/87.56 ((node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1))) <=> ((~node19(c_e_h_2, c_f, s0, s1)) | node16(c_e_h_2, c_f, s0) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13034,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s0, s1)) | node16(c_e_h_2, c_f, s0) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1)))),
% 87.32/87.56 inference(monotonicity,[status(thm)],[13033])).
% 87.32/87.56 tff(13035,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s0, s1)) | node16(c_e_h_2, c_f, s0) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1))),
% 87.32/87.56 inference(transitivity,[status(thm)],[13034, 13032])).
% 87.32/87.56 tff(13036,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13037,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s0, s1)) | node16(c_e_h_2, c_f, s0) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13036, 13035])).
% 87.32/87.56 tff(13038,plain,
% 87.32/87.56 (node16(c_e_h_2, c_f, s0) | node15(c_e_h_2, c_f, s0, s1) | node14(c_e_h_2, c_f, s0, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13037, 189, 12971])).
% 87.32/87.56 tff(13039,plain,
% 87.32/87.56 (node15(c_e_h_2, c_f, s0, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13038, 13031, 13015])).
% 87.32/87.56 tff(13040,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13041,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13042,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13041, 13040])).
% 87.32/87.56 tff(13043,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13042, 173, 10611, 13039, 12957])).
% 87.32/87.56 tff(13044,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13045,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_q, s1)), introduced(assumption)).
% 87.32/87.56 tff(13046,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s1)), introduced(assumption)).
% 87.32/87.56 tff(13047,plain,
% 87.32/87.56 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13048,plain,
% 87.32/87.56 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13049,plain,
% 87.32/87.56 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13048, 13047])).
% 87.32/87.56 tff(13050,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13049, 1666, 13046, 13045])).
% 87.32/87.56 tff(13051,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13052,plain,
% 87.32/87.56 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13051, 13044])).
% 87.32/87.56 tff(13053,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)), introduced(assumption)).
% 87.32/87.56 tff(13054,assumption,(node20(c_e_h_2, c_q, s1)), introduced(assumption)).
% 87.32/87.56 tff(13055,plain,
% 87.32/87.56 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13056,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13057,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13056, 13055])).
% 87.32/87.56 tff(13058,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13057, 37, 13054, 13053])).
% 87.32/87.56 tff(13059,plain,((~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13060,plain,
% 87.32/87.56 (~node20(c_e_h_2, c_q, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13059, 13052])).
% 87.32/87.56 tff(13061,assumption,(~node20(c_e_h_2, c_q, s1)), introduced(assumption)).
% 87.32/87.56 tff(13062,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s2)), introduced(assumption)).
% 87.32/87.56 tff(13063,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13064,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13065,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2))),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13064, 13063])).
% 87.32/87.56 tff(13066,plain,
% 87.32/87.56 (node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2))),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13065, 51])).
% 87.32/87.56 tff(13067,plain,
% 87.32/87.56 (~node21(c_e_h_2, c_q, s1, s2)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13066, 13062, 13061])).
% 87.32/87.56 tff(13068,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13069,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13070,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13069, 13068])).
% 87.32/87.56 tff(13071,plain,
% 87.32/87.56 (node22(c_e_h_2, c_q, s1, s2)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13070, 81, 344, 13067])).
% 87.32/87.56 tff(13072,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13073,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13074,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13073, 13072])).
% 87.32/87.56 tff(13075,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13074, 107, 13062, 10639, 13071])).
% 87.32/87.56 tff(13076,plain,((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | node20(c_e_h_2, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13077,plain,
% 87.32/87.56 (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13076, 13060])).
% 87.32/87.56 tff(13078,plain,
% 87.32/87.56 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s2))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13079,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s2))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13080,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s2)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13079, 13078])).
% 87.32/87.56 tff(13081,plain,
% 87.32/87.56 (node3(c_e_h_2, c_e_h_3, s2)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13080, 7448, 814])).
% 87.32/87.56 tff(13082,plain,
% 87.32/87.56 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s2)) | (~node3(c_e_h_2, c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s2)) | (~node3(c_e_h_2, c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13083,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s2)) | (~node3(c_e_h_2, c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13084,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s2)) | (~node3(c_e_h_2, c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13083, 13082])).
% 87.32/87.56 tff(13085,plain,
% 87.32/87.56 ((~m_cell_v_ack(c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13084, 836, 13081])).
% 87.32/87.56 tff(13086,plain,
% 87.32/87.56 (~m_cell_v_ack(c_e_h_3, s2)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13085, 13077])).
% 87.32/87.56 tff(13087,plain,
% 87.32/87.56 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)) | m_cell_v_ack(c_e_h_3, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)) | m_cell_v_ack(c_e_h_3, s2))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13088,plain,
% 87.32/87.56 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)) | m_cell_v_ack(c_e_h_3, s2))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13089,plain,
% 87.32/87.56 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)) | m_cell_v_ack(c_e_h_3, s2)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13088, 13087])).
% 87.32/87.56 tff(13090,plain,
% 87.32/87.56 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13089, 848, 13086])).
% 87.32/87.56 tff(13091,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s3)), introduced(assumption)).
% 87.32/87.56 tff(13092,assumption,(node6(c_e_h_3, c_j, s2, s3)), introduced(assumption)).
% 87.32/87.56 tff(13093,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13094,plain,
% 87.32/87.56 (((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13095,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3))))),
% 87.32/87.56 inference(monotonicity,[status(thm)],[13094])).
% 87.32/87.56 tff(13096,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 87.32/87.56 inference(transitivity,[status(thm)],[13095, 13093])).
% 87.32/87.56 tff(13097,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13098,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3))),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13097, 13096])).
% 87.32/87.56 tff(13099,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13098, 899, 10661, 13091, 13092])).
% 87.32/87.56 tff(13100,plain,((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13101,plain,
% 87.32/87.56 (~node6(c_e_h_3, c_j, s2, s3)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13100, 13091])).
% 87.32/87.56 tff(13102,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)), introduced(assumption)).
% 87.32/87.56 tff(13103,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s1)), introduced(assumption)).
% 87.32/87.56 tff(13104,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s0)), introduced(assumption)).
% 87.32/87.56 tff(13105,plain,
% 87.32/87.56 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13106,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13105, 299, 13104])).
% 87.32/87.56 tff(13107,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13108,plain,
% 87.32/87.56 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X)))),
% 87.32/87.56 inference(bind,[status(th)],[])).
% 87.32/87.56 tff(13109,plain,
% 87.32/87.56 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 87.32/87.56 inference(quant_intro,[status(thm)],[13108])).
% 87.32/87.56 tff(13110,plain,
% 87.32/87.56 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13111,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_44')).
% 87.32/87.56 tff(13112,plain,
% 87.32/87.56 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13111, 13110])).
% 87.32/87.56 tff(13113,plain,(
% 87.32/87.56 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 87.32/87.56 inference(skolemize,[status(sab)],[13112])).
% 87.32/87.56 tff(13114,plain,
% 87.32/87.56 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13113, 13109])).
% 87.32/87.56 tff(13115,plain,
% 87.32/87.56 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13116,plain,
% 87.32/87.56 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13117,plain,
% 87.32/87.56 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13116, 13115])).
% 87.32/87.56 tff(13118,plain,
% 87.32/87.56 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13117, 13114, 13107])).
% 87.32/87.56 tff(13119,plain,
% 87.32/87.56 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s0))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13120,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s0))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13121,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s0)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13120, 13119])).
% 87.32/87.56 tff(13122,plain,
% 87.32/87.56 (~node20(c_e_h_3, c_k, s0)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13121, 37, 13118])).
% 87.32/87.56 tff(13123,assumption,(~node20(c_e_h_3, c_k, s0)), introduced(assumption)).
% 87.32/87.56 tff(13124,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s1)), introduced(assumption)).
% 87.32/87.56 tff(13125,assumption,(node22(c_e_h_3, c_k, s0, s1)), introduced(assumption)).
% 87.32/87.56 tff(13126,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13127,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13128,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13127, 13126])).
% 87.32/87.56 tff(13129,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13128, 107, 10547, 13125, 13124])).
% 87.32/87.56 tff(13130,plain,((~node22(c_e_h_3, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13131,plain,
% 87.32/87.56 (~node22(c_e_h_3, c_k, s0, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13130, 13124])).
% 87.32/87.56 tff(13132,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13133,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13134,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13133, 13132])).
% 87.32/87.56 tff(13135,plain,
% 87.32/87.56 (node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13134, 81, 71])).
% 87.32/87.56 tff(13136,plain,
% 87.32/87.56 (node21(c_e_h_3, c_k, s0, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13135, 13131])).
% 87.32/87.56 tff(13137,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1)))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13138,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1)))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13139,plain,
% 87.32/87.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1))),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13138, 13137])).
% 87.32/87.56 tff(13140,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13139, 51, 13136, 13124, 13123])).
% 87.32/87.56 tff(13141,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | node20(c_e_h_3, c_k, s0)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13142,plain,
% 87.32/87.56 (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13141, 13122])).
% 87.32/87.56 tff(13143,plain,
% 87.32/87.56 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13144,plain,
% 87.32/87.56 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13145,plain,
% 87.32/87.56 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13144, 13143])).
% 87.32/87.56 tff(13146,plain,
% 87.32/87.56 ($false),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13145, 10554, 13142, 13103])).
% 87.32/87.56 tff(13147,plain,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.56 tff(13148,plain,
% 87.32/87.56 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s1))),
% 87.32/87.56 inference(rewrite,[status(thm)],[])).
% 87.32/87.56 tff(13149,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s1))),
% 87.32/87.56 inference(quant_inst,[status(thm)],[])).
% 87.32/87.56 tff(13150,plain,
% 87.32/87.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s1)),
% 87.32/87.56 inference(modus_ponens,[status(thm)],[13149, 13148])).
% 87.32/87.56 tff(13151,plain,
% 87.32/87.56 (~node20(c_e_h_3, c_l, s1)),
% 87.32/87.56 inference(unit_resolution,[status(thm)],[13150, 37, 13147])).
% 87.32/87.56 tff(13152,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s2)), introduced(assumption)).
% 87.32/87.56 tff(13153,plain,
% 87.32/87.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13154,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13155,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1)),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13154, 13153])).
% 87.32/87.57 tff(13156,plain,
% 87.32/87.57 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2))),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13155, 107, 10581])).
% 87.32/87.57 tff(13157,plain,
% 87.32/87.57 (~node22(c_e_h_3, c_l, s1, s2)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13156, 13152])).
% 87.32/87.57 tff(13158,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13159,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13160,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2)),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13159, 13158])).
% 87.32/87.57 tff(13161,plain,
% 87.32/87.57 (node21(c_e_h_3, c_l, s1, s2)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13160, 81, 344, 13157])).
% 87.32/87.57 tff(13162,assumption,(~node20(c_e_h_3, c_l, s1)), introduced(assumption)).
% 87.32/87.57 tff(13163,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2)))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13164,plain,
% 87.32/87.57 ((node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2)))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13165,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2))))),
% 87.32/87.57 inference(monotonicity,[status(thm)],[13164])).
% 87.32/87.57 tff(13166,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2)))),
% 87.32/87.57 inference(transitivity,[status(thm)],[13165, 13163])).
% 87.32/87.57 tff(13167,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2)))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13168,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2))),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13167, 13166])).
% 87.32/87.57 tff(13169,plain,
% 87.32/87.57 ($false),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13168, 51, 13152, 13162, 13161])).
% 87.32/87.57 tff(13170,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.57 tff(13171,plain,
% 87.32/87.57 (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13170, 13151])).
% 87.32/87.57 tff(13172,plain,
% 87.32/87.57 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13173,plain,
% 87.32/87.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13174,plain,
% 87.32/87.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2)),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13173, 13172])).
% 87.32/87.57 tff(13175,plain,
% 87.32/87.57 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13174, 801, 13171])).
% 87.32/87.57 tff(13176,assumption,(node5(c_e_h_3, c_j, s2, s3)), introduced(assumption)).
% 87.32/87.57 tff(13177,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)), introduced(assumption)).
% 87.32/87.57 tff(13178,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13179,plain,
% 87.32/87.57 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13180,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3))))),
% 87.32/87.57 inference(monotonicity,[status(thm)],[13179])).
% 87.32/87.57 tff(13181,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)))),
% 87.32/87.57 inference(transitivity,[status(thm)],[13180, 13178])).
% 87.32/87.57 tff(13182,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13183,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3))),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13182, 13181])).
% 87.32/87.57 tff(13184,plain,
% 87.32/87.57 ($false),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13183, 862, 13091, 13102, 13177, 13176])).
% 87.32/87.57 tff(13185,plain,((~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.57 tff(13186,plain,
% 87.32/87.57 (~node5(c_e_h_3, c_j, s2, s3)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13185, 13091, 13175, 13102])).
% 87.32/87.57 tff(13187,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13188,plain,
% 87.32/87.57 ((node6(c_e_h_3, c_j, s2, s3) | node5(c_e_h_3, c_j, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13189,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s2, s3) | node5(c_e_h_3, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3)))),
% 87.32/87.57 inference(monotonicity,[status(thm)],[13188])).
% 87.32/87.57 tff(13190,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s2, s3) | node5(c_e_h_3, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3))),
% 87.32/87.57 inference(transitivity,[status(thm)],[13189, 13187])).
% 87.32/87.57 tff(13191,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s2, s3) | node5(c_e_h_3, c_j, s2, s3) | (~trans(s2, s3)))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13192,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3)),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13191, 13190])).
% 87.32/87.57 tff(13193,plain,
% 87.32/87.57 (node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13192, 881, 582])).
% 87.32/87.57 tff(13194,plain,
% 87.32/87.57 ($false),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13193, 13186, 13101])).
% 87.32/87.57 tff(13195,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.57 tff(13196,plain,
% 87.32/87.57 (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13195, 13090])).
% 87.32/87.57 tff(13197,plain,
% 87.32/87.57 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13198,plain,
% 87.32/87.57 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13199,plain,
% 87.32/87.57 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3)),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13198, 13197])).
% 87.32/87.57 tff(13200,plain,
% 87.32/87.57 (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13199, 309, 13196])).
% 87.32/87.57 tff(13201,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s4)), introduced(assumption)).
% 87.32/87.57 tff(13202,assumption,(node18(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 87.32/87.57 tff(13203,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s3)), introduced(assumption)).
% 87.32/87.57 tff(13204,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13205,plain,
% 87.32/87.57 (((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~node18(c_e_h_3, c_h, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13206,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~node18(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4))))),
% 87.32/87.57 inference(monotonicity,[status(thm)],[13205])).
% 87.32/87.57 tff(13207,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~node18(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.57 inference(transitivity,[status(thm)],[13206, 13204])).
% 87.32/87.57 tff(13208,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~node18(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13209,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4))),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13208, 13207])).
% 87.32/87.57 tff(13210,plain,
% 87.32/87.57 ($false),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13209, 124, 13203, 13201, 13202])).
% 87.32/87.57 tff(13211,plain,((~node18(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.57 tff(13212,plain,
% 87.32/87.57 ((~node18(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13211, 10718])).
% 87.32/87.57 tff(13213,plain,
% 87.32/87.57 (~node18(c_e_h_3, c_h, s3, s4)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13212, 13201])).
% 87.32/87.57 tff(13214,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s3)), introduced(assumption)).
% 87.32/87.57 tff(13215,assumption,(node15(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 87.32/87.57 tff(13216,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13217,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13218,plain,
% 87.32/87.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13217, 13216])).
% 87.32/87.57 tff(13219,plain,
% 87.32/87.57 ($false),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13218, 173, 13203, 13201, 13215])).
% 87.32/87.57 tff(13220,plain,((~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.57 tff(13221,plain,
% 87.32/87.57 ((~node15(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13220, 10718])).
% 87.32/87.57 tff(13222,plain,
% 87.32/87.57 (~node15(c_e_h_3, c_h, s3, s4)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13221, 13201])).
% 87.32/87.57 tff(13223,assumption,(node17(c_e_h_3, c_h, s3)), introduced(assumption)).
% 87.32/87.57 tff(13224,plain,
% 87.32/87.57 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13225,plain,
% 87.32/87.57 ((m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3))) <=> ((~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13226,plain,
% 87.32/87.57 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3)))),
% 87.32/87.57 inference(monotonicity,[status(thm)],[13225])).
% 87.32/87.57 tff(13227,plain,
% 87.32/87.57 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3))),
% 87.32/87.57 inference(transitivity,[status(thm)],[13226, 13224])).
% 87.32/87.57 tff(13228,plain,
% 87.32/87.57 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))),
% 87.32/87.57 inference(quant_inst,[status(thm)],[])).
% 87.32/87.57 tff(13229,plain,
% 87.32/87.57 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3)),
% 87.32/87.57 inference(modus_ponens,[status(thm)],[13228, 13227])).
% 87.32/87.57 tff(13230,plain,
% 87.32/87.57 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13229, 245, 13223])).
% 87.32/87.57 tff(13231,plain,
% 87.32/87.57 (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 87.32/87.57 inference(unit_resolution,[status(thm)],[13230, 13214])).
% 87.32/87.57 tff(13232,assumption,(~node15(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 87.32/87.57 tff(13233,assumption,(node14(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 87.32/87.57 tff(13234,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13235,plain,
% 87.32/87.57 (((~node14(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.57 inference(rewrite,[status(thm)],[])).
% 87.32/87.57 tff(13236,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4))))),
% 87.32/87.57 inference(monotonicity,[status(thm)],[13235])).
% 87.32/87.57 tff(13237,plain,
% 87.32/87.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.57 inference(transitivity,[status(thm)],[13236, 13234])).
% 87.32/87.58 tff(13238,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13239,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4))),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13238, 13237])).
% 87.32/87.58 tff(13240,plain,
% 87.32/87.58 ($false),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13239, 283, 13201, 13233, 13214])).
% 87.32/87.58 tff(13241,plain,((~node14(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.58 tff(13242,plain,
% 87.32/87.58 (~node14(c_e_h_3, c_h, s3, s4)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13241, 13214, 13201])).
% 87.32/87.58 tff(13243,assumption,(~node19(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 87.32/87.58 tff(13244,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_h, s3, s4))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13245,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_h, s3, s4))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13246,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_h, s3, s4)),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13245, 13244])).
% 87.32/87.58 tff(13247,plain,
% 87.32/87.58 ($false),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13246, 141, 679, 13243])).
% 87.32/87.58 tff(13248,plain,(node19(c_e_h_3, c_h, s3, s4)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.58 tff(13249,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s3) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s3) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13250,plain,
% 87.32/87.58 ((node16(c_e_h_3, c_h, s3) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4))) <=> (node16(c_e_h_3, c_h, s3) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13251,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s3) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s3) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4))))),
% 87.32/87.58 inference(monotonicity,[status(thm)],[13250])).
% 87.32/87.58 tff(13252,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s3) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s3) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.58 inference(transitivity,[status(thm)],[13251, 13249])).
% 87.32/87.58 tff(13253,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s3) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13254,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s3) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4))),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13253, 13252])).
% 87.32/87.58 tff(13255,plain,
% 87.32/87.58 (node16(c_e_h_3, c_h, s3) | node15(c_e_h_3, c_h, s3, s4) | node14(c_e_h_3, c_h, s3, s4)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13254, 189, 13248])).
% 87.32/87.58 tff(13256,plain,
% 87.32/87.58 (node16(c_e_h_3, c_h, s3)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13255, 13242, 13232])).
% 87.32/87.58 tff(13257,plain,
% 87.32/87.58 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13258,plain,
% 87.32/87.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13259,plain,
% 87.32/87.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13258, 13257])).
% 87.32/87.58 tff(13260,plain,
% 87.32/87.58 ($false),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13259, 228, 13256, 13214, 13231])).
% 87.32/87.58 tff(13261,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s3) | node15(c_e_h_3, c_h, s3, s4) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 87.32/87.58 tff(13262,plain,
% 87.32/87.58 (~node17(c_e_h_3, c_h, s3)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13261, 13222, 13214, 13201])).
% 87.32/87.58 tff(13263,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13264,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13265,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4))),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13264, 13263])).
% 87.32/87.58 tff(13266,plain,
% 87.32/87.58 (node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13265, 156, 13248])).
% 87.32/87.58 tff(13267,plain,
% 87.32/87.58 ($false),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13266, 13262, 13213])).
% 87.32/87.58 tff(13268,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.58 tff(13269,plain,
% 87.32/87.58 (m_c_h_element_v_in1(c_e_h_3, c_h, s3)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13268, 13201])).
% 87.32/87.58 tff(13270,plain,
% 87.32/87.58 (node17(c_e_h_3, c_h, s3)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13266, 13213])).
% 87.32/87.58 tff(13271,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s3)), introduced(assumption)).
% 87.32/87.58 tff(13272,plain,
% 87.32/87.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13273,plain,
% 87.32/87.58 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13274,plain,
% 87.32/87.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3))))),
% 87.32/87.58 inference(monotonicity,[status(thm)],[13273])).
% 87.32/87.58 tff(13275,plain,
% 87.32/87.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))),
% 87.32/87.58 inference(transitivity,[status(thm)],[13274, 13272])).
% 87.32/87.58 tff(13276,plain,
% 87.32/87.58 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13277,plain,
% 87.32/87.58 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3))),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13276, 13275])).
% 87.32/87.58 tff(13278,plain,
% 87.32/87.58 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3))),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13277, 209, 13271])).
% 87.32/87.58 tff(13279,plain,
% 87.32/87.58 ($false),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13278, 13270, 13269])).
% 87.32/87.58 tff(13280,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.58 tff(13281,plain,
% 87.32/87.58 (~m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13280, 13200])).
% 87.32/87.58 tff(13282,plain,
% 87.32/87.58 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13283,plain,
% 87.32/87.58 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13284,plain,
% 87.32/87.58 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13283, 13282])).
% 87.32/87.58 tff(13285,plain,
% 87.32/87.58 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13284, 23, 13281])).
% 87.32/87.58 tff(13286,plain,
% 87.32/87.58 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13287,plain,
% 87.32/87.58 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13288,plain,
% 87.32/87.58 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4)),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13287, 13286])).
% 87.32/87.58 tff(13289,plain,
% 87.32/87.58 (~node20(c_e_h_3, c_i, s4)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13288, 37, 13285])).
% 87.32/87.58 tff(13290,assumption,(~node20(c_e_h_3, c_i, s4)), introduced(assumption)).
% 87.32/87.58 tff(13291,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s5)), introduced(assumption)).
% 87.32/87.58 tff(13292,assumption,(node21(c_e_h_3, c_i, s4, s5)), introduced(assumption)).
% 87.32/87.58 tff(13293,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node21(c_e_h_3, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node21(c_e_h_3, c_i, s4, s5)))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13294,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node21(c_e_h_3, c_i, s4, s5)))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13295,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node21(c_e_h_3, c_i, s4, s5))),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13294, 13293])).
% 87.32/87.58 tff(13296,plain,
% 87.32/87.58 ($false),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13295, 51, 13291, 13292, 13290])).
% 87.32/87.58 tff(13297,plain,((~node21(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.58 tff(13298,plain,
% 87.32/87.58 (~node21(c_e_h_3, c_i, s4, s5)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13297, 13291, 13290])).
% 87.32/87.58 tff(13299,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13300,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13301,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5)),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13300, 13299])).
% 87.32/87.58 tff(13302,plain,
% 87.32/87.58 (node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13301, 81, 1432])).
% 87.32/87.58 tff(13303,plain,
% 87.32/87.58 (node22(c_e_h_3, c_i, s4, s5)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13302, 13298])).
% 87.32/87.58 tff(13304,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node22(c_e_h_3, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node22(c_e_h_3, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13305,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node22(c_e_h_3, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13306,plain,
% 87.32/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node22(c_e_h_3, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13305, 13304])).
% 87.32/87.58 tff(13307,plain,
% 87.32/87.58 ($false),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13306, 107, 13291, 10743, 13303])).
% 87.32/87.58 tff(13308,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4) | node20(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.58 tff(13309,plain,
% 87.32/87.58 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13308, 10741])).
% 87.32/87.58 tff(13310,plain,
% 87.32/87.58 (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13309, 13289])).
% 87.32/87.58 tff(13311,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s5)), introduced(assumption)).
% 87.32/87.58 tff(13312,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s5)), introduced(assumption)).
% 87.32/87.58 tff(13313,plain,
% 87.32/87.58 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 87.32/87.58 inference(rewrite,[status(thm)],[])).
% 87.32/87.58 tff(13314,plain,
% 87.32/87.58 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 87.32/87.58 inference(quant_inst,[status(thm)],[])).
% 87.32/87.58 tff(13315,plain,
% 87.32/87.58 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 87.32/87.58 inference(modus_ponens,[status(thm)],[13314, 13313])).
% 87.32/87.58 tff(13316,plain,
% 87.32/87.58 ($false),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13315, 2218, 13312, 13311])).
% 87.32/87.58 tff(13317,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 87.32/87.58 tff(13318,plain,
% 87.32/87.58 (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 87.32/87.58 inference(unit_resolution,[status(thm)],[13317, 13310])).
% 87.32/87.58 tff(13319,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s5)), introduced(assumption)).
% 87.32/87.58 tff(13320,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s6)), introduced(assumption)).
% 87.32/87.58 tff(13321,assumption,(node18(c_e_h_3, c_f, s5, s6)), introduced(assumption)).
% 87.32/87.58 tff(13322,plain,
% 87.32/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node18(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node18(c_e_h_3, c_f, s5, s6)))),
% 87.41/87.58 inference(rewrite,[status(thm)],[])).
% 87.41/87.58 tff(13323,plain,
% 87.41/87.58 (((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node18(c_e_h_3, c_f, s5, s6)))),
% 87.41/87.58 inference(rewrite,[status(thm)],[])).
% 87.41/87.58 tff(13324,plain,
% 87.41/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node18(c_e_h_3, c_f, s5, s6))))),
% 87.41/87.58 inference(monotonicity,[status(thm)],[13323])).
% 87.41/87.58 tff(13325,plain,
% 87.41/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node18(c_e_h_3, c_f, s5, s6)))),
% 87.41/87.58 inference(transitivity,[status(thm)],[13324, 13322])).
% 87.41/87.58 tff(13326,plain,
% 87.41/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)))),
% 87.41/87.58 inference(quant_inst,[status(thm)],[])).
% 87.41/87.58 tff(13327,plain,
% 87.41/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node18(c_e_h_3, c_f, s5, s6))),
% 87.41/87.58 inference(modus_ponens,[status(thm)],[13326, 13325])).
% 87.41/87.58 tff(13328,plain,
% 87.41/87.58 ($false),
% 87.41/87.58 inference(unit_resolution,[status(thm)],[13327, 124, 11947, 13320, 13321])).
% 87.41/87.58 tff(13329,plain,((~node18(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 87.41/87.58 tff(13330,plain,
% 87.41/87.58 (~node18(c_e_h_3, c_f, s5, s6)),
% 87.41/87.58 inference(unit_resolution,[status(thm)],[13329, 11947, 13320])).
% 87.41/87.58 tff(13331,plain,
% 87.41/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_f, s5, s6))),
% 87.41/87.58 inference(rewrite,[status(thm)],[])).
% 87.41/87.58 tff(13332,plain,
% 87.41/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_f, s5, s6))),
% 87.41/87.58 inference(quant_inst,[status(thm)],[])).
% 87.41/87.58 tff(13333,plain,
% 87.41/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_f, s5, s6)),
% 87.41/87.58 inference(modus_ponens,[status(thm)],[13332, 13331])).
% 87.41/87.58 tff(13334,plain,
% 87.41/87.58 (node19(c_e_h_3, c_f, s5, s6)),
% 87.41/87.58 inference(unit_resolution,[status(thm)],[13333, 141, 1499])).
% 87.41/87.58 tff(13335,plain,
% 87.41/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6))),
% 87.41/87.58 inference(rewrite,[status(thm)],[])).
% 87.41/87.58 tff(13336,plain,
% 87.41/87.58 ((node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6))) <=> (node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6))),
% 87.41/87.58 inference(rewrite,[status(thm)],[])).
% 87.41/87.58 tff(13337,plain,
% 87.41/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6)))),
% 87.41/87.58 inference(monotonicity,[status(thm)],[13336])).
% 87.41/87.58 tff(13338,plain,
% 87.41/87.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6))),
% 87.41/87.58 inference(transitivity,[status(thm)],[13337, 13335])).
% 87.41/87.58 tff(13339,plain,
% 87.41/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))),
% 87.41/87.58 inference(quant_inst,[status(thm)],[])).
% 87.41/87.58 tff(13340,plain,
% 87.41/87.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6)),
% 87.41/87.58 inference(modus_ponens,[status(thm)],[13339, 13338])).
% 87.41/87.58 tff(13341,plain,
% 87.41/87.58 (node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6)),
% 87.41/87.58 inference(unit_resolution,[status(thm)],[13340, 156, 13334])).
% 87.41/87.58 tff(13342,plain,
% 87.41/87.58 (node17(c_e_h_3, c_f, s5)),
% 87.41/87.58 inference(unit_resolution,[status(thm)],[13341, 13330])).
% 87.41/87.58 tff(13343,plain,
% 87.41/87.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5)))),
% 87.41/87.58 inference(rewrite,[status(thm)],[])).
% 87.41/87.58 tff(13344,plain,
% 87.41/87.58 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5))) <=> (m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5)))),
% 87.41/87.58 inference(rewrite,[status(thm)],[])).
% 87.41/87.58 tff(13345,plain,
% 87.41/87.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5))))),
% 87.41/87.58 inference(monotonicity,[status(thm)],[13344])).
% 87.41/87.58 tff(13346,plain,
% 87.41/87.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5)))),
% 87.41/87.58 inference(transitivity,[status(thm)],[13345, 13343])).
% 87.41/87.58 tff(13347,plain,
% 87.41/87.58 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13348,plain,
% 87.41/87.59 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13347, 13346])).
% 87.41/87.59 tff(13349,plain,
% 87.41/87.59 (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13348, 209, 13342, 13319])).
% 87.41/87.59 tff(13350,assumption,(node15(c_e_h_3, c_f, s5, s6)), introduced(assumption)).
% 87.41/87.59 tff(13351,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13352,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13353,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13352, 13351])).
% 87.41/87.59 tff(13354,plain,
% 87.41/87.59 ($false),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13353, 173, 11947, 13320, 13350])).
% 87.41/87.59 tff(13355,plain,((~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 87.41/87.59 tff(13356,plain,
% 87.41/87.59 (~node15(c_e_h_3, c_f, s5, s6)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13355, 11947, 13320])).
% 87.41/87.59 tff(13357,assumption,(node17(c_e_h_3, c_f, s5)), introduced(assumption)).
% 87.41/87.59 tff(13358,assumption,(node16(c_e_h_3, c_f, s5)), introduced(assumption)).
% 87.41/87.59 tff(13359,plain,
% 87.41/87.59 (m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13348, 209, 13357])).
% 87.41/87.59 tff(13360,plain,
% 87.41/87.59 (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13359, 13319])).
% 87.41/87.59 tff(13361,plain,
% 87.41/87.59 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13362,plain,
% 87.41/87.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13363,plain,
% 87.41/87.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13362, 13361])).
% 87.41/87.59 tff(13364,plain,
% 87.41/87.59 (m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13363, 228, 13358])).
% 87.41/87.59 tff(13365,plain,
% 87.41/87.59 ($false),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13364, 13360, 13319])).
% 87.41/87.59 tff(13366,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node16(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 87.41/87.59 tff(13367,plain,
% 87.41/87.59 (m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13366, 13358, 13357])).
% 87.41/87.59 tff(13368,plain,
% 87.41/87.59 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13369,plain,
% 87.41/87.59 ((m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13370,plain,
% 87.41/87.59 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5))))),
% 87.41/87.59 inference(monotonicity,[status(thm)],[13369])).
% 87.41/87.59 tff(13371,plain,
% 87.41/87.59 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(transitivity,[status(thm)],[13370, 13368])).
% 87.41/87.59 tff(13372,plain,
% 87.41/87.59 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13373,plain,
% 87.41/87.59 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13372, 13371])).
% 87.41/87.59 tff(13374,plain,
% 87.41/87.59 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13373, 245, 13357])).
% 87.41/87.59 tff(13375,plain,
% 87.41/87.59 (m_c_h_element_v_in1(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13374, 13367])).
% 87.41/87.59 tff(13376,plain,
% 87.41/87.59 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node16(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node16(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13377,plain,
% 87.41/87.59 (((~node16(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node16(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13378,plain,
% 87.41/87.59 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node16(c_e_h_3, c_f, s5))))),
% 87.41/87.59 inference(monotonicity,[status(thm)],[13377])).
% 87.41/87.59 tff(13379,plain,
% 87.41/87.59 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node16(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(transitivity,[status(thm)],[13378, 13376])).
% 87.41/87.59 tff(13380,plain,
% 87.41/87.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13381,plain,
% 87.41/87.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | (~node16(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13380, 13379])).
% 87.41/87.59 tff(13382,plain,
% 87.41/87.59 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13381, 263, 13358])).
% 87.41/87.59 tff(13383,plain,
% 87.41/87.59 ($false),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13382, 13375, 13367])).
% 87.41/87.59 tff(13384,plain,((~node16(c_e_h_3, c_f, s5)) | (~node17(c_e_h_3, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 87.41/87.59 tff(13385,plain,
% 87.41/87.59 (~node16(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13384, 13342])).
% 87.41/87.59 tff(13386,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13387,plain,
% 87.41/87.59 ((node16(c_e_h_3, c_f, s5) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6))) <=> (node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13388,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s5) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(monotonicity,[status(thm)],[13387])).
% 87.41/87.59 tff(13389,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s5) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(transitivity,[status(thm)],[13388, 13386])).
% 87.41/87.59 tff(13390,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s5) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13391,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13390, 13389])).
% 87.41/87.59 tff(13392,plain,
% 87.41/87.59 (node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | node16(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13391, 189, 13334])).
% 87.41/87.59 tff(13393,plain,
% 87.41/87.59 (node14(c_e_h_3, c_f, s5, s6)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13392, 13385, 13356])).
% 87.41/87.59 tff(13394,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13395,plain,
% 87.41/87.59 (((~node14(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6))) <=> ((~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13396,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5)))),
% 87.41/87.59 inference(monotonicity,[status(thm)],[13395])).
% 87.41/87.59 tff(13397,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5))),
% 87.41/87.59 inference(transitivity,[status(thm)],[13396, 13394])).
% 87.41/87.59 tff(13398,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13399,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13398, 13397])).
% 87.41/87.59 tff(13400,plain,
% 87.41/87.59 ($false),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13399, 283, 13320, 13393, 13349])).
% 87.41/87.59 tff(13401,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 87.41/87.59 tff(13402,plain,
% 87.41/87.59 ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13401, 10813])).
% 87.41/87.59 tff(13403,plain,
% 87.41/87.59 (~m_c_h_element_v_out(c_e_h_3, c_f, s6)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13402, 13318])).
% 87.41/87.59 tff(13404,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)), introduced(assumption)).
% 87.41/87.59 tff(13405,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s6)), introduced(assumption)).
% 87.41/87.59 tff(13406,plain,
% 87.41/87.59 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13407,plain,
% 87.41/87.59 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13408,plain,
% 87.41/87.59 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6)),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13407, 13406])).
% 87.41/87.59 tff(13409,plain,
% 87.41/87.59 ($false),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13408, 6389, 13405, 13404])).
% 87.41/87.59 tff(13410,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s6) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 87.41/87.59 tff(13411,plain,
% 87.41/87.59 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13410, 13403])).
% 87.41/87.59 tff(13412,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)), introduced(assumption)).
% 87.41/87.59 tff(13413,plain,
% 87.41/87.59 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13414,plain,
% 87.41/87.59 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13415,plain,
% 87.41/87.59 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13414, 13413])).
% 87.41/87.59 tff(13416,plain,
% 87.41/87.59 ($false),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13415, 6378, 12002, 13412])).
% 87.41/87.59 tff(13417,plain,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 87.41/87.59 tff(13418,plain,
% 87.41/87.59 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13417, 11479])).
% 87.41/87.59 tff(13419,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)), introduced(assumption)).
% 87.41/87.59 tff(13420,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)), introduced(assumption)).
% 87.41/87.59 tff(13421,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)), introduced(assumption)).
% 87.41/87.59 tff(13422,assumption,(node10(c_e_h_3, c_m, s6, s7)), introduced(assumption)).
% 87.41/87.59 tff(13423,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7)))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13424,plain,
% 87.41/87.59 (((~node10(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7)))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13425,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7))))),
% 87.41/87.59 inference(monotonicity,[status(thm)],[13424])).
% 87.41/87.59 tff(13426,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7)))),
% 87.41/87.59 inference(transitivity,[status(thm)],[13425, 13423])).
% 87.41/87.59 tff(13427,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13428,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7))),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13427, 13426])).
% 87.41/87.59 tff(13429,plain,
% 87.41/87.59 ($false),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13428, 1191, 13421, 13422, 13419, 13420])).
% 87.41/87.59 tff(13430,plain,((~node10(c_e_h_3, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 87.41/87.59 tff(13431,plain,
% 87.41/87.59 (~node10(c_e_h_3, c_m, s6, s7)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13430, 13421, 13420, 13419])).
% 87.41/87.59 tff(13432,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13433,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13434,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7)),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13433, 13432])).
% 87.41/87.59 tff(13435,plain,
% 87.41/87.59 (node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13434, 1092, 1552])).
% 87.41/87.59 tff(13436,plain,
% 87.41/87.59 (node11(c_e_h_3, c_m, s6, s7)),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13435, 13431])).
% 87.41/87.59 tff(13437,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7)))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13438,plain,
% 87.41/87.59 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~node11(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7)))),
% 87.41/87.59 inference(rewrite,[status(thm)],[])).
% 87.41/87.59 tff(13439,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~node11(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7))))),
% 87.41/87.59 inference(monotonicity,[status(thm)],[13438])).
% 87.41/87.59 tff(13440,plain,
% 87.41/87.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~node11(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7)))),
% 87.41/87.59 inference(transitivity,[status(thm)],[13439, 13437])).
% 87.41/87.59 tff(13441,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~node11(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))),
% 87.41/87.59 inference(quant_inst,[status(thm)],[])).
% 87.41/87.59 tff(13442,plain,
% 87.41/87.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7))),
% 87.41/87.59 inference(modus_ponens,[status(thm)],[13441, 13440])).
% 87.41/87.59 tff(13443,plain,
% 87.41/87.59 ($false),
% 87.41/87.59 inference(unit_resolution,[status(thm)],[13442, 1161, 13421, 13436, 11986])).
% 87.41/87.59 tff(13444,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 87.41/87.60 tff(13445,plain,
% 87.41/87.60 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))),
% 87.41/87.60 inference(unit_resolution,[status(thm)],[13444, 13418])).
% 87.41/87.60 tff(13446,plain,
% 87.41/87.60 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))),
% 87.41/87.60 inference(unit_resolution,[status(thm)],[13445, 11984])).
% 87.41/87.60 tff(13447,plain,
% 87.41/87.60 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)),
% 87.41/87.60 inference(unit_resolution,[status(thm)],[13446, 13411])).
% 87.41/87.60 tff(13448,plain,
% 87.41/87.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))),
% 87.41/87.60 inference(rewrite,[status(thm)],[])).
% 87.41/87.60 tff(13449,plain,
% 87.41/87.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))),
% 87.41/87.60 inference(quant_inst,[status(thm)],[])).
% 87.41/87.60 tff(13450,plain,
% 87.41/87.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))),
% 87.41/87.60 inference(modus_ponens,[status(thm)],[13449, 13448])).
% 87.41/87.60 tff(13451,plain,
% 87.41/87.60 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)),
% 87.41/87.60 inference(unit_resolution,[status(thm)],[13450, 6442, 13447])).
% 87.41/87.60 tff(13452,plain,
% 87.41/87.60 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7))),
% 87.41/87.60 inference(rewrite,[status(thm)],[])).
% 87.41/87.60 tff(13453,plain,
% 87.41/87.60 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7))),
% 87.41/87.60 inference(quant_inst,[status(thm)],[])).
% 87.41/87.60 tff(13454,plain,
% 87.41/87.60 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)),
% 87.41/87.60 inference(modus_ponens,[status(thm)],[13453, 13452])).
% 87.41/87.60 tff(13455,plain,
% 87.41/87.60 (~node9(c_e_h_3, c_n, s7)),
% 87.41/87.60 inference(unit_resolution,[status(thm)],[13454, 1062, 13451])).
% 87.41/87.60 tff(13456,assumption,(~node9(c_e_h_3, c_n, s7)), introduced(assumption)).
% 87.41/87.60 tff(13457,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)), introduced(assumption)).
% 87.41/87.60 tff(13458,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)), introduced(assumption)).
% 87.41/87.60 tff(13459,assumption,(node11(c_e_h_3, c_n, s7, s8)), introduced(assumption)).
% 87.41/87.60 tff(13460,plain,
% 87.41/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 87.41/87.60 inference(rewrite,[status(thm)],[])).
% 87.41/87.60 tff(13461,plain,
% 87.41/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13462,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13461, 13460])).
% 87.42/87.60 tff(13463,plain,
% 87.42/87.60 ($false),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13462, 1130, 13457, 13458, 13459])).
% 87.42/87.60 tff(13464,plain,((~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 87.42/87.60 tff(13465,plain,
% 87.42/87.60 (~node11(c_e_h_3, c_n, s7, s8)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13464, 13458, 13457])).
% 87.42/87.60 tff(13466,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13467,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13468,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13467, 13466])).
% 87.42/87.60 tff(13469,plain,
% 87.42/87.60 (node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13468, 1092, 2152])).
% 87.42/87.60 tff(13470,plain,
% 87.42/87.60 (node10(c_e_h_3, c_n, s7, s8)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13469, 13465])).
% 87.42/87.60 tff(13471,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)) | node9(c_e_h_3, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)) | node9(c_e_h_3, c_n, s7))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13472,plain,
% 87.42/87.60 ((node9(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)) | node9(c_e_h_3, c_n, s7))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13473,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)) | node9(c_e_h_3, c_n, s7)))),
% 87.42/87.60 inference(monotonicity,[status(thm)],[13472])).
% 87.42/87.60 tff(13474,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)) | node9(c_e_h_3, c_n, s7))),
% 87.42/87.60 inference(transitivity,[status(thm)],[13473, 13471])).
% 87.42/87.60 tff(13475,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13476,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)) | node9(c_e_h_3, c_n, s7)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13475, 13474])).
% 87.42/87.60 tff(13477,plain,
% 87.42/87.60 ($false),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13476, 1076, 13458, 13470, 13456])).
% 87.42/87.60 tff(13478,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | node9(c_e_h_3, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.60 tff(13479,plain,
% 87.42/87.60 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | node9(c_e_h_3, c_n, s7)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13478, 12025])).
% 87.42/87.60 tff(13480,plain,
% 87.42/87.60 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13479, 13455])).
% 87.42/87.60 tff(13481,plain,
% 87.42/87.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13482,plain,
% 87.42/87.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13483,plain,
% 87.42/87.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13482, 13481])).
% 87.42/87.60 tff(13484,plain,
% 87.42/87.60 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13483, 6513, 13480])).
% 87.42/87.60 tff(13485,plain,
% 87.42/87.60 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s8))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13486,plain,
% 87.42/87.60 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s8))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13487,plain,
% 87.42/87.60 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s8)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13486, 13485])).
% 87.42/87.60 tff(13488,plain,
% 87.42/87.60 (~node20(c_e_h_3, c_q, s8)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13487, 1535, 13484])).
% 87.42/87.60 tff(13489,assumption,(~node20(c_e_h_3, c_q, s8)), introduced(assumption)).
% 87.42/87.60 tff(13490,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s8)), introduced(assumption)).
% 87.42/87.60 tff(13491,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s9)), introduced(assumption)).
% 87.42/87.60 tff(13492,assumption,(node22(c_e_h_3, c_q, s8, s9)), introduced(assumption)).
% 87.42/87.60 tff(13493,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13494,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13495,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13494, 13493])).
% 87.42/87.60 tff(13496,plain,
% 87.42/87.60 ($false),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13495, 107, 13490, 13491, 13492])).
% 87.42/87.60 tff(13497,plain,((~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9))), inference(lemma,lemma(discharge,[]))).
% 87.42/87.60 tff(13498,plain,
% 87.42/87.60 (~node22(c_e_h_3, c_q, s8, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13497, 13491, 13490])).
% 87.42/87.60 tff(13499,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13500,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13501,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13500, 13499])).
% 87.42/87.60 tff(13502,plain,
% 87.42/87.60 (node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13501, 81, 2636])).
% 87.42/87.60 tff(13503,plain,
% 87.42/87.60 (node21(c_e_h_3, c_q, s8, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13502, 13498])).
% 87.42/87.60 tff(13504,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9)))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13505,plain,
% 87.42/87.60 ((node20(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node21(c_e_h_3, c_q, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9)))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13506,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node21(c_e_h_3, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9))))),
% 87.42/87.60 inference(monotonicity,[status(thm)],[13505])).
% 87.42/87.60 tff(13507,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node21(c_e_h_3, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9)))),
% 87.42/87.60 inference(transitivity,[status(thm)],[13506, 13504])).
% 87.42/87.60 tff(13508,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node21(c_e_h_3, c_q, s8, s9)))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13509,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9))),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13508, 13507])).
% 87.42/87.60 tff(13510,plain,
% 87.42/87.60 ($false),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13509, 51, 13491, 13503, 13489])).
% 87.42/87.60 tff(13511,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | m_and_h_gate_v_out(c_e_h_3, c_q, s8)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.60 tff(13512,plain,
% 87.42/87.60 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13511, 12059])).
% 87.42/87.60 tff(13513,plain,
% 87.42/87.60 (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13512, 13488])).
% 87.42/87.60 tff(13514,plain,
% 87.42/87.60 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s9))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13515,plain,
% 87.42/87.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s9))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13516,plain,
% 87.42/87.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s9)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13515, 13514])).
% 87.42/87.60 tff(13517,plain,
% 87.42/87.60 (node3(c_e_h_3, c_e_h_1, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13516, 3860, 814])).
% 87.42/87.60 tff(13518,plain,
% 87.42/87.60 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s9)) | (~node3(c_e_h_3, c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s9)) | (~node3(c_e_h_3, c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13519,plain,
% 87.42/87.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s9)) | (~node3(c_e_h_3, c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13520,plain,
% 87.42/87.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s9)) | (~node3(c_e_h_3, c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13519, 13518])).
% 87.42/87.60 tff(13521,plain,
% 87.42/87.60 ((~m_cell_v_ack(c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13520, 836, 13517])).
% 87.42/87.60 tff(13522,plain,
% 87.42/87.60 (~m_cell_v_ack(c_e_h_1, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13521, 13513])).
% 87.42/87.60 tff(13523,plain,
% 87.42/87.60 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)) | m_cell_v_ack(c_e_h_1, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)) | m_cell_v_ack(c_e_h_1, s9))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13524,plain,
% 87.42/87.60 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)) | m_cell_v_ack(c_e_h_1, s9))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13525,plain,
% 87.42/87.60 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)) | m_cell_v_ack(c_e_h_1, s9)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13524, 13523])).
% 87.42/87.60 tff(13526,plain,
% 87.42/87.60 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13525, 848, 13522])).
% 87.42/87.60 tff(13527,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13528,plain,
% 87.42/87.60 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13529,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10))))),
% 87.42/87.60 inference(monotonicity,[status(thm)],[13528])).
% 87.42/87.60 tff(13530,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)))),
% 87.42/87.60 inference(transitivity,[status(thm)],[13529, 13527])).
% 87.42/87.60 tff(13531,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13532,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10))),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13531, 13530])).
% 87.42/87.60 tff(13533,plain,
% 87.42/87.60 ($false),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13532, 862, 13526, 12956, 12923, 12897])).
% 87.42/87.60 tff(13534,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.60 tff(13535,plain,
% 87.42/87.60 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13536,plain,
% 87.42/87.60 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13537,plain,
% 87.42/87.60 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)),
% 87.42/87.60 inference(modus_ponens,[status(thm)],[13536, 13535])).
% 87.42/87.60 tff(13538,plain,
% 87.42/87.60 (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13537, 309, 13534])).
% 87.42/87.60 tff(13539,plain,
% 87.42/87.60 (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[12248, 309, 12903])).
% 87.42/87.60 tff(13540,plain,
% 87.42/87.60 (m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[12244, 11678])).
% 87.42/87.60 tff(13541,plain,
% 87.42/87.60 (~m_c_h_element_v_out(c_e_h_1, c_h, s10)),
% 87.42/87.60 inference(unit_resolution,[status(thm)],[13540, 13539])).
% 87.42/87.60 tff(13542,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s10)), introduced(assumption)).
% 87.42/87.60 tff(13543,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s11)), introduced(assumption)).
% 87.42/87.60 tff(13544,assumption,(node18(c_e_h_1, c_h, s10, s11)), introduced(assumption)).
% 87.42/87.60 tff(13545,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13546,plain,
% 87.42/87.60 (((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))),
% 87.42/87.60 inference(rewrite,[status(thm)],[])).
% 87.42/87.60 tff(13547,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11))))),
% 87.42/87.60 inference(monotonicity,[status(thm)],[13546])).
% 87.42/87.60 tff(13548,plain,
% 87.42/87.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))),
% 87.42/87.60 inference(transitivity,[status(thm)],[13547, 13545])).
% 87.42/87.60 tff(13549,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)))),
% 87.42/87.60 inference(quant_inst,[status(thm)],[])).
% 87.42/87.60 tff(13550,plain,
% 87.42/87.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13549, 13548])).
% 87.42/87.61 tff(13551,plain,
% 87.42/87.61 ($false),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13550, 124, 13542, 13543, 13544])).
% 87.42/87.61 tff(13552,plain,((~node18(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 87.42/87.61 tff(13553,plain,
% 87.42/87.61 (~node18(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13552, 13543, 13542])).
% 87.42/87.61 tff(13554,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s10)), introduced(assumption)).
% 87.42/87.61 tff(13555,assumption,(~node14(c_e_h_1, c_h, s10, s11)), introduced(assumption)).
% 87.42/87.61 tff(13556,plain,
% 87.42/87.61 (~node18(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13552, 13542, 13543])).
% 87.42/87.61 tff(13557,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13558,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13559,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13558, 13557])).
% 87.42/87.61 tff(13560,plain,
% 87.42/87.61 (node19(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13559, 141, 3778])).
% 87.42/87.61 tff(13561,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13562,plain,
% 87.42/87.61 ((node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11))) <=> (node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13563,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11)))),
% 87.42/87.61 inference(monotonicity,[status(thm)],[13562])).
% 87.42/87.61 tff(13564,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(transitivity,[status(thm)],[13563, 13561])).
% 87.42/87.61 tff(13565,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13566,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13565, 13564])).
% 87.42/87.61 tff(13567,plain,
% 87.42/87.61 (node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13566, 156, 13560])).
% 87.42/87.61 tff(13568,plain,
% 87.42/87.61 (node17(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13567, 13556])).
% 87.42/87.61 tff(13569,assumption,(node17(c_e_h_1, c_h, s10)), introduced(assumption)).
% 87.42/87.61 tff(13570,assumption,(node16(c_e_h_1, c_h, s10)), introduced(assumption)).
% 87.42/87.61 tff(13571,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13572,plain,
% 87.42/87.61 ((m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13573,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10))))),
% 87.42/87.61 inference(monotonicity,[status(thm)],[13572])).
% 87.42/87.61 tff(13574,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(transitivity,[status(thm)],[13573, 13571])).
% 87.42/87.61 tff(13575,plain,
% 87.42/87.61 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13576,plain,
% 87.42/87.61 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13575, 13574])).
% 87.42/87.61 tff(13577,plain,
% 87.42/87.61 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13576, 245, 13569])).
% 87.42/87.61 tff(13578,plain,
% 87.42/87.61 (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13577, 13554])).
% 87.42/87.61 tff(13579,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13580,plain,
% 87.42/87.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13581,plain,
% 87.42/87.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13580, 13579])).
% 87.42/87.61 tff(13582,plain,
% 87.42/87.61 (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13581, 228, 13570])).
% 87.42/87.61 tff(13583,plain,
% 87.42/87.61 ($false),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13582, 13578, 13554])).
% 87.42/87.61 tff(13584,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~node16(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 87.42/87.61 tff(13585,plain,
% 87.42/87.61 (m_c_h_element_v_in1(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13584, 13570, 13569])).
% 87.42/87.61 tff(13586,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13587,plain,
% 87.42/87.61 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13588,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))))),
% 87.42/87.61 inference(monotonicity,[status(thm)],[13587])).
% 87.42/87.61 tff(13589,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(transitivity,[status(thm)],[13588, 13586])).
% 87.42/87.61 tff(13590,plain,
% 87.42/87.61 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13591,plain,
% 87.42/87.61 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13590, 13589])).
% 87.42/87.61 tff(13592,plain,
% 87.42/87.61 (m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13591, 209, 13569])).
% 87.42/87.61 tff(13593,plain,
% 87.42/87.61 (m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13592, 13585])).
% 87.42/87.61 tff(13594,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node16(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node16(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13595,plain,
% 87.42/87.61 (((~node16(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node16(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13596,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node16(c_e_h_1, c_h, s10))))),
% 87.42/87.61 inference(monotonicity,[status(thm)],[13595])).
% 87.42/87.61 tff(13597,plain,
% 87.42/87.61 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node16(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(transitivity,[status(thm)],[13596, 13594])).
% 87.42/87.61 tff(13598,plain,
% 87.42/87.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13599,plain,
% 87.42/87.61 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node16(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13598, 13597])).
% 87.42/87.61 tff(13600,plain,
% 87.42/87.61 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13599, 263, 13570])).
% 87.42/87.61 tff(13601,plain,
% 87.42/87.61 ($false),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13600, 13593, 13585])).
% 87.42/87.61 tff(13602,plain,((~node16(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 87.42/87.61 tff(13603,plain,
% 87.42/87.61 (~node16(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13602, 13568])).
% 87.42/87.61 tff(13604,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s10, s11) | node16(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s10, s11) | node16(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13605,plain,
% 87.42/87.61 ((node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11))) <=> (node14(c_e_h_1, c_h, s10, s11) | node16(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13606,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s10, s11) | node16(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11)))),
% 87.42/87.61 inference(monotonicity,[status(thm)],[13605])).
% 87.42/87.61 tff(13607,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s10, s11) | node16(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(transitivity,[status(thm)],[13606, 13604])).
% 87.42/87.61 tff(13608,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13609,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s10, s11) | node16(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13608, 13607])).
% 87.42/87.61 tff(13610,plain,
% 87.42/87.61 (node14(c_e_h_1, c_h, s10, s11) | node16(c_e_h_1, c_h, s10) | node15(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13609, 189, 13560])).
% 87.42/87.61 tff(13611,plain,
% 87.42/87.61 (node15(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13610, 13603, 13555])).
% 87.42/87.61 tff(13612,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node15(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node15(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13613,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node15(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13614,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node15(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13613, 13612])).
% 87.42/87.61 tff(13615,plain,
% 87.42/87.61 ($false),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13614, 173, 13542, 13543, 13611])).
% 87.42/87.61 tff(13616,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | node14(c_e_h_1, c_h, s10, s11)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.61 tff(13617,plain,
% 87.42/87.61 (node14(c_e_h_1, c_h, s10, s11)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13616, 13543, 13542])).
% 87.42/87.61 tff(13618,assumption,(node14(c_e_h_1, c_h, s10, s11)), introduced(assumption)).
% 87.42/87.61 tff(13619,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11)))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13620,plain,
% 87.42/87.61 (((~node14(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11)))),
% 87.42/87.61 inference(rewrite,[status(thm)],[])).
% 87.42/87.61 tff(13621,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11))))),
% 87.42/87.61 inference(monotonicity,[status(thm)],[13620])).
% 87.42/87.61 tff(13622,plain,
% 87.42/87.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11)))),
% 87.42/87.61 inference(transitivity,[status(thm)],[13621, 13619])).
% 87.42/87.61 tff(13623,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))),
% 87.42/87.61 inference(quant_inst,[status(thm)],[])).
% 87.42/87.61 tff(13624,plain,
% 87.42/87.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11))),
% 87.42/87.61 inference(modus_ponens,[status(thm)],[13623, 13622])).
% 87.42/87.61 tff(13625,plain,
% 87.42/87.61 ($false),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13624, 283, 13543, 13618, 13554])).
% 87.42/87.61 tff(13626,plain,((~node14(c_e_h_1, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.61 tff(13627,plain,
% 87.42/87.61 ($false),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13626, 13617, 13543, 13554])).
% 87.42/87.61 tff(13628,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_out(c_e_h_1, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.61 tff(13629,plain,
% 87.42/87.61 (m_c_h_element_v_in1(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13628, 13543, 13542])).
% 87.42/87.61 tff(13630,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s10)), introduced(assumption)).
% 87.42/87.61 tff(13631,plain,
% 87.42/87.61 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13591, 209, 13630])).
% 87.42/87.61 tff(13632,plain,
% 87.42/87.61 (~node17(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13631, 13629])).
% 87.42/87.61 tff(13633,plain,
% 87.42/87.61 ($false),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13567, 13632, 13553])).
% 87.42/87.61 tff(13634,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | m_c_h_element_v_out(c_e_h_1, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.61 tff(13635,plain,
% 87.42/87.61 ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13634, 13541])).
% 87.42/87.61 tff(13636,plain,
% 87.42/87.61 (~m_c_h_element_v_out(c_e_h_1, c_h, s11)),
% 87.42/87.61 inference(unit_resolution,[status(thm)],[13635, 13538])).
% 87.42/87.61 tff(13637,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_i, s11)), introduced(assumption)).
% 87.42/87.61 tff(13638,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s11)), introduced(assumption)).
% 87.42/87.61 tff(13639,plain,
% 87.42/87.62 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13640,plain,
% 87.42/87.62 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13641,plain,
% 87.42/87.62 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13640, 13639])).
% 87.42/87.62 tff(13642,plain,
% 87.42/87.62 ($false),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13641, 23, 13638, 13637])).
% 87.42/87.62 tff(13643,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.62 tff(13644,plain,
% 87.42/87.62 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13643, 13636])).
% 87.42/87.62 tff(13645,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)), introduced(assumption)).
% 87.42/87.62 tff(13646,assumption,(node20(c_e_h_1, c_i, s11)), introduced(assumption)).
% 87.42/87.62 tff(13647,plain,
% 87.42/87.62 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13648,plain,
% 87.42/87.62 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13649,plain,
% 87.42/87.62 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13648, 13647])).
% 87.42/87.62 tff(13650,plain,
% 87.42/87.62 ($false),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13649, 37, 13646, 13645])).
% 87.42/87.62 tff(13651,plain,((~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.62 tff(13652,plain,
% 87.42/87.62 (~node20(c_e_h_1, c_i, s11)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13651, 13644])).
% 87.42/87.62 tff(13653,plain,
% 87.42/87.62 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[12182, 23, 13541])).
% 87.42/87.62 tff(13654,plain,
% 87.42/87.62 (~node20(c_e_h_1, c_i, s10)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[12178, 37, 13653])).
% 87.42/87.62 tff(13655,plain,
% 87.42/87.62 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | node20(c_e_h_1, c_i, s10)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[12100, 11710])).
% 87.42/87.62 tff(13656,plain,
% 87.42/87.62 (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13655, 13654])).
% 87.42/87.62 tff(13657,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s12)), introduced(assumption)).
% 87.42/87.62 tff(13658,assumption,(node22(c_e_h_1, c_i, s11, s12)), introduced(assumption)).
% 87.42/87.62 tff(13659,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13660,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13661,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13660, 13659])).
% 87.42/87.62 tff(13662,plain,
% 87.42/87.62 ($false),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13661, 107, 12103, 13657, 13658])).
% 87.42/87.62 tff(13663,plain,((~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12))), inference(lemma,lemma(discharge,[]))).
% 87.42/87.62 tff(13664,plain,
% 87.42/87.62 (~node22(c_e_h_1, c_i, s11, s12)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13663, 13657, 12103])).
% 87.42/87.62 tff(13665,assumption,(~node20(c_e_h_1, c_i, s11)), introduced(assumption)).
% 87.42/87.62 tff(13666,assumption,(node21(c_e_h_1, c_i, s11, s12)), introduced(assumption)).
% 87.42/87.62 tff(13667,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node21(c_e_h_1, c_i, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node21(c_e_h_1, c_i, s11, s12)))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13668,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node21(c_e_h_1, c_i, s11, s12)))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13669,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node21(c_e_h_1, c_i, s11, s12))),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13668, 13667])).
% 87.42/87.62 tff(13670,plain,
% 87.42/87.62 ($false),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13669, 51, 13665, 13657, 13666])).
% 87.42/87.62 tff(13671,plain,((~node21(c_e_h_1, c_i, s11, s12)) | node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12))), inference(lemma,lemma(discharge,[]))).
% 87.42/87.62 tff(13672,plain,
% 87.42/87.62 (~node21(c_e_h_1, c_i, s11, s12)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13671, 13657, 13665])).
% 87.42/87.62 tff(13673,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13674,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13675,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13674, 13673])).
% 87.42/87.62 tff(13676,plain,
% 87.42/87.62 (node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13675, 81, 4461])).
% 87.42/87.62 tff(13677,plain,
% 87.42/87.62 ($false),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13676, 13672, 13664])).
% 87.42/87.62 tff(13678,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | node20(c_e_h_1, c_i, s11) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.62 tff(13679,plain,
% 87.42/87.62 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | node20(c_e_h_1, c_i, s11)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13678, 13656])).
% 87.42/87.62 tff(13680,plain,
% 87.42/87.62 (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13679, 13652])).
% 87.42/87.62 tff(13681,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s12)), introduced(assumption)).
% 87.42/87.62 tff(13682,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s12)), introduced(assumption)).
% 87.42/87.62 tff(13683,plain,
% 87.42/87.62 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13684,plain,
% 87.42/87.62 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13685,plain,
% 87.42/87.62 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13684, 13683])).
% 87.42/87.62 tff(13686,plain,
% 87.42/87.62 ($false),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13685, 365, 13682, 13681])).
% 87.42/87.62 tff(13687,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.62 tff(13688,plain,
% 87.42/87.62 (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13687, 13680])).
% 87.42/87.62 tff(13689,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s12)), introduced(assumption)).
% 87.42/87.62 tff(13690,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s13)), introduced(assumption)).
% 87.42/87.62 tff(13691,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s12)), introduced(assumption)).
% 87.42/87.62 tff(13692,assumption,(~node16(c_e_h_1, c_e, s12)), introduced(assumption)).
% 87.42/87.62 tff(13693,assumption,(node14(c_e_h_1, c_e, s12, s13)), introduced(assumption)).
% 87.42/87.62 tff(13694,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13695,plain,
% 87.42/87.62 (((~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13696,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12)))),
% 87.42/87.62 inference(monotonicity,[status(thm)],[13695])).
% 87.42/87.62 tff(13697,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(transitivity,[status(thm)],[13696, 13694])).
% 87.42/87.62 tff(13698,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13699,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13698, 13697])).
% 87.42/87.62 tff(13700,plain,
% 87.42/87.62 ($false),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13699, 283, 13690, 13693, 13691])).
% 87.42/87.62 tff(13701,plain,((~node14(c_e_h_1, c_e, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.62 tff(13702,plain,
% 87.42/87.62 (~node14(c_e_h_1, c_e, s12, s13)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13701, 13690, 13691])).
% 87.42/87.62 tff(13703,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_e, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_e, s12, s13))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13704,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_e, s12, s13))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13705,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_e, s12, s13)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13704, 13703])).
% 87.42/87.62 tff(13706,plain,
% 87.42/87.62 (node19(c_e_h_1, c_e, s12, s13)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13705, 141, 9599])).
% 87.42/87.62 tff(13707,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s12, s13) | node14(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s12, s13) | node14(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13708,plain,
% 87.42/87.62 ((node16(c_e_h_1, c_e, s12) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13))) <=> (node15(c_e_h_1, c_e, s12, s13) | node14(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13709,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s12) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s12, s13) | node14(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12)))),
% 87.42/87.62 inference(monotonicity,[status(thm)],[13708])).
% 87.42/87.62 tff(13710,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s12) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s12, s13) | node14(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(transitivity,[status(thm)],[13709, 13707])).
% 87.42/87.62 tff(13711,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s12) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13712,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s12, s13) | node14(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13711, 13710])).
% 87.42/87.62 tff(13713,plain,
% 87.42/87.62 (node15(c_e_h_1, c_e, s12, s13) | node14(c_e_h_1, c_e, s12, s13) | node16(c_e_h_1, c_e, s12)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13712, 189, 13706])).
% 87.42/87.62 tff(13714,plain,
% 87.42/87.62 (node15(c_e_h_1, c_e, s12, s13)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13713, 13702, 13692])).
% 87.42/87.62 tff(13715,plain,
% 87.42/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node15(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node15(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13716,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node15(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13717,plain,
% 87.42/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node15(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13716, 13715])).
% 87.42/87.62 tff(13718,plain,
% 87.42/87.62 ($false),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13717, 173, 12321, 13690, 13714])).
% 87.42/87.62 tff(13719,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | node16(c_e_h_1, c_e, s12) | m_c_h_element_v_in1(c_e_h_1, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 87.42/87.62 tff(13720,plain,
% 87.42/87.62 (node16(c_e_h_1, c_e, s12)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13719, 13690, 12321, 13691])).
% 87.42/87.62 tff(13721,plain,
% 87.42/87.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(rewrite,[status(thm)],[])).
% 87.42/87.62 tff(13722,plain,
% 87.42/87.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12))),
% 87.42/87.62 inference(quant_inst,[status(thm)],[])).
% 87.42/87.62 tff(13723,plain,
% 87.42/87.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12)),
% 87.42/87.62 inference(modus_ponens,[status(thm)],[13722, 13721])).
% 87.42/87.62 tff(13724,plain,
% 87.42/87.62 (m_c_h_element_v_in2(c_e_h_1, c_e, s12)),
% 87.42/87.62 inference(unit_resolution,[status(thm)],[13723, 228, 13720, 13691])).
% 87.42/87.62 tff(13725,plain,
% 87.42/87.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))),
% 87.45/87.62 inference(rewrite,[status(thm)],[])).
% 87.45/87.62 tff(13726,plain,
% 87.45/87.62 ((m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))),
% 87.45/87.62 inference(rewrite,[status(thm)],[])).
% 87.45/87.62 tff(13727,plain,
% 87.45/87.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12))))),
% 87.45/87.62 inference(monotonicity,[status(thm)],[13726])).
% 87.45/87.62 tff(13728,plain,
% 87.45/87.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))),
% 87.45/87.62 inference(transitivity,[status(thm)],[13727, 13725])).
% 87.45/87.62 tff(13729,plain,
% 87.45/87.62 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))),
% 87.45/87.62 inference(quant_inst,[status(thm)],[])).
% 87.45/87.62 tff(13730,plain,
% 87.45/87.62 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12))),
% 87.45/87.62 inference(modus_ponens,[status(thm)],[13729, 13728])).
% 87.45/87.62 tff(13731,plain,
% 87.45/87.62 (~node17(c_e_h_1, c_e, s12)),
% 87.45/87.62 inference(unit_resolution,[status(thm)],[13730, 245, 13691, 13724])).
% 87.45/87.62 tff(13732,plain,
% 87.45/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s12, s13)) | node18(c_e_h_1, c_e, s12, s13) | node17(c_e_h_1, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s12, s13)) | node18(c_e_h_1, c_e, s12, s13) | node17(c_e_h_1, c_e, s12))),
% 87.45/87.62 inference(rewrite,[status(thm)],[])).
% 87.45/87.62 tff(13733,plain,
% 87.45/87.62 ((node17(c_e_h_1, c_e, s12) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13))) <=> ((~node19(c_e_h_1, c_e, s12, s13)) | node18(c_e_h_1, c_e, s12, s13) | node17(c_e_h_1, c_e, s12))),
% 87.45/87.62 inference(rewrite,[status(thm)],[])).
% 87.45/87.62 tff(13734,plain,
% 87.45/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s12) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s12, s13)) | node18(c_e_h_1, c_e, s12, s13) | node17(c_e_h_1, c_e, s12)))),
% 87.45/87.62 inference(monotonicity,[status(thm)],[13733])).
% 87.45/87.62 tff(13735,plain,
% 87.45/87.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s12) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s12, s13)) | node18(c_e_h_1, c_e, s12, s13) | node17(c_e_h_1, c_e, s12))),
% 87.45/87.62 inference(transitivity,[status(thm)],[13734, 13732])).
% 87.45/87.62 tff(13736,plain,
% 87.45/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s12) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))),
% 87.45/87.62 inference(quant_inst,[status(thm)],[])).
% 87.45/87.62 tff(13737,plain,
% 87.45/87.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s12, s13)) | node18(c_e_h_1, c_e, s12, s13) | node17(c_e_h_1, c_e, s12)),
% 87.45/87.62 inference(modus_ponens,[status(thm)],[13736, 13735])).
% 87.45/87.62 tff(13738,plain,
% 87.45/87.62 (node18(c_e_h_1, c_e, s12, s13) | node17(c_e_h_1, c_e, s12)),
% 87.45/87.62 inference(unit_resolution,[status(thm)],[13737, 156, 13706])).
% 87.45/87.62 tff(13739,plain,
% 87.45/87.63 (node18(c_e_h_1, c_e, s12, s13)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13738, 13731])).
% 87.45/87.63 tff(13740,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node18(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node18(c_e_h_1, c_e, s12, s13)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13741,plain,
% 87.45/87.63 (((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~node18(c_e_h_1, c_e, s12, s13))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node18(c_e_h_1, c_e, s12, s13)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13742,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~node18(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node18(c_e_h_1, c_e, s12, s13))))),
% 87.45/87.63 inference(monotonicity,[status(thm)],[13741])).
% 87.45/87.63 tff(13743,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~node18(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node18(c_e_h_1, c_e, s12, s13)))),
% 87.45/87.63 inference(transitivity,[status(thm)],[13742, 13740])).
% 87.45/87.63 tff(13744,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~node18(c_e_h_1, c_e, s12, s13)))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13745,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node18(c_e_h_1, c_e, s12, s13))),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13744, 13743])).
% 87.45/87.63 tff(13746,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13745, 124, 12321, 13690, 13739])).
% 87.45/87.63 tff(13747,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | m_c_h_element_v_in1(c_e_h_1, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13748,plain,
% 87.45/87.63 (m_c_h_element_v_in1(c_e_h_1, c_e, s12)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13747, 12321, 13690])).
% 87.45/87.63 tff(13749,assumption,(node18(c_e_h_1, c_e, s12, s13)), introduced(assumption)).
% 87.45/87.63 tff(13750,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13745, 124, 12321, 13690, 13749])).
% 87.45/87.63 tff(13751,plain,((~node18(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13752,plain,
% 87.45/87.63 (~node18(c_e_h_1, c_e, s12, s13)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13751, 12321, 13690])).
% 87.45/87.63 tff(13753,plain,
% 87.45/87.63 (node17(c_e_h_1, c_e, s12)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13738, 13752])).
% 87.45/87.63 tff(13754,plain,
% 87.45/87.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13755,plain,
% 87.45/87.63 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13756,plain,
% 87.45/87.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12))))),
% 87.45/87.63 inference(monotonicity,[status(thm)],[13755])).
% 87.45/87.63 tff(13757,plain,
% 87.45/87.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))),
% 87.45/87.63 inference(transitivity,[status(thm)],[13756, 13754])).
% 87.45/87.63 tff(13758,plain,
% 87.45/87.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13759,plain,
% 87.45/87.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12))),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13758, 13757])).
% 87.45/87.63 tff(13760,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13759, 209, 13753, 13748, 13689])).
% 87.45/87.63 tff(13761,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13762,plain,
% 87.45/87.63 (m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13761, 12319])).
% 87.45/87.63 tff(13763,plain,
% 87.45/87.63 (~m_c_h_element_v_out(c_e_h_1, c_e, s13)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13762, 13688])).
% 87.45/87.63 tff(13764,plain,
% 87.45/87.63 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13765,plain,
% 87.45/87.63 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13766,plain,
% 87.45/87.63 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13)),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13765, 13764])).
% 87.45/87.63 tff(13767,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13766, 976, 13763])).
% 87.45/87.63 tff(13768,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)), introduced(assumption)).
% 87.45/87.63 tff(13769,plain,
% 87.45/87.63 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13770,plain,
% 87.45/87.63 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13771,plain,
% 87.45/87.63 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13770, 13769])).
% 87.45/87.63 tff(13772,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13771, 1142, 12341, 13768])).
% 87.45/87.63 tff(13773,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13774,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13773, 11860])).
% 87.45/87.63 tff(13775,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[12400, 11210])).
% 87.45/87.63 tff(13776,plain,
% 87.45/87.63 (~m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[11123, 11035, 8303])).
% 87.45/87.63 tff(13777,plain,
% 87.45/87.63 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X)) <=> ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X)))),
% 87.45/87.63 inference(bind,[status(th)],[])).
% 87.45/87.63 tff(13778,plain,
% 87.45/87.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))),
% 87.45/87.63 inference(quant_intro,[status(thm)],[13777])).
% 87.45/87.63 tff(13779,plain,
% 87.45/87.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13780,plain,
% 87.45/87.63 (^[I0: $i, X: $i] : rewrite((m_c_h_element_v_in2(I0, c_e, X) | (~m_and_h_gate_v_out(I0, c_i, X))) <=> ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X)))),
% 87.45/87.63 inference(bind,[status(th)],[])).
% 87.45/87.63 tff(13781,plain,
% 87.45/87.63 (![I0: $i, X: $i] : (m_c_h_element_v_in2(I0, c_e, X) | (~m_and_h_gate_v_out(I0, c_i, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))),
% 87.45/87.63 inference(quant_intro,[status(thm)],[13780])).
% 87.45/87.63 tff(13782,axiom,(![I0: $i, X: $i] : (m_c_h_element_v_in2(I0, c_e, X) | (~m_and_h_gate_v_out(I0, c_i, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_21')).
% 87.45/87.63 tff(13783,plain,
% 87.45/87.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13782, 13781])).
% 87.45/87.63 tff(13784,plain,
% 87.45/87.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13783, 13779])).
% 87.45/87.63 tff(13785,plain,(
% 87.45/87.63 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))),
% 87.45/87.63 inference(skolemize,[status(sab)],[13784])).
% 87.45/87.63 tff(13786,plain,
% 87.45/87.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13785, 13778])).
% 87.45/87.63 tff(13787,plain,
% 87.45/87.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13788,plain,
% 87.45/87.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13789,plain,
% 87.45/87.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_e, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13788, 13787])).
% 87.45/87.63 tff(13790,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13789, 13786, 11012, 11035])).
% 87.45/87.63 tff(13791,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13792,plain,
% 87.45/87.63 (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13791, 11035])).
% 87.45/87.63 tff(13793,plain,
% 87.45/87.63 (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[11709, 13792, 11696])).
% 87.45/87.63 tff(13794,plain,
% 87.45/87.63 (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[11717, 13793])).
% 87.45/87.63 tff(13795,plain,
% 87.45/87.63 (~node9(c_e_h_1, c_m, s9)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[7361, 1062, 11172])).
% 87.45/87.63 tff(13796,plain,
% 87.45/87.63 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[7385, 13795, 7364])).
% 87.45/87.63 tff(13797,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[8343, 11038, 11034, 8327])).
% 87.45/87.63 tff(13798,plain,
% 87.45/87.63 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[8348, 1048, 13797])).
% 87.45/87.63 tff(13799,plain,
% 87.45/87.63 (~node9(c_e_h_1, c_m, s10)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[8352, 1062, 13798])).
% 87.45/87.63 tff(13800,plain,
% 87.45/87.63 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[8376, 13799, 13796])).
% 87.45/87.63 tff(13801,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[11791, 1142, 13800])).
% 87.45/87.63 tff(13802,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[11174, 11035, 8327, 8303, 7364])).
% 87.45/87.63 tff(13803,plain,
% 87.45/87.63 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[11821, 13802, 11795, 13801])).
% 87.45/87.63 tff(13804,plain,
% 87.45/87.63 (m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[11783, 13803])).
% 87.45/87.63 tff(13805,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[11775, 13804, 13794, 13776])).
% 87.45/87.63 tff(13806,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13807,plain,
% 87.45/87.63 (m_c_h_element_v_in2(c_e_h_1, c_e, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | node20(c_e_h_1, c_i, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13806, 7354, 6887])).
% 87.45/87.63 tff(13808,plain,
% 87.45/87.63 (m_c_h_element_v_in2(c_e_h_1, c_e, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | node20(c_e_h_1, c_i, s9)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13807, 8301])).
% 87.45/87.63 tff(13809,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13808, 11686, 11033])).
% 87.45/87.63 tff(13810,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[12393, 13809, 13775, 12327])).
% 87.45/87.63 tff(13811,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)), introduced(assumption)).
% 87.45/87.63 tff(13812,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)), introduced(assumption)).
% 87.45/87.63 tff(13813,assumption,(node11(c_e_h_1, c_n, s13, s14)), introduced(assumption)).
% 87.45/87.63 tff(13814,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13815,plain,
% 87.45/87.63 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13816,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14))))),
% 87.45/87.63 inference(monotonicity,[status(thm)],[13815])).
% 87.45/87.63 tff(13817,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)))),
% 87.45/87.63 inference(transitivity,[status(thm)],[13816, 13814])).
% 87.45/87.63 tff(13818,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13819,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14))),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13818, 13817])).
% 87.45/87.63 tff(13820,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13819, 1161, 13811, 13812, 13813])).
% 87.45/87.63 tff(13821,plain,((~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13822,plain,
% 87.45/87.63 (~node11(c_e_h_1, c_n, s13, s14)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13821, 13812, 13811])).
% 87.45/87.63 tff(13823,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)), introduced(assumption)).
% 87.45/87.63 tff(13824,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)), introduced(assumption)).
% 87.45/87.63 tff(13825,assumption,(node10(c_e_h_1, c_n, s13, s14)), introduced(assumption)).
% 87.45/87.63 tff(13826,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13827,plain,
% 87.45/87.63 (((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13828,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13))))),
% 87.45/87.63 inference(monotonicity,[status(thm)],[13827])).
% 87.45/87.63 tff(13829,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)))),
% 87.45/87.63 inference(transitivity,[status(thm)],[13828, 13826])).
% 87.45/87.63 tff(13830,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13831,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13))),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13830, 13829])).
% 87.45/87.63 tff(13832,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13831, 1191, 13812, 13825, 13824, 13823])).
% 87.45/87.63 tff(13833,plain,((~node10(c_e_h_1, c_n, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13834,plain,
% 87.45/87.63 (~node10(c_e_h_1, c_n, s13, s14)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13833, 13812, 13824, 13823])).
% 87.45/87.63 tff(13835,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13836,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13837,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14)),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13836, 13835])).
% 87.45/87.63 tff(13838,plain,
% 87.45/87.63 (node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13837, 1092, 10040])).
% 87.45/87.63 tff(13839,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13838, 13834, 13822])).
% 87.45/87.63 tff(13840,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13841,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13))),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13840, 13810, 13774])).
% 87.45/87.63 tff(13842,plain,
% 87.45/87.63 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13841, 13767])).
% 87.45/87.63 tff(13843,plain,
% 87.45/87.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13844,plain,
% 87.45/87.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13845,plain,
% 87.45/87.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13844, 13843])).
% 87.45/87.63 tff(13846,plain,
% 87.45/87.63 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13845, 1048, 13842])).
% 87.45/87.63 tff(13847,plain,
% 87.45/87.63 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13848,plain,
% 87.45/87.63 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13849,plain,
% 87.45/87.63 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13848, 13847])).
% 87.45/87.63 tff(13850,plain,
% 87.45/87.63 (~node9(c_e_h_1, c_m, s14)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13849, 1062, 13846])).
% 87.45/87.63 tff(13851,assumption,(~node9(c_e_h_1, c_m, s14)), introduced(assumption)).
% 87.45/87.63 tff(13852,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)), introduced(assumption)).
% 87.45/87.63 tff(13853,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)), introduced(assumption)).
% 87.45/87.63 tff(13854,assumption,(node11(c_e_h_1, c_m, s14, s15)), introduced(assumption)).
% 87.45/87.63 tff(13855,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13856,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13857,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13856, 13855])).
% 87.45/87.63 tff(13858,plain,
% 87.45/87.63 ($false),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13857, 1130, 13852, 13853, 13854])).
% 87.45/87.63 tff(13859,plain,((~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.63 tff(13860,plain,
% 87.45/87.63 (~node11(c_e_h_1, c_m, s14, s15)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13859, 13853, 13852])).
% 87.45/87.63 tff(13861,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15))),
% 87.45/87.63 inference(rewrite,[status(thm)],[])).
% 87.45/87.63 tff(13862,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15))),
% 87.45/87.63 inference(quant_inst,[status(thm)],[])).
% 87.45/87.63 tff(13863,plain,
% 87.45/87.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15)),
% 87.45/87.63 inference(modus_ponens,[status(thm)],[13862, 13861])).
% 87.45/87.63 tff(13864,plain,
% 87.45/87.63 (node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13863, 1092, 10504])).
% 87.45/87.63 tff(13865,plain,
% 87.45/87.63 (node10(c_e_h_1, c_m, s14, s15)),
% 87.45/87.63 inference(unit_resolution,[status(thm)],[13864, 13860])).
% 87.45/87.63 tff(13866,plain,
% 87.45/87.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13867,plain,
% 87.45/87.64 ((node9(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node10(c_e_h_1, c_m, s14, s15))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13868,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node10(c_e_h_1, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15))))),
% 87.45/87.64 inference(monotonicity,[status(thm)],[13867])).
% 87.45/87.64 tff(13869,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node10(c_e_h_1, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15)))),
% 87.45/87.64 inference(transitivity,[status(thm)],[13868, 13866])).
% 87.45/87.64 tff(13870,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node10(c_e_h_1, c_m, s14, s15)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13871,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13870, 13869])).
% 87.45/87.64 tff(13872,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13871, 1076, 13853, 13865, 13851])).
% 87.45/87.64 tff(13873,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13874,plain,
% 87.45/87.64 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13873, 12408])).
% 87.45/87.64 tff(13875,plain,
% 87.45/87.64 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13874, 13850])).
% 87.45/87.64 tff(13876,plain,
% 87.45/87.64 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13877,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13878,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13877, 13876])).
% 87.45/87.64 tff(13879,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13878, 1521, 13875, 12896])).
% 87.45/87.64 tff(13880,plain,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13881,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)), introduced(assumption)).
% 87.45/87.64 tff(13882,assumption,(node20(c_e_h_1, c_r, s15)), introduced(assumption)).
% 87.45/87.64 tff(13883,plain,
% 87.45/87.64 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s15))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13884,plain,
% 87.45/87.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s15))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13885,plain,
% 87.45/87.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s15)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13884, 13883])).
% 87.45/87.64 tff(13886,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13885, 1535, 13882, 13881])).
% 87.45/87.64 tff(13887,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s15) | (~node20(c_e_h_1, c_r, s15))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13888,plain,
% 87.45/87.64 (~node20(c_e_h_1, c_r, s15)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13887, 13880])).
% 87.45/87.64 tff(13889,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s16)), introduced(assumption)).
% 87.45/87.64 tff(13890,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s15)), introduced(assumption)).
% 87.45/87.64 tff(13891,assumption,(~node20(c_e_h_1, c_r, s15)), introduced(assumption)).
% 87.45/87.64 tff(13892,assumption,(node21(c_e_h_1, c_r, s15, s16)), introduced(assumption)).
% 87.45/87.64 tff(13893,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15) | (~node21(c_e_h_1, c_r, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15) | (~node21(c_e_h_1, c_r, s15, s16)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13894,plain,
% 87.45/87.64 ((node20(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node21(c_e_h_1, c_r, s15, s16))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15) | (~node21(c_e_h_1, c_r, s15, s16)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13895,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node21(c_e_h_1, c_r, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15) | (~node21(c_e_h_1, c_r, s15, s16))))),
% 87.45/87.64 inference(monotonicity,[status(thm)],[13894])).
% 87.45/87.64 tff(13896,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node21(c_e_h_1, c_r, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15) | (~node21(c_e_h_1, c_r, s15, s16)))),
% 87.45/87.64 inference(transitivity,[status(thm)],[13895, 13893])).
% 87.45/87.64 tff(13897,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node21(c_e_h_1, c_r, s15, s16)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13898,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15) | (~node21(c_e_h_1, c_r, s15, s16))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13897, 13896])).
% 87.45/87.64 tff(13899,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13898, 51, 13892, 13889, 13891])).
% 87.45/87.64 tff(13900,plain,((~node21(c_e_h_1, c_r, s15, s16)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13901,plain,
% 87.45/87.64 (~node21(c_e_h_1, c_r, s15, s16)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13900, 13889, 13891])).
% 87.45/87.64 tff(13902,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13903,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13904,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13903, 13902])).
% 87.45/87.64 tff(13905,plain,
% 87.45/87.64 (node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13904, 81, 12879])).
% 87.45/87.64 tff(13906,plain,
% 87.45/87.64 (node22(c_e_h_1, c_r, s15, s16)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13905, 13901])).
% 87.45/87.64 tff(13907,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13908,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13909,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13908, 13907])).
% 87.45/87.64 tff(13910,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13909, 107, 13906, 13890, 13889])).
% 87.45/87.64 tff(13911,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15) | node20(c_e_h_1, c_r, s15)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13912,plain,
% 87.45/87.64 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13911, 12437])).
% 87.45/87.64 tff(13913,plain,
% 87.45/87.64 (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13912, 13888])).
% 87.45/87.64 tff(13914,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s16)), introduced(assumption)).
% 87.45/87.64 tff(13915,assumption,(m_user_v_ack(c_e_h_1, c_u, s16)), introduced(assumption)).
% 87.45/87.64 tff(13916,plain,
% 87.45/87.64 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13917,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13918,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13917, 13916])).
% 87.45/87.64 tff(13919,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13918, 4481, 13915, 13914])).
% 87.45/87.64 tff(13920,plain,((~m_user_v_ack(c_e_h_1, c_u, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13921,plain,
% 87.45/87.64 (~m_user_v_ack(c_e_h_1, c_u, s16)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13920, 13913])).
% 87.45/87.64 tff(13922,plain,
% 87.45/87.64 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s16) | (~node24(s16)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s16) | (~node24(s16)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13923,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s16) | (~node24(s16)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13924,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s16) | (~node24(s16))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13923, 13922])).
% 87.45/87.64 tff(13925,plain,
% 87.45/87.64 (~node24(s16)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13924, 8407, 13921])).
% 87.45/87.64 tff(13926,plain,
% 87.45/87.64 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s16)) | m_user_v_ack(c_e_h_1, c_u, s16))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s16)) | m_user_v_ack(c_e_h_1, c_u, s16))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13927,plain,
% 87.45/87.64 ((m_user_v_ack(c_e_h_1, c_u, s16) | (~node23(s16))) <=> ((~node23(s16)) | m_user_v_ack(c_e_h_1, c_u, s16))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13928,plain,
% 87.45/87.64 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s16) | (~node23(s16)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s16)) | m_user_v_ack(c_e_h_1, c_u, s16)))),
% 87.45/87.64 inference(monotonicity,[status(thm)],[13927])).
% 87.45/87.64 tff(13929,plain,
% 87.45/87.64 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s16) | (~node23(s16)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s16)) | m_user_v_ack(c_e_h_1, c_u, s16))),
% 87.45/87.64 inference(transitivity,[status(thm)],[13928, 13926])).
% 87.45/87.64 tff(13930,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s16) | (~node23(s16)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13931,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s16)) | m_user_v_ack(c_e_h_1, c_u, s16)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13930, 13929])).
% 87.45/87.64 tff(13932,plain,
% 87.45/87.64 (~node23(s16)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13931, 8418, 13921])).
% 87.45/87.64 tff(13933,plain,
% 87.45/87.64 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s16) | node24(s16) | node25(s16) | (~node26(s16)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s16) | node24(s16) | node25(s16) | (~node26(s16)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13934,plain,
% 87.45/87.64 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s16) | node24(s16) | node25(s16) | (~node26(s16)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13935,plain,
% 87.45/87.64 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s16) | node24(s16) | node25(s16) | (~node26(s16))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13934, 13933])).
% 87.45/87.64 tff(13936,plain,
% 87.45/87.64 (node25(s16) | (~node26(s16))),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13935, 8435, 13932, 13925])).
% 87.45/87.64 tff(13937,plain,
% 87.45/87.64 (~node26(s16)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13936, 12895])).
% 87.45/87.64 tff(13938,plain,
% 87.45/87.64 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13939,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13940,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s13)) | m_and_h_gate_v_out(c_e_h_2, c_r, s13)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13939, 13938])).
% 87.45/87.64 tff(13941,plain,
% 87.45/87.64 (~m_user_v_ack(c_e_h_2, c_u, s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13940, 4481, 9612])).
% 87.45/87.64 tff(13942,plain,
% 87.45/87.64 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s13) | (~node25(s13)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s13) | (~node25(s13)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13943,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s13) | (~node25(s13)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13944,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s13) | (~node25(s13))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13943, 13942])).
% 87.45/87.64 tff(13945,plain,
% 87.45/87.64 (~node25(s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13944, 4492, 13941])).
% 87.45/87.64 tff(13946,assumption,(m_user_v_ack(c_e_h_1, c_u, s13)), introduced(assumption)).
% 87.45/87.64 tff(13947,plain,
% 87.45/87.64 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13948,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13949,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13948, 13947])).
% 87.45/87.64 tff(13950,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13949, 4481, 11887, 13946])).
% 87.45/87.64 tff(13951,plain,((~m_user_v_ack(c_e_h_1, c_u, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13952,plain,
% 87.45/87.64 (~m_user_v_ack(c_e_h_1, c_u, s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13951, 11239])).
% 87.45/87.64 tff(13953,plain,
% 87.45/87.64 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s13) | (~node24(s13)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s13) | (~node24(s13)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13954,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s13) | (~node24(s13)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13955,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s13) | (~node24(s13))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13954, 13953])).
% 87.45/87.64 tff(13956,plain,
% 87.45/87.64 (~node24(s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13955, 8407, 13952])).
% 87.45/87.64 tff(13957,plain,
% 87.45/87.64 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s13) | (~node23(s13)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s13) | (~node23(s13)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13958,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s13) | (~node23(s13)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13959,plain,
% 87.45/87.64 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s13) | (~node23(s13))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13958, 13957])).
% 87.45/87.64 tff(13960,plain,
% 87.45/87.64 (~node23(s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13959, 8418, 13952])).
% 87.45/87.64 tff(13961,plain,
% 87.45/87.64 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s13) | node24(s13) | node25(s13) | (~node26(s13)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s13) | node24(s13) | node25(s13) | (~node26(s13)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13962,plain,
% 87.45/87.64 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s13) | node24(s13) | node25(s13) | (~node26(s13)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13963,plain,
% 87.45/87.64 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s13) | node24(s13) | node25(s13) | (~node26(s13))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13962, 13961])).
% 87.45/87.64 tff(13964,plain,
% 87.45/87.64 (node25(s13) | (~node26(s13))),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13963, 8435, 13960, 13956])).
% 87.45/87.64 tff(13965,plain,
% 87.45/87.64 (~node26(s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13964, 13945])).
% 87.45/87.64 tff(13966,plain,
% 87.45/87.64 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12607, 9574])).
% 87.45/87.64 tff(13967,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)), introduced(assumption)).
% 87.45/87.64 tff(13968,plain,
% 87.45/87.64 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14) | m_c_h_element_v_out(c_e_h_2, c_e, s14))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14) | m_c_h_element_v_out(c_e_h_2, c_e, s14))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13969,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14) | m_c_h_element_v_out(c_e_h_2, c_e, s14))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13970,plain,
% 87.45/87.64 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14) | m_c_h_element_v_out(c_e_h_2, c_e, s14)),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13969, 13968])).
% 87.45/87.64 tff(13971,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13970, 976, 10465, 13967])).
% 87.45/87.64 tff(13972,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s14) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13973,plain,
% 87.45/87.64 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13972, 10463])).
% 87.45/87.64 tff(13974,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)), introduced(assumption)).
% 87.45/87.64 tff(13975,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)), introduced(assumption)).
% 87.45/87.64 tff(13976,plain,
% 87.45/87.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12571, 12486, 4433, 12472, 12473, 9152])).
% 87.45/87.64 tff(13977,plain,
% 87.45/87.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12784, 12486, 3705, 4335, 3061])).
% 87.45/87.64 tff(13978,plain,
% 87.45/87.64 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12648, 1048, 13977])).
% 87.45/87.64 tff(13979,plain,
% 87.45/87.64 (~node9(c_e_h_2, c_m, s11)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12652, 1062, 13978])).
% 87.45/87.64 tff(13980,plain,
% 87.45/87.64 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12643, 13979, 4433])).
% 87.45/87.64 tff(13981,plain,
% 87.45/87.64 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12617, 13980])).
% 87.45/87.64 tff(13982,plain,
% 87.45/87.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12600, 13981, 12573, 13976])).
% 87.45/87.64 tff(13983,plain,
% 87.45/87.64 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12696, 1048, 13976])).
% 87.45/87.64 tff(13984,plain,
% 87.45/87.64 (~node9(c_e_h_2, c_m, s12)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12700, 1062, 13983])).
% 87.45/87.64 tff(13985,plain,
% 87.45/87.64 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12725, 13984, 13980])).
% 87.45/87.64 tff(13986,plain,
% 87.45/87.64 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12691, 13985])).
% 87.45/87.64 tff(13987,plain,
% 87.45/87.64 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[12683, 13986, 12471, 13982])).
% 87.45/87.64 tff(13988,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)), introduced(assumption)).
% 87.45/87.64 tff(13989,assumption,(node11(c_e_h_2, c_n, s14, s15)), introduced(assumption)).
% 87.45/87.64 tff(13990,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13991,plain,
% 87.45/87.64 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(13992,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15))))),
% 87.45/87.64 inference(monotonicity,[status(thm)],[13991])).
% 87.45/87.64 tff(13993,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15)))),
% 87.45/87.64 inference(transitivity,[status(thm)],[13992, 13990])).
% 87.45/87.64 tff(13994,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(13995,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~node11(c_e_h_2, c_n, s14, s15))),
% 87.45/87.64 inference(modus_ponens,[status(thm)],[13994, 13993])).
% 87.45/87.64 tff(13996,plain,
% 87.45/87.64 ($false),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13995, 1161, 13988, 13975, 13989])).
% 87.45/87.64 tff(13997,plain,((~node11(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.64 tff(13998,plain,
% 87.45/87.64 (~node11(c_e_h_2, c_n, s14, s15)),
% 87.45/87.64 inference(unit_resolution,[status(thm)],[13997, 13975, 13988])).
% 87.45/87.64 tff(13999,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)), introduced(assumption)).
% 87.45/87.64 tff(14000,assumption,(node10(c_e_h_2, c_n, s14, s15)), introduced(assumption)).
% 87.45/87.64 tff(14001,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~node10(c_e_h_2, c_n, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~node10(c_e_h_2, c_n, s14, s15)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(14002,plain,
% 87.45/87.64 (((~node10(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~node10(c_e_h_2, c_n, s14, s15)))),
% 87.45/87.64 inference(rewrite,[status(thm)],[])).
% 87.45/87.64 tff(14003,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~node10(c_e_h_2, c_n, s14, s15))))),
% 87.45/87.64 inference(monotonicity,[status(thm)],[14002])).
% 87.45/87.64 tff(14004,plain,
% 87.45/87.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~node10(c_e_h_2, c_n, s14, s15)))),
% 87.45/87.64 inference(transitivity,[status(thm)],[14003, 14001])).
% 87.45/87.64 tff(14005,plain,
% 87.45/87.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15))),
% 87.45/87.64 inference(quant_inst,[status(thm)],[])).
% 87.45/87.64 tff(14006,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~node10(c_e_h_2, c_n, s14, s15))),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14005, 14004])).
% 87.45/87.65 tff(14007,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14006, 1191, 13975, 14000, 13974, 13999])).
% 87.45/87.65 tff(14008,plain,((~node10(c_e_h_2, c_n, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14009,plain,
% 87.45/87.65 (~node10(c_e_h_2, c_n, s14, s15)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14008, 13975, 13999, 13974])).
% 87.45/87.65 tff(14010,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_2, c_n, s14, s15) | node11(c_e_h_2, c_n, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_2, c_n, s14, s15) | node11(c_e_h_2, c_n, s14, s15))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14011,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_2, c_n, s14, s15) | node11(c_e_h_2, c_n, s14, s15))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14012,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_2, c_n, s14, s15) | node11(c_e_h_2, c_n, s14, s15)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14011, 14010])).
% 87.45/87.65 tff(14013,plain,
% 87.45/87.65 (node10(c_e_h_2, c_n, s14, s15) | node11(c_e_h_2, c_n, s14, s15)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14012, 1092, 10504])).
% 87.45/87.65 tff(14014,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14013, 14009, 13998])).
% 87.45/87.65 tff(14015,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14016,plain,
% 87.45/87.65 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14015, 13987, 13975, 13974])).
% 87.45/87.65 tff(14017,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)), introduced(assumption)).
% 87.45/87.65 tff(14018,plain,
% 87.45/87.65 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14019,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14020,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14019, 14018])).
% 87.45/87.65 tff(14021,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14020, 1142, 14017, 12823])).
% 87.45/87.65 tff(14022,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14023,plain,
% 87.45/87.65 (m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14022, 14016])).
% 87.45/87.65 tff(14024,plain,
% 87.45/87.65 (~node11(c_e_h_2, c_m, s13, s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[12807, 14023, 13985])).
% 87.45/87.65 tff(14025,plain,
% 87.45/87.65 (node10(c_e_h_2, c_m, s13, s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[12812, 14024])).
% 87.45/87.65 tff(14026,plain,
% 87.45/87.65 (node9(c_e_h_2, c_m, s13)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[12819, 1076, 14025, 14023])).
% 87.45/87.65 tff(14027,plain,
% 87.45/87.65 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[12794, 1048, 13982])).
% 87.45/87.65 tff(14028,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[12798, 1062, 14027, 14026])).
% 87.45/87.65 tff(14029,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14030,plain,
% 87.45/87.65 ((~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9))),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14029, 4272])).
% 87.45/87.65 tff(14031,plain,
% 87.45/87.65 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14030, 13973, 3676, 12741, 12462, 13966, 4431, 12461, 9075, 12469, 12745])).
% 87.45/87.65 tff(14032,plain,
% 87.45/87.65 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14033,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14034,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15))),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14033, 14032])).
% 87.45/87.65 tff(14035,plain,
% 87.45/87.65 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14034, 1048, 14031])).
% 87.45/87.65 tff(14036,plain,
% 87.45/87.65 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14037,plain,
% 87.45/87.65 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14038,plain,
% 87.45/87.65 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s15)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14037, 14036])).
% 87.45/87.65 tff(14039,plain,
% 87.45/87.65 (~node9(c_e_h_2, c_m, s15)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14038, 1062, 14035])).
% 87.45/87.65 tff(14040,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)), introduced(assumption)).
% 87.45/87.65 tff(14041,assumption,(~node9(c_e_h_2, c_m, s15)), introduced(assumption)).
% 87.45/87.65 tff(14042,assumption,(node10(c_e_h_2, c_m, s15, s16)), introduced(assumption)).
% 87.45/87.65 tff(14043,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | (~node10(c_e_h_2, c_m, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | (~node10(c_e_h_2, c_m, s15, s16)))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14044,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | (~node10(c_e_h_2, c_m, s15, s16)))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14045,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | (~node10(c_e_h_2, c_m, s15, s16))),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14044, 14043])).
% 87.45/87.65 tff(14046,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14045, 1076, 14042, 14040, 14041])).
% 87.45/87.65 tff(14047,plain,((~node10(c_e_h_2, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | node9(c_e_h_2, c_m, s15)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14048,plain,
% 87.45/87.65 (~node10(c_e_h_2, c_m, s15, s16)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14047, 14040, 14041])).
% 87.45/87.65 tff(14049,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_2, c_m, s15, s16) | node11(c_e_h_2, c_m, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_2, c_m, s15, s16) | node11(c_e_h_2, c_m, s15, s16))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14050,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_2, c_m, s15, s16) | node11(c_e_h_2, c_m, s15, s16))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14051,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_2, c_m, s15, s16) | node11(c_e_h_2, c_m, s15, s16)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14050, 14049])).
% 87.45/87.65 tff(14052,plain,
% 87.45/87.65 (node10(c_e_h_2, c_m, s15, s16) | node11(c_e_h_2, c_m, s15, s16)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14051, 1092, 12879])).
% 87.45/87.65 tff(14053,plain,
% 87.45/87.65 (node11(c_e_h_2, c_m, s15, s16)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14052, 14048])).
% 87.45/87.65 tff(14054,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)), introduced(assumption)).
% 87.45/87.65 tff(14055,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | (~node11(c_e_h_2, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | (~node11(c_e_h_2, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14056,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | (~node11(c_e_h_2, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14057,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | (~node11(c_e_h_2, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14056, 14055])).
% 87.45/87.65 tff(14058,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14057, 1130, 14054, 14053, 14040])).
% 87.45/87.65 tff(14059,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15) | node9(c_e_h_2, c_m, s15)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14060,plain,
% 87.45/87.65 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14059, 12843, 14039])).
% 87.45/87.65 tff(14061,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_r, s16)), introduced(assumption)).
% 87.45/87.65 tff(14062,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)), introduced(assumption)).
% 87.45/87.65 tff(14063,plain,
% 87.45/87.65 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14064,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14065,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14064, 14063])).
% 87.45/87.65 tff(14066,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14065, 1521, 14062, 14061])).
% 87.45/87.65 tff(14067,plain,((~m_and_h_gate_v_in2(c_e_h_2, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14068,plain,
% 87.45/87.65 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s16)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14067, 14060])).
% 87.45/87.65 tff(14069,assumption,(~m_and_h_gate_v_in2(c_e_h_2, c_r, s16)), introduced(assumption)).
% 87.45/87.65 tff(14070,assumption,(node20(c_e_h_2, c_r, s16)), introduced(assumption)).
% 87.45/87.65 tff(14071,plain,
% 87.45/87.65 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s16))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14072,plain,
% 87.45/87.65 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s16))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14073,plain,
% 87.45/87.65 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s16)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14072, 14071])).
% 87.45/87.65 tff(14074,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14073, 1535, 14070, 14069])).
% 87.45/87.65 tff(14075,plain,((~node20(c_e_h_2, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s16)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14076,plain,
% 87.45/87.65 (~node20(c_e_h_2, c_r, s16)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14075, 14068])).
% 87.45/87.65 tff(14077,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s17)), introduced(assumption)).
% 87.45/87.65 tff(14078,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s16)), introduced(assumption)).
% 87.45/87.65 tff(14079,assumption,(~node20(c_e_h_2, c_r, s16)), introduced(assumption)).
% 87.45/87.65 tff(14080,assumption,(node21(c_e_h_2, c_r, s16, s17)), introduced(assumption)).
% 87.45/87.65 tff(14081,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | node20(c_e_h_2, c_r, s16) | (~node21(c_e_h_2, c_r, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | node20(c_e_h_2, c_r, s16) | (~node21(c_e_h_2, c_r, s16, s17)))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14082,plain,
% 87.45/87.65 ((node20(c_e_h_2, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | (~node21(c_e_h_2, c_r, s16, s17))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | node20(c_e_h_2, c_r, s16) | (~node21(c_e_h_2, c_r, s16, s17)))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14083,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | (~node21(c_e_h_2, c_r, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | node20(c_e_h_2, c_r, s16) | (~node21(c_e_h_2, c_r, s16, s17))))),
% 87.45/87.65 inference(monotonicity,[status(thm)],[14082])).
% 87.45/87.65 tff(14084,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | (~node21(c_e_h_2, c_r, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | node20(c_e_h_2, c_r, s16) | (~node21(c_e_h_2, c_r, s16, s17)))),
% 87.45/87.65 inference(transitivity,[status(thm)],[14083, 14081])).
% 87.45/87.65 tff(14085,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | (~node21(c_e_h_2, c_r, s16, s17)))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14086,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | node20(c_e_h_2, c_r, s16) | (~node21(c_e_h_2, c_r, s16, s17))),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14085, 14084])).
% 87.45/87.65 tff(14087,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14086, 51, 14079, 14080, 14077])).
% 87.45/87.65 tff(14088,plain,((~node21(c_e_h_2, c_r, s16, s17)) | node20(c_e_h_2, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14089,plain,
% 87.45/87.65 (~node21(c_e_h_2, c_r, s16, s17)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14088, 14077, 14079])).
% 87.45/87.65 tff(14090,plain,
% 87.45/87.65 (succ(s16, s17) <=> succ(s16, s17)),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14091,axiom,(succ(s16, s17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound17')).
% 87.45/87.65 tff(14092,plain,
% 87.45/87.65 (succ(s16, s17)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14091, 14090])).
% 87.45/87.65 tff(14093,plain,
% 87.45/87.65 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14094,plain,
% 87.45/87.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14095,plain,
% 87.45/87.65 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14094, 14093])).
% 87.45/87.65 tff(14096,plain,
% 87.45/87.65 (trans(s16, s17)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14095, 14092, 64])).
% 87.45/87.65 tff(14097,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_2, c_r, s16, s17) | node22(c_e_h_2, c_r, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_2, c_r, s16, s17) | node22(c_e_h_2, c_r, s16, s17))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14098,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_2, c_r, s16, s17) | node22(c_e_h_2, c_r, s16, s17))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14099,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_2, c_r, s16, s17) | node22(c_e_h_2, c_r, s16, s17)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14098, 14097])).
% 87.45/87.65 tff(14100,plain,
% 87.45/87.65 (node21(c_e_h_2, c_r, s16, s17) | node22(c_e_h_2, c_r, s16, s17)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14099, 81, 14096])).
% 87.45/87.65 tff(14101,plain,
% 87.45/87.65 (node22(c_e_h_2, c_r, s16, s17)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14100, 14089])).
% 87.45/87.65 tff(14102,plain,
% 87.45/87.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | (~node22(c_e_h_2, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | (~node22(c_e_h_2, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14103,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | (~node22(c_e_h_2, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14104,plain,
% 87.45/87.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | (~node22(c_e_h_2, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14103, 14102])).
% 87.45/87.65 tff(14105,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14104, 107, 14101, 14078, 14077])).
% 87.45/87.65 tff(14106,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16) | node20(c_e_h_2, c_r, s16)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14107,plain,
% 87.45/87.65 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s16)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14106, 14076])).
% 87.45/87.65 tff(14108,plain,
% 87.45/87.65 (~m_and_h_gate_v_out(c_e_h_2, c_r, s17)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14107, 12887])).
% 87.45/87.65 tff(14109,plain,
% 87.45/87.65 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14110,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14111,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s14)) | m_and_h_gate_v_out(c_e_h_2, c_r, s14)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14110, 14109])).
% 87.45/87.65 tff(14112,plain,
% 87.45/87.65 (~m_user_v_ack(c_e_h_2, c_u, s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14111, 4481, 10048])).
% 87.45/87.65 tff(14113,plain,
% 87.45/87.65 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s14) | (~node25(s14)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s14) | (~node25(s14)))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14114,plain,
% 87.45/87.65 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s14) | (~node25(s14)))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14115,plain,
% 87.45/87.65 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s14) | (~node25(s14))),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14114, 14113])).
% 87.45/87.65 tff(14116,plain,
% 87.45/87.65 (~node25(s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14115, 4492, 14112])).
% 87.45/87.65 tff(14117,assumption,(m_user_v_ack(c_e_h_1, c_u, s14)), introduced(assumption)).
% 87.45/87.65 tff(14118,plain,
% 87.45/87.65 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14119,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14120,plain,
% 87.45/87.65 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14)),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14119, 14118])).
% 87.45/87.65 tff(14121,plain,
% 87.45/87.65 ($false),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14120, 4481, 14117, 12418])).
% 87.45/87.65 tff(14122,plain,((~m_user_v_ack(c_e_h_1, c_u, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.65 tff(14123,plain,
% 87.45/87.65 (~m_user_v_ack(c_e_h_1, c_u, s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14122, 11894])).
% 87.45/87.65 tff(14124,plain,
% 87.45/87.65 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s14) | (~node24(s14)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s14) | (~node24(s14)))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14125,plain,
% 87.45/87.65 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s14) | (~node24(s14)))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14126,plain,
% 87.45/87.65 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s14) | (~node24(s14))),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14125, 14124])).
% 87.45/87.65 tff(14127,plain,
% 87.45/87.65 (~node24(s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14126, 8407, 14123])).
% 87.45/87.65 tff(14128,plain,
% 87.45/87.65 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s14) | (~node23(s14)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s14) | (~node23(s14)))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14129,plain,
% 87.45/87.65 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s14) | (~node23(s14)))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14130,plain,
% 87.45/87.65 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s14) | (~node23(s14))),
% 87.45/87.65 inference(modus_ponens,[status(thm)],[14129, 14128])).
% 87.45/87.65 tff(14131,plain,
% 87.45/87.65 (~node23(s14)),
% 87.45/87.65 inference(unit_resolution,[status(thm)],[14130, 8418, 14123])).
% 87.45/87.65 tff(14132,plain,
% 87.45/87.65 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s14) | node24(s14) | node25(s14) | (~node26(s14)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s14) | node24(s14) | node25(s14) | (~node26(s14)))),
% 87.45/87.65 inference(rewrite,[status(thm)],[])).
% 87.45/87.65 tff(14133,plain,
% 87.45/87.65 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s14) | node24(s14) | node25(s14) | (~node26(s14)))),
% 87.45/87.65 inference(quant_inst,[status(thm)],[])).
% 87.45/87.65 tff(14134,plain,
% 87.45/87.65 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s14) | node24(s14) | node25(s14) | (~node26(s14))),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14133, 14132])).
% 87.45/87.66 tff(14135,plain,
% 87.45/87.66 (node25(s14) | (~node26(s14))),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14134, 8435, 14131, 14127])).
% 87.45/87.66 tff(14136,plain,
% 87.45/87.66 (~node26(s14)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14135, 14116])).
% 87.45/87.66 tff(14137,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_l, s11)), introduced(assumption)).
% 87.45/87.66 tff(14138,plain,
% 87.45/87.66 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14139,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14140,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14139, 14138])).
% 87.45/87.66 tff(14141,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14140, 1638, 4433, 14137])).
% 87.45/87.66 tff(14142,plain,((~m_and_h_gate_v_in2(c_e_h_2, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14143,plain,
% 87.45/87.66 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s11)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14142, 4431])).
% 87.45/87.66 tff(14144,assumption,(~m_and_h_gate_v_in2(c_e_h_2, c_l, s11)), introduced(assumption)).
% 87.45/87.66 tff(14145,assumption,(node20(c_e_h_2, c_l, s11)), introduced(assumption)).
% 87.45/87.66 tff(14146,plain,
% 87.45/87.66 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s11))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14147,plain,
% 87.45/87.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s11))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14148,plain,
% 87.45/87.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s11)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14147, 14146])).
% 87.45/87.66 tff(14149,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14148, 1535, 14145, 14144])).
% 87.45/87.66 tff(14150,plain,((~node20(c_e_h_2, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14151,plain,
% 87.45/87.66 (~node20(c_e_h_2, c_l, s11)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14150, 14143])).
% 87.45/87.66 tff(14152,plain,
% 87.45/87.66 (~m_and_h_gate_v_out(c_e_h_2, c_l, s10)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[10087, 10049])).
% 87.45/87.66 tff(14153,plain,
% 87.45/87.66 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14154,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14155,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14154, 14153])).
% 87.45/87.66 tff(14156,plain,
% 87.45/87.66 ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14155, 1638])).
% 87.45/87.66 tff(14157,plain,
% 87.45/87.66 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s10)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14156, 3750])).
% 87.45/87.66 tff(14158,plain,
% 87.45/87.66 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s10))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14159,plain,
% 87.45/87.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s10))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14160,plain,
% 87.45/87.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s10)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14159, 14158])).
% 87.45/87.66 tff(14161,plain,
% 87.45/87.66 (~node20(c_e_h_2, c_l, s10)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14160, 1535, 14157])).
% 87.45/87.66 tff(14162,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s11)), introduced(assumption)).
% 87.45/87.66 tff(14163,assumption,(node22(c_e_h_2, c_l, s10, s11)), introduced(assumption)).
% 87.45/87.66 tff(14164,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | (~node22(c_e_h_2, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | (~node22(c_e_h_2, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14165,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | (~node22(c_e_h_2, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14166,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | (~node22(c_e_h_2, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14165, 14164])).
% 87.45/87.66 tff(14167,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14166, 107, 10089, 14162, 14163])).
% 87.45/87.66 tff(14168,plain,((~node22(c_e_h_2, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s11))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14169,plain,
% 87.45/87.66 (~node22(c_e_h_2, c_l, s10, s11)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14168, 14162, 10089])).
% 87.45/87.66 tff(14170,assumption,(~node20(c_e_h_2, c_l, s10)), introduced(assumption)).
% 87.45/87.66 tff(14171,assumption,(node21(c_e_h_2, c_l, s10, s11)), introduced(assumption)).
% 87.45/87.66 tff(14172,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | (~node21(c_e_h_2, c_l, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | (~node21(c_e_h_2, c_l, s10, s11)))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14173,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | (~node21(c_e_h_2, c_l, s10, s11)))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14174,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | (~node21(c_e_h_2, c_l, s10, s11))),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14173, 14172])).
% 87.45/87.66 tff(14175,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14174, 51, 14162, 14170, 14171])).
% 87.45/87.66 tff(14176,plain,((~node21(c_e_h_2, c_l, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | node20(c_e_h_2, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14177,plain,
% 87.45/87.66 (~node21(c_e_h_2, c_l, s10, s11)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14176, 14162, 14170])).
% 87.45/87.66 tff(14178,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_2, c_l, s10, s11) | node22(c_e_h_2, c_l, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_2, c_l, s10, s11) | node22(c_e_h_2, c_l, s10, s11))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14179,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_2, c_l, s10, s11) | node22(c_e_h_2, c_l, s10, s11))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14180,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_2, c_l, s10, s11) | node22(c_e_h_2, c_l, s10, s11)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14179, 14178])).
% 87.45/87.66 tff(14181,plain,
% 87.45/87.66 (node21(c_e_h_2, c_l, s10, s11) | node22(c_e_h_2, c_l, s10, s11)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14180, 81, 3778])).
% 87.45/87.66 tff(14182,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14181, 14177, 14169])).
% 87.45/87.66 tff(14183,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s11)) | node20(c_e_h_2, c_l, s10) | m_and_h_gate_v_out(c_e_h_2, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14184,plain,
% 87.45/87.66 (~m_and_h_gate_v_out(c_e_h_2, c_l, s11)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14183, 14161, 14152])).
% 87.45/87.66 tff(14185,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s11)), introduced(assumption)).
% 87.45/87.66 tff(14186,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s12)), introduced(assumption)).
% 87.45/87.66 tff(14187,assumption,(node22(c_e_h_2, c_l, s11, s12)), introduced(assumption)).
% 87.45/87.66 tff(14188,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | (~node22(c_e_h_2, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | (~node22(c_e_h_2, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14189,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | (~node22(c_e_h_2, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14190,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | (~node22(c_e_h_2, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14189, 14188])).
% 87.45/87.66 tff(14191,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14190, 107, 14186, 14185, 14187])).
% 87.45/87.66 tff(14192,plain,((~node22(c_e_h_2, c_l, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14193,plain,
% 87.45/87.66 (~node22(c_e_h_2, c_l, s11, s12)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14192, 14186, 14185])).
% 87.45/87.66 tff(14194,assumption,(~node20(c_e_h_2, c_l, s11)), introduced(assumption)).
% 87.45/87.66 tff(14195,assumption,(node21(c_e_h_2, c_l, s11, s12)), introduced(assumption)).
% 87.45/87.66 tff(14196,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | (~node21(c_e_h_2, c_l, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | (~node21(c_e_h_2, c_l, s11, s12)))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14197,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | (~node21(c_e_h_2, c_l, s11, s12)))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14198,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | (~node21(c_e_h_2, c_l, s11, s12))),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14197, 14196])).
% 87.45/87.66 tff(14199,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14198, 51, 14186, 14194, 14195])).
% 87.45/87.66 tff(14200,plain,((~node21(c_e_h_2, c_l, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | node20(c_e_h_2, c_l, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14201,plain,
% 87.45/87.66 (~node21(c_e_h_2, c_l, s11, s12)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14200, 14186, 14194])).
% 87.45/87.66 tff(14202,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_2, c_l, s11, s12) | node22(c_e_h_2, c_l, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_2, c_l, s11, s12) | node22(c_e_h_2, c_l, s11, s12))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14203,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_2, c_l, s11, s12) | node22(c_e_h_2, c_l, s11, s12))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14204,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_2, c_l, s11, s12) | node22(c_e_h_2, c_l, s11, s12)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14203, 14202])).
% 87.45/87.66 tff(14205,plain,
% 87.45/87.66 (node21(c_e_h_2, c_l, s11, s12) | node22(c_e_h_2, c_l, s11, s12)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14204, 81, 4461])).
% 87.45/87.66 tff(14206,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14205, 14201, 14193])).
% 87.45/87.66 tff(14207,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s12)) | node20(c_e_h_2, c_l, s11) | m_and_h_gate_v_out(c_e_h_2, c_l, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14208,plain,
% 87.45/87.66 (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14207, 14184, 14151])).
% 87.45/87.66 tff(14209,plain,
% 87.45/87.66 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14210,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14211,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s12)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14210, 14209])).
% 87.45/87.66 tff(14212,plain,
% 87.45/87.66 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s12)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14211, 1638, 12789])).
% 87.45/87.66 tff(14213,plain,
% 87.45/87.66 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s12)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s12)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s12))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14214,plain,
% 87.45/87.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s12)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s12))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14215,plain,
% 87.45/87.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s12)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s12)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14214, 14213])).
% 87.45/87.66 tff(14216,plain,
% 87.45/87.66 (~node20(c_e_h_2, c_l, s12)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14215, 1535, 14212])).
% 87.45/87.66 tff(14217,assumption,(~node20(c_e_h_2, c_l, s12)), introduced(assumption)).
% 87.45/87.66 tff(14218,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s12)), introduced(assumption)).
% 87.45/87.66 tff(14219,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s13)), introduced(assumption)).
% 87.45/87.66 tff(14220,assumption,(node22(c_e_h_2, c_l, s12, s13)), introduced(assumption)).
% 87.45/87.66 tff(14221,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | (~node22(c_e_h_2, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | (~node22(c_e_h_2, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14222,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | (~node22(c_e_h_2, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14223,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | (~node22(c_e_h_2, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14222, 14221])).
% 87.45/87.66 tff(14224,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14223, 107, 14218, 14219, 14220])).
% 87.45/87.66 tff(14225,plain,((~node22(c_e_h_2, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s13))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14226,plain,
% 87.45/87.66 (~node22(c_e_h_2, c_l, s12, s13)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14225, 14219, 14218])).
% 87.45/87.66 tff(14227,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_2, c_l, s12, s13) | node22(c_e_h_2, c_l, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_2, c_l, s12, s13) | node22(c_e_h_2, c_l, s12, s13))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14228,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_2, c_l, s12, s13) | node22(c_e_h_2, c_l, s12, s13))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14229,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_2, c_l, s12, s13) | node22(c_e_h_2, c_l, s12, s13)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14228, 14227])).
% 87.45/87.66 tff(14230,plain,
% 87.45/87.66 (node21(c_e_h_2, c_l, s12, s13) | node22(c_e_h_2, c_l, s12, s13)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14229, 81, 9599])).
% 87.45/87.66 tff(14231,plain,
% 87.45/87.66 (node21(c_e_h_2, c_l, s12, s13)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14230, 14226])).
% 87.45/87.66 tff(14232,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | (~node21(c_e_h_2, c_l, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | (~node21(c_e_h_2, c_l, s12, s13)))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14233,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | (~node21(c_e_h_2, c_l, s12, s13)))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14234,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | (~node21(c_e_h_2, c_l, s12, s13))),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14233, 14232])).
% 87.45/87.66 tff(14235,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14234, 51, 14219, 14231, 14217])).
% 87.45/87.66 tff(14236,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s13)) | node20(c_e_h_2, c_l, s12) | m_and_h_gate_v_out(c_e_h_2, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14237,plain,
% 87.45/87.66 (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14236, 14216, 14208])).
% 87.45/87.66 tff(14238,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s13)), introduced(assumption)).
% 87.45/87.66 tff(14239,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s13)), introduced(assumption)).
% 87.45/87.66 tff(14240,plain,
% 87.45/87.66 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14241,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14242,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14241, 14240])).
% 87.45/87.66 tff(14243,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14242, 801, 14239, 14238])).
% 87.45/87.66 tff(14244,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14245,plain,
% 87.45/87.66 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14244, 14237])).
% 87.45/87.66 tff(14246,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s11)), introduced(assumption)).
% 87.45/87.66 tff(14247,plain,
% 87.45/87.66 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14248,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14249,plain,
% 87.45/87.66 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11)),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14248, 14247])).
% 87.45/87.66 tff(14250,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14249, 801, 14185, 14246])).
% 87.45/87.66 tff(14251,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s11)) | m_and_h_gate_v_out(c_e_h_2, c_l, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14252,plain,
% 87.45/87.66 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s11)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14251, 14184])).
% 87.45/87.66 tff(14253,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s12)), introduced(assumption)).
% 87.45/87.66 tff(14254,assumption,(node6(c_e_h_2, c_j, s11, s12)), introduced(assumption)).
% 87.45/87.66 tff(14255,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | (~node6(c_e_h_2, c_j, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | (~node6(c_e_h_2, c_j, s11, s12)))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14256,plain,
% 87.45/87.66 (((~node6(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | (~node6(c_e_h_2, c_j, s11, s12)))),
% 87.45/87.66 inference(rewrite,[status(thm)],[])).
% 87.45/87.66 tff(14257,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | (~node6(c_e_h_2, c_j, s11, s12))))),
% 87.45/87.66 inference(monotonicity,[status(thm)],[14256])).
% 87.45/87.66 tff(14258,plain,
% 87.45/87.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | (~node6(c_e_h_2, c_j, s11, s12)))),
% 87.45/87.66 inference(transitivity,[status(thm)],[14257, 14255])).
% 87.45/87.66 tff(14259,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11))),
% 87.45/87.66 inference(quant_inst,[status(thm)],[])).
% 87.45/87.66 tff(14260,plain,
% 87.45/87.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | (~node6(c_e_h_2, c_j, s11, s12))),
% 87.45/87.66 inference(modus_ponens,[status(thm)],[14259, 14258])).
% 87.45/87.66 tff(14261,plain,
% 87.45/87.66 ($false),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14260, 899, 14253, 10262, 14254])).
% 87.45/87.66 tff(14262,plain,((~node6(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.66 tff(14263,plain,
% 87.45/87.66 (~node6(c_e_h_2, c_j, s11, s12)),
% 87.45/87.66 inference(unit_resolution,[status(thm)],[14262, 14253, 10262])).
% 87.45/87.66 tff(14264,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s11)), introduced(assumption)).
% 87.45/87.67 tff(14265,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s11)), introduced(assumption)).
% 87.45/87.67 tff(14266,plain,
% 87.45/87.67 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14267,plain,
% 87.45/87.67 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14268,plain,
% 87.45/87.67 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14267, 14266])).
% 87.45/87.67 tff(14269,plain,
% 87.45/87.67 (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14268, 2218, 11029])).
% 87.45/87.67 tff(14270,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s10)), introduced(assumption)).
% 87.45/87.67 tff(14271,assumption,(node18(c_e_h_1, c_f, s9, s10)), introduced(assumption)).
% 87.45/87.67 tff(14272,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14273,plain,
% 87.45/87.67 (((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~node18(c_e_h_1, c_f, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14274,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~node18(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10))))),
% 87.45/87.67 inference(monotonicity,[status(thm)],[14273])).
% 87.45/87.67 tff(14275,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~node18(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(transitivity,[status(thm)],[14274, 14272])).
% 87.45/87.67 tff(14276,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~node18(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14277,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14276, 14275])).
% 87.45/87.67 tff(14278,plain,
% 87.45/87.67 ($false),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14277, 124, 14270, 10182, 14271])).
% 87.45/87.67 tff(14279,plain,((~node18(c_e_h_1, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.67 tff(14280,plain,
% 87.45/87.67 (~node18(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14279, 14270, 10182])).
% 87.45/87.67 tff(14281,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_f, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14282,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14283,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14282, 14281])).
% 87.45/87.67 tff(14284,plain,
% 87.45/87.67 (node19(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14283, 141, 3175])).
% 87.45/87.67 tff(14285,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14286,plain,
% 87.45/87.67 ((node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10))) <=> ((~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14287,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(monotonicity,[status(thm)],[14286])).
% 87.45/87.67 tff(14288,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(transitivity,[status(thm)],[14287, 14285])).
% 87.45/87.67 tff(14289,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14290,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14289, 14288])).
% 87.45/87.67 tff(14291,plain,
% 87.45/87.67 (node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14290, 156, 14284])).
% 87.45/87.67 tff(14292,plain,
% 87.45/87.67 (node17(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14291, 14280])).
% 87.45/87.67 tff(14293,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s9)), introduced(assumption)).
% 87.45/87.67 tff(14294,plain,
% 87.45/87.67 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9)))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14295,plain,
% 87.45/87.67 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9)))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14296,plain,
% 87.45/87.67 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9))),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14295, 14294])).
% 87.45/87.67 tff(14297,plain,
% 87.45/87.67 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9))),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14296, 245, 14293])).
% 87.45/87.67 tff(14298,plain,
% 87.45/87.67 (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14297, 14292])).
% 87.45/87.67 tff(14299,plain,
% 87.45/87.67 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14300,plain,
% 87.45/87.67 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14301,plain,
% 87.45/87.67 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14300, 14299])).
% 87.45/87.67 tff(14302,plain,
% 87.45/87.67 ((~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14301, 228, 14293])).
% 87.45/87.67 tff(14303,plain,
% 87.45/87.67 (~node16(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14302, 14298])).
% 87.45/87.67 tff(14304,assumption,(node14(c_e_h_1, c_f, s9, s10)), introduced(assumption)).
% 87.45/87.67 tff(14305,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node14(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node14(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14306,plain,
% 87.45/87.67 (((~node14(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node14(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14307,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node14(c_e_h_1, c_f, s9, s10))))),
% 87.45/87.67 inference(monotonicity,[status(thm)],[14306])).
% 87.45/87.67 tff(14308,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node14(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(transitivity,[status(thm)],[14307, 14305])).
% 87.45/87.67 tff(14309,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14310,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node14(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14309, 14308])).
% 87.45/87.67 tff(14311,plain,
% 87.45/87.67 ($false),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14310, 283, 14270, 14304, 14293])).
% 87.45/87.67 tff(14312,plain,((~node14(c_e_h_1, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.67 tff(14313,plain,
% 87.45/87.67 (~node14(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14312, 14270, 14293])).
% 87.45/87.67 tff(14314,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14315,plain,
% 87.45/87.67 ((node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10))) <=> ((~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14316,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(monotonicity,[status(thm)],[14315])).
% 87.45/87.67 tff(14317,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10))),
% 87.45/87.67 inference(transitivity,[status(thm)],[14316, 14314])).
% 87.45/87.67 tff(14318,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14319,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14318, 14317])).
% 87.45/87.67 tff(14320,plain,
% 87.45/87.67 (node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14319, 189, 14284])).
% 87.45/87.67 tff(14321,plain,
% 87.45/87.67 (node15(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14320, 14313, 14303])).
% 87.45/87.67 tff(14322,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14323,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14324,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14323, 14322])).
% 87.45/87.67 tff(14325,plain,
% 87.45/87.67 ($false),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14324, 173, 14270, 10182, 14321])).
% 87.45/87.67 tff(14326,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | m_c_h_element_v_in1(c_e_h_1, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.67 tff(14327,plain,
% 87.45/87.67 (m_c_h_element_v_in1(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14326, 10182, 14270])).
% 87.45/87.67 tff(14328,plain,
% 87.45/87.67 (~node18(c_e_h_1, c_f, s9, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14279, 10182, 14270])).
% 87.45/87.67 tff(14329,plain,
% 87.45/87.67 (node17(c_e_h_1, c_f, s9)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14291, 14328])).
% 87.45/87.67 tff(14330,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s9)), introduced(assumption)).
% 87.45/87.67 tff(14331,plain,
% 87.45/87.67 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14332,plain,
% 87.45/87.67 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14333,plain,
% 87.45/87.67 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9))),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14332, 14331])).
% 87.45/87.67 tff(14334,plain,
% 87.45/87.67 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9))),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14333, 209, 14330])).
% 87.45/87.67 tff(14335,plain,
% 87.45/87.67 ($false),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14334, 14329, 14327])).
% 87.45/87.67 tff(14336,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.67 tff(14337,plain,
% 87.45/87.67 (m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14336, 14269])).
% 87.45/87.67 tff(14338,plain,
% 87.45/87.67 (~m_c_h_element_v_out(c_e_h_1, c_f, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14337, 10180])).
% 87.45/87.67 tff(14339,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s10)), introduced(assumption)).
% 87.45/87.67 tff(14340,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s10)), introduced(assumption)).
% 87.45/87.67 tff(14341,plain,
% 87.45/87.67 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14342,plain,
% 87.45/87.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14343,plain,
% 87.45/87.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14342, 14341])).
% 87.45/87.67 tff(14344,plain,
% 87.45/87.67 ($false),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14343, 1666, 14340, 14339])).
% 87.45/87.67 tff(14345,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.67 tff(14346,plain,
% 87.45/87.67 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14345, 14338])).
% 87.45/87.67 tff(14347,assumption,(node20(c_e_h_1, c_q, s10)), introduced(assumption)).
% 87.45/87.67 tff(14348,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)), introduced(assumption)).
% 87.45/87.67 tff(14349,plain,
% 87.45/87.67 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14350,plain,
% 87.45/87.67 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10))),
% 87.45/87.67 inference(quant_inst,[status(thm)],[])).
% 87.45/87.67 tff(14351,plain,
% 87.45/87.67 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10)),
% 87.45/87.67 inference(modus_ponens,[status(thm)],[14350, 14349])).
% 87.45/87.67 tff(14352,plain,
% 87.45/87.67 ($false),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14351, 37, 14348, 14347])).
% 87.45/87.67 tff(14353,plain,((~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.67 tff(14354,plain,
% 87.45/87.67 (~node20(c_e_h_1, c_q, s10)),
% 87.45/87.67 inference(unit_resolution,[status(thm)],[14353, 14346])).
% 87.45/87.67 tff(14355,assumption,(~node20(c_e_h_1, c_q, s10)), introduced(assumption)).
% 87.45/87.67 tff(14356,assumption,(node21(c_e_h_1, c_q, s10, s11)), introduced(assumption)).
% 87.45/87.67 tff(14357,plain,
% 87.45/87.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node21(c_e_h_1, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node21(c_e_h_1, c_q, s10, s11)))),
% 87.45/87.67 inference(rewrite,[status(thm)],[])).
% 87.45/87.67 tff(14358,plain,
% 87.45/87.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node21(c_e_h_1, c_q, s10, s11)))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14359,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node21(c_e_h_1, c_q, s10, s11))),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14358, 14357])).
% 87.45/87.68 tff(14360,plain,
% 87.45/87.68 ($false),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14359, 51, 14265, 14356, 14355])).
% 87.45/87.68 tff(14361,plain,((~node21(c_e_h_1, c_q, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.68 tff(14362,plain,
% 87.45/87.68 ((~node21(c_e_h_1, c_q, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14361, 14354])).
% 87.45/87.68 tff(14363,plain,
% 87.45/87.68 (~node21(c_e_h_1, c_q, s10, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14362, 14265])).
% 87.45/87.68 tff(14364,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s10)), introduced(assumption)).
% 87.45/87.68 tff(14365,assumption,(node22(c_e_h_1, c_q, s10, s11)), introduced(assumption)).
% 87.45/87.68 tff(14366,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14367,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14368,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14367, 14366])).
% 87.45/87.68 tff(14369,plain,
% 87.45/87.68 ($false),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14368, 107, 14364, 14265, 14365])).
% 87.45/87.68 tff(14370,plain,((~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.68 tff(14371,plain,
% 87.45/87.68 (~node22(c_e_h_1, c_q, s10, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14370, 14265, 14364])).
% 87.45/87.68 tff(14372,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14373,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14374,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14373, 14372])).
% 87.45/87.68 tff(14375,plain,
% 87.45/87.68 (node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14374, 81, 3778])).
% 87.45/87.68 tff(14376,plain,
% 87.45/87.68 ($false),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14375, 14371, 14363])).
% 87.45/87.68 tff(14377,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.68 tff(14378,plain,
% 87.45/87.68 (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14377, 10220])).
% 87.45/87.68 tff(14379,plain,
% 87.45/87.68 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s11))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s11))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14380,plain,
% 87.45/87.68 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s11))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14381,plain,
% 87.45/87.68 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s11)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14380, 14379])).
% 87.45/87.68 tff(14382,plain,
% 87.45/87.68 (node3(c_e_h_1, c_e_h_2, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14381, 817, 814])).
% 87.45/87.68 tff(14383,plain,
% 87.45/87.68 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s11)) | (~node3(c_e_h_1, c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s11)) | (~node3(c_e_h_1, c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14384,plain,
% 87.45/87.68 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s11)) | (~node3(c_e_h_1, c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14385,plain,
% 87.45/87.68 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s11)) | (~node3(c_e_h_1, c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14384, 14383])).
% 87.45/87.68 tff(14386,plain,
% 87.45/87.68 ((~m_cell_v_ack(c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14385, 836, 14382])).
% 87.45/87.68 tff(14387,plain,
% 87.45/87.68 (~m_cell_v_ack(c_e_h_2, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14386, 14378])).
% 87.45/87.68 tff(14388,plain,
% 87.45/87.68 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)) | m_cell_v_ack(c_e_h_2, s11))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)) | m_cell_v_ack(c_e_h_2, s11))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14389,plain,
% 87.45/87.68 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)) | m_cell_v_ack(c_e_h_2, s11))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14390,plain,
% 87.45/87.68 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)) | m_cell_v_ack(c_e_h_2, s11)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14389, 14388])).
% 87.45/87.68 tff(14391,plain,
% 87.45/87.68 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14390, 848, 14387])).
% 87.45/87.68 tff(14392,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)), introduced(assumption)).
% 87.45/87.68 tff(14393,assumption,(node5(c_e_h_2, c_j, s11, s12)), introduced(assumption)).
% 87.45/87.68 tff(14394,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12)))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14395,plain,
% 87.45/87.68 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12))) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12)))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14396,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12))))),
% 87.45/87.68 inference(monotonicity,[status(thm)],[14395])).
% 87.45/87.68 tff(14397,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12)))),
% 87.45/87.68 inference(transitivity,[status(thm)],[14396, 14394])).
% 87.45/87.68 tff(14398,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14399,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | (~node5(c_e_h_2, c_j, s11, s12))),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14398, 14397])).
% 87.45/87.68 tff(14400,plain,
% 87.45/87.68 ($false),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14399, 862, 14253, 14393, 14392, 14264])).
% 87.45/87.68 tff(14401,plain,((~node5(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s11) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.68 tff(14402,plain,
% 87.45/87.68 ((~node5(c_e_h_2, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14401, 14391])).
% 87.45/87.68 tff(14403,plain,
% 87.45/87.68 (~node5(c_e_h_2, c_j, s11, s12)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14402, 14253, 14264])).
% 87.45/87.68 tff(14404,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s11, s12)) | node5(c_e_h_2, c_j, s11, s12) | node6(c_e_h_2, c_j, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_2, c_j, s11, s12) | node6(c_e_h_2, c_j, s11, s12))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14405,plain,
% 87.45/87.68 ((node6(c_e_h_2, c_j, s11, s12) | node5(c_e_h_2, c_j, s11, s12) | (~trans(s11, s12))) <=> ((~trans(s11, s12)) | node5(c_e_h_2, c_j, s11, s12) | node6(c_e_h_2, c_j, s11, s12))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14406,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s11, s12) | node5(c_e_h_2, c_j, s11, s12) | (~trans(s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s11, s12)) | node5(c_e_h_2, c_j, s11, s12) | node6(c_e_h_2, c_j, s11, s12)))),
% 87.45/87.68 inference(monotonicity,[status(thm)],[14405])).
% 87.45/87.68 tff(14407,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s11, s12) | node5(c_e_h_2, c_j, s11, s12) | (~trans(s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_2, c_j, s11, s12) | node6(c_e_h_2, c_j, s11, s12))),
% 87.45/87.68 inference(transitivity,[status(thm)],[14406, 14404])).
% 87.45/87.68 tff(14408,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s11, s12) | node5(c_e_h_2, c_j, s11, s12) | (~trans(s11, s12)))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14409,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_2, c_j, s11, s12) | node6(c_e_h_2, c_j, s11, s12)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14408, 14407])).
% 87.45/87.68 tff(14410,plain,
% 87.45/87.68 (node5(c_e_h_2, c_j, s11, s12) | node6(c_e_h_2, c_j, s11, s12)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14409, 881, 4461])).
% 87.45/87.68 tff(14411,plain,
% 87.45/87.68 ($false),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14410, 14403, 14263])).
% 87.45/87.68 tff(14412,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s12)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s11) | m_or_h_gate_v_out(c_e_h_2, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.68 tff(14413,plain,
% 87.45/87.68 (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14412, 14252, 10260])).
% 87.45/87.68 tff(14414,plain,
% 87.45/87.68 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14415,plain,
% 87.45/87.68 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14416,plain,
% 87.45/87.68 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s12)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14415, 14414])).
% 87.45/87.68 tff(14417,plain,
% 87.45/87.68 (~m_c_h_element_v_in2(c_e_h_2, c_h, s12)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14416, 309, 14413])).
% 87.45/87.68 tff(14418,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s13)), introduced(assumption)).
% 87.45/87.68 tff(14419,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s12)), introduced(assumption)).
% 87.45/87.68 tff(14420,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s12)), introduced(assumption)).
% 87.45/87.68 tff(14421,assumption,(node15(c_e_h_2, c_h, s12, s13)), introduced(assumption)).
% 87.45/87.68 tff(14422,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node15(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node15(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14423,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node15(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14424,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node15(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14423, 14422])).
% 87.45/87.68 tff(14425,plain,
% 87.45/87.68 ($false),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14424, 173, 14418, 14420, 14421])).
% 87.45/87.68 tff(14426,plain,((~node15(c_e_h_2, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.68 tff(14427,plain,
% 87.45/87.68 (~node15(c_e_h_2, c_h, s12, s13)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14426, 14418, 14420])).
% 87.45/87.68 tff(14428,assumption,(node18(c_e_h_2, c_h, s12, s13)), introduced(assumption)).
% 87.45/87.68 tff(14429,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node18(c_e_h_2, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node18(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14430,plain,
% 87.45/87.68 (((~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~node18(c_e_h_2, c_h, s12, s13))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node18(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14431,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~node18(c_e_h_2, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node18(c_e_h_2, c_h, s12, s13))))),
% 87.45/87.68 inference(monotonicity,[status(thm)],[14430])).
% 87.45/87.68 tff(14432,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~node18(c_e_h_2, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node18(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.68 inference(transitivity,[status(thm)],[14431, 14429])).
% 87.45/87.68 tff(14433,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~node18(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14434,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node18(c_e_h_2, c_h, s12, s13))),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14433, 14432])).
% 87.45/87.68 tff(14435,plain,
% 87.45/87.68 ($false),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14434, 124, 14418, 14420, 14428])).
% 87.45/87.68 tff(14436,plain,((~node18(c_e_h_2, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.68 tff(14437,plain,
% 87.45/87.68 (~node18(c_e_h_2, c_h, s12, s13)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14436, 14418, 14420])).
% 87.45/87.68 tff(14438,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_2, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_2, c_h, s12, s13))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14439,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_2, c_h, s12, s13))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14440,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_2, c_h, s12, s13)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14439, 14438])).
% 87.45/87.68 tff(14441,plain,
% 87.45/87.68 (node19(c_e_h_2, c_h, s12, s13)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14440, 141, 9599])).
% 87.45/87.68 tff(14442,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s12) | (~node19(c_e_h_2, c_h, s12, s13)) | node18(c_e_h_2, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s12) | (~node19(c_e_h_2, c_h, s12, s13)) | node18(c_e_h_2, c_h, s12, s13))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14443,plain,
% 87.45/87.68 ((node17(c_e_h_2, c_h, s12) | node18(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13))) <=> (node17(c_e_h_2, c_h, s12) | (~node19(c_e_h_2, c_h, s12, s13)) | node18(c_e_h_2, c_h, s12, s13))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14444,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s12) | node18(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s12) | (~node19(c_e_h_2, c_h, s12, s13)) | node18(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.68 inference(monotonicity,[status(thm)],[14443])).
% 87.45/87.68 tff(14445,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s12) | node18(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s12) | (~node19(c_e_h_2, c_h, s12, s13)) | node18(c_e_h_2, c_h, s12, s13))),
% 87.45/87.68 inference(transitivity,[status(thm)],[14444, 14442])).
% 87.45/87.68 tff(14446,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s12) | node18(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14447,plain,
% 87.45/87.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s12) | (~node19(c_e_h_2, c_h, s12, s13)) | node18(c_e_h_2, c_h, s12, s13)),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14446, 14445])).
% 87.45/87.68 tff(14448,plain,
% 87.45/87.68 (node17(c_e_h_2, c_h, s12) | node18(c_e_h_2, c_h, s12, s13)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14447, 156, 14441])).
% 87.45/87.68 tff(14449,plain,
% 87.45/87.68 (node17(c_e_h_2, c_h, s12)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14448, 14437])).
% 87.45/87.68 tff(14450,assumption,(~node15(c_e_h_2, c_h, s12, s13)), introduced(assumption)).
% 87.45/87.68 tff(14451,assumption,(node17(c_e_h_2, c_h, s12)), introduced(assumption)).
% 87.45/87.68 tff(14452,plain,
% 87.45/87.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s12)))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14453,plain,
% 87.45/87.68 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~node17(c_e_h_2, c_h, s12))) <=> ((~node17(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s12)))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14454,plain,
% 87.45/87.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~node17(c_e_h_2, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s12))))),
% 87.45/87.68 inference(monotonicity,[status(thm)],[14453])).
% 87.45/87.68 tff(14455,plain,
% 87.45/87.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~node17(c_e_h_2, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s12)))),
% 87.45/87.68 inference(transitivity,[status(thm)],[14454, 14452])).
% 87.45/87.68 tff(14456,plain,
% 87.45/87.68 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~node17(c_e_h_2, c_h, s12)))),
% 87.45/87.68 inference(quant_inst,[status(thm)],[])).
% 87.45/87.68 tff(14457,plain,
% 87.45/87.68 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s12)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s12))),
% 87.45/87.68 inference(modus_ponens,[status(thm)],[14456, 14455])).
% 87.45/87.68 tff(14458,plain,
% 87.45/87.68 (m_c_h_element_v_in2(c_e_h_2, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s12))),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14457, 209, 14451])).
% 87.45/87.68 tff(14459,plain,
% 87.45/87.68 (~m_c_h_element_v_in1(c_e_h_2, c_h, s12)),
% 87.45/87.68 inference(unit_resolution,[status(thm)],[14458, 14419])).
% 87.45/87.68 tff(14460,assumption,(node14(c_e_h_2, c_h, s12, s13)), introduced(assumption)).
% 87.45/87.68 tff(14461,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s12)), introduced(assumption)).
% 87.45/87.68 tff(14462,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node14(c_e_h_2, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node14(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14463,plain,
% 87.45/87.68 (((~node14(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node14(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.68 inference(rewrite,[status(thm)],[])).
% 87.45/87.68 tff(14464,plain,
% 87.45/87.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node14(c_e_h_2, c_h, s12, s13))))),
% 87.45/87.69 inference(monotonicity,[status(thm)],[14463])).
% 87.45/87.69 tff(14465,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node14(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.69 inference(transitivity,[status(thm)],[14464, 14462])).
% 87.45/87.69 tff(14466,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14467,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node14(c_e_h_2, c_h, s12, s13))),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14466, 14465])).
% 87.45/87.69 tff(14468,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14467, 283, 14461, 14418, 14460])).
% 87.45/87.69 tff(14469,plain,((~node14(c_e_h_2, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14470,plain,
% 87.45/87.69 (~node14(c_e_h_2, c_h, s12, s13)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14469, 14459, 14418])).
% 87.45/87.69 tff(14471,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)) | node15(c_e_h_2, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)) | node15(c_e_h_2, c_h, s12, s13))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14472,plain,
% 87.45/87.69 ((node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | node15(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13))) <=> (node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)) | node15(c_e_h_2, c_h, s12, s13))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14473,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | node15(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)) | node15(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.69 inference(monotonicity,[status(thm)],[14472])).
% 87.45/87.69 tff(14474,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | node15(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)) | node15(c_e_h_2, c_h, s12, s13))),
% 87.45/87.69 inference(transitivity,[status(thm)],[14473, 14471])).
% 87.45/87.69 tff(14475,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | node15(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14476,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | (~node19(c_e_h_2, c_h, s12, s13)) | node15(c_e_h_2, c_h, s12, s13)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14475, 14474])).
% 87.45/87.69 tff(14477,plain,
% 87.45/87.69 (node16(c_e_h_2, c_h, s12) | node14(c_e_h_2, c_h, s12, s13) | node15(c_e_h_2, c_h, s12, s13)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14476, 189, 14441])).
% 87.45/87.69 tff(14478,plain,
% 87.45/87.69 (node16(c_e_h_2, c_h, s12)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14477, 14470, 14450])).
% 87.45/87.69 tff(14479,plain,
% 87.45/87.69 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | m_c_h_element_v_in2(c_e_h_2, c_h, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | m_c_h_element_v_in2(c_e_h_2, c_h, s12))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14480,plain,
% 87.45/87.69 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | m_c_h_element_v_in2(c_e_h_2, c_h, s12))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14481,plain,
% 87.45/87.69 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s12)) | m_c_h_element_v_in1(c_e_h_2, c_h, s12) | m_c_h_element_v_in2(c_e_h_2, c_h, s12)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14480, 14479])).
% 87.45/87.69 tff(14482,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14481, 228, 14459, 14478, 14419])).
% 87.45/87.69 tff(14483,plain,(m_c_h_element_v_in2(c_e_h_2, c_h, s12) | node15(c_e_h_2, c_h, s12, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14484,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14483, 14449, 14427, 14419, 14418])).
% 87.45/87.69 tff(14485,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s13)) | m_c_h_element_v_in2(c_e_h_2, c_h, s12) | m_c_h_element_v_out(c_e_h_2, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14486,plain,
% 87.45/87.69 (~m_c_h_element_v_out(c_e_h_2, c_h, s13)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14485, 14417, 10345])).
% 87.45/87.69 tff(14487,plain,
% 87.45/87.69 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s13))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14488,plain,
% 87.45/87.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s13))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14489,plain,
% 87.45/87.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s13)) | m_c_h_element_v_out(c_e_h_2, c_h, s13)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14488, 14487])).
% 87.45/87.69 tff(14490,plain,
% 87.45/87.69 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s13)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14489, 23, 14486])).
% 87.45/87.69 tff(14491,plain,
% 87.45/87.69 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s13))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14492,plain,
% 87.45/87.69 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s13))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14493,plain,
% 87.45/87.69 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s13)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14492, 14491])).
% 87.45/87.69 tff(14494,plain,
% 87.45/87.69 (~node20(c_e_h_2, c_i, s13)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14493, 37, 14490])).
% 87.45/87.69 tff(14495,assumption,(~node20(c_e_h_2, c_i, s13)), introduced(assumption)).
% 87.45/87.69 tff(14496,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s14)), introduced(assumption)).
% 87.45/87.69 tff(14497,assumption,(node21(c_e_h_2, c_i, s13, s14)), introduced(assumption)).
% 87.45/87.69 tff(14498,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s13) | (~node21(c_e_h_2, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s13) | (~node21(c_e_h_2, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14499,plain,
% 87.45/87.69 ((node20(c_e_h_2, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | (~node21(c_e_h_2, c_i, s13, s14))) <=> (node20(c_e_h_2, c_i, s13) | (~node21(c_e_h_2, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14500,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | (~node21(c_e_h_2, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s13) | (~node21(c_e_h_2, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14))))),
% 87.45/87.69 inference(monotonicity,[status(thm)],[14499])).
% 87.45/87.69 tff(14501,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | (~node21(c_e_h_2, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s13) | (~node21(c_e_h_2, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)))),
% 87.45/87.69 inference(transitivity,[status(thm)],[14500, 14498])).
% 87.45/87.69 tff(14502,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | (~node21(c_e_h_2, c_i, s13, s14)))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14503,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s13) | (~node21(c_e_h_2, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14))),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14502, 14501])).
% 87.45/87.69 tff(14504,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14503, 51, 14496, 14497, 14495])).
% 87.45/87.69 tff(14505,plain,((~node21(c_e_h_2, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | node20(c_e_h_2, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14506,plain,
% 87.45/87.69 (~node21(c_e_h_2, c_i, s13, s14)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14505, 14496, 14495])).
% 87.45/87.69 tff(14507,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_2, c_i, s13, s14) | node22(c_e_h_2, c_i, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_2, c_i, s13, s14) | node22(c_e_h_2, c_i, s13, s14))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14508,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_2, c_i, s13, s14) | node22(c_e_h_2, c_i, s13, s14))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14509,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_2, c_i, s13, s14) | node22(c_e_h_2, c_i, s13, s14)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14508, 14507])).
% 87.45/87.69 tff(14510,plain,
% 87.45/87.69 (node21(c_e_h_2, c_i, s13, s14) | node22(c_e_h_2, c_i, s13, s14)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14509, 81, 10040])).
% 87.45/87.69 tff(14511,plain,
% 87.45/87.69 (node22(c_e_h_2, c_i, s13, s14)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14510, 14506])).
% 87.45/87.69 tff(14512,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | (~node22(c_e_h_2, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | (~node22(c_e_h_2, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14513,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | (~node22(c_e_h_2, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14514,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | (~node22(c_e_h_2, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14513, 14512])).
% 87.45/87.69 tff(14515,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14514, 107, 10378, 14496, 14511])).
% 87.45/87.69 tff(14516,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13) | node20(c_e_h_2, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14517,plain,
% 87.45/87.69 (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14516, 14494, 10376])).
% 87.45/87.69 tff(14518,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s12)), introduced(assumption)).
% 87.45/87.69 tff(14519,plain,
% 87.45/87.69 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14520,plain,
% 87.45/87.69 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14521,plain,
% 87.45/87.69 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14520, 14519])).
% 87.45/87.69 tff(14522,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14521, 801, 14518, 14218])).
% 87.45/87.69 tff(14523,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)) | m_and_h_gate_v_out(c_e_h_2, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14524,plain,
% 87.45/87.69 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14523, 14208])).
% 87.45/87.69 tff(14525,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s12)), introduced(assumption)).
% 87.45/87.69 tff(14526,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s13)), introduced(assumption)).
% 87.45/87.69 tff(14527,assumption,(node6(c_e_h_2, c_j, s12, s13)), introduced(assumption)).
% 87.45/87.69 tff(14528,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12) | (~node6(c_e_h_2, c_j, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12) | (~node6(c_e_h_2, c_j, s12, s13)))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14529,plain,
% 87.45/87.69 (((~node6(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12)) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12) | (~node6(c_e_h_2, c_j, s12, s13)))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14530,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12) | (~node6(c_e_h_2, c_j, s12, s13))))),
% 87.45/87.69 inference(monotonicity,[status(thm)],[14529])).
% 87.45/87.69 tff(14531,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12) | (~node6(c_e_h_2, c_j, s12, s13)))),
% 87.45/87.69 inference(transitivity,[status(thm)],[14530, 14528])).
% 87.45/87.69 tff(14532,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14533,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12) | (~node6(c_e_h_2, c_j, s12, s13))),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14532, 14531])).
% 87.45/87.69 tff(14534,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14533, 899, 14525, 14526, 14527])).
% 87.45/87.69 tff(14535,plain,((~node6(c_e_h_2, c_j, s12, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14536,plain,
% 87.45/87.69 (~node6(c_e_h_2, c_j, s12, s13)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14535, 14526, 14525])).
% 87.45/87.69 tff(14537,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)), introduced(assumption)).
% 87.45/87.69 tff(14538,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s12)), introduced(assumption)).
% 87.45/87.69 tff(14539,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s10)), introduced(assumption)).
% 87.45/87.69 tff(14540,plain,
% 87.45/87.69 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14541,plain,
% 87.45/87.69 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14542,plain,
% 87.45/87.69 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14541, 14540])).
% 87.45/87.69 tff(14543,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14542, 2218, 11712, 14539])).
% 87.45/87.69 tff(14544,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14545,plain,
% 87.45/87.69 (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14544, 11710])).
% 87.45/87.69 tff(14546,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s11)), introduced(assumption)).
% 87.45/87.69 tff(14547,assumption,(node18(c_e_h_1, c_f, s10, s11)), introduced(assumption)).
% 87.45/87.69 tff(14548,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14549,plain,
% 87.45/87.69 (((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~node18(c_e_h_1, c_f, s10, s11))) <=> ((~node18(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14550,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~node18(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11))))),
% 87.45/87.69 inference(monotonicity,[status(thm)],[14549])).
% 87.45/87.69 tff(14551,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~node18(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))),
% 87.45/87.69 inference(transitivity,[status(thm)],[14550, 14548])).
% 87.45/87.69 tff(14552,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~node18(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14553,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14552, 14551])).
% 87.45/87.69 tff(14554,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14553, 124, 14546, 14547, 14340])).
% 87.45/87.69 tff(14555,plain,((~node18(c_e_h_1, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14556,plain,
% 87.45/87.69 (~node18(c_e_h_1, c_f, s10, s11)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14555, 14546, 14340])).
% 87.45/87.69 tff(14557,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_f, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_f, s10, s11))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14558,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_f, s10, s11))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14559,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_f, s10, s11)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14558, 14557])).
% 87.45/87.69 tff(14560,plain,
% 87.45/87.69 (node19(c_e_h_1, c_f, s10, s11)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14559, 141, 3778])).
% 87.45/87.69 tff(14561,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14562,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14563,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11))),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14562, 14561])).
% 87.45/87.69 tff(14564,plain,
% 87.45/87.69 (node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14563, 156, 14560])).
% 87.45/87.69 tff(14565,plain,
% 87.45/87.69 (node17(c_e_h_1, c_f, s10)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14564, 14556])).
% 87.45/87.69 tff(14566,assumption,(node15(c_e_h_1, c_f, s10, s11)), introduced(assumption)).
% 87.45/87.69 tff(14567,plain,
% 87.45/87.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node15(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node15(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 87.45/87.69 inference(rewrite,[status(thm)],[])).
% 87.45/87.69 tff(14568,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node15(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 87.45/87.69 inference(quant_inst,[status(thm)],[])).
% 87.45/87.69 tff(14569,plain,
% 87.45/87.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node15(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)),
% 87.45/87.69 inference(modus_ponens,[status(thm)],[14568, 14567])).
% 87.45/87.69 tff(14570,plain,
% 87.45/87.69 ($false),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14569, 173, 14546, 14566, 14340])).
% 87.45/87.69 tff(14571,plain,((~node15(c_e_h_1, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.69 tff(14572,plain,
% 87.45/87.69 (~node15(c_e_h_1, c_f, s10, s11)),
% 87.45/87.69 inference(unit_resolution,[status(thm)],[14571, 14546, 14340])).
% 87.45/87.69 tff(14573,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s10)), introduced(assumption)).
% 87.45/87.69 tff(14574,assumption,(~node15(c_e_h_1, c_f, s10, s11)), introduced(assumption)).
% 87.45/87.70 tff(14575,assumption,(node17(c_e_h_1, c_f, s10)), introduced(assumption)).
% 87.45/87.70 tff(14576,plain,
% 87.45/87.70 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14577,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14578,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10))),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14577, 14576])).
% 87.45/87.70 tff(14579,plain,
% 87.45/87.70 (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10))),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14578, 245, 14575])).
% 87.45/87.70 tff(14580,plain,
% 87.45/87.70 (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14579, 14573])).
% 87.45/87.70 tff(14581,plain,
% 87.45/87.70 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14582,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14583,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10)),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14582, 14581])).
% 87.45/87.70 tff(14584,plain,
% 87.45/87.70 (~node16(c_e_h_1, c_f, s10)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14583, 228, 14573, 14580])).
% 87.45/87.70 tff(14585,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14586,plain,
% 87.45/87.70 ((node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11))) <=> (node14(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14587,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11))))),
% 87.45/87.70 inference(monotonicity,[status(thm)],[14586])).
% 87.45/87.70 tff(14588,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.70 inference(transitivity,[status(thm)],[14587, 14585])).
% 87.45/87.70 tff(14589,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14590,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11))),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14589, 14588])).
% 87.45/87.70 tff(14591,plain,
% 87.45/87.70 (node14(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node15(c_e_h_1, c_f, s10, s11)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14590, 189, 14560])).
% 87.45/87.70 tff(14592,plain,
% 87.45/87.70 (node14(c_e_h_1, c_f, s10, s11)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14591, 14584, 14574])).
% 87.45/87.70 tff(14593,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node14(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node14(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14594,plain,
% 87.45/87.70 (((~node14(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node14(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14595,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node14(c_e_h_1, c_f, s10, s11))))),
% 87.45/87.70 inference(monotonicity,[status(thm)],[14594])).
% 87.45/87.70 tff(14596,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node14(c_e_h_1, c_f, s10, s11)))),
% 87.45/87.70 inference(transitivity,[status(thm)],[14595, 14593])).
% 87.45/87.70 tff(14597,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14598,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node14(c_e_h_1, c_f, s10, s11))),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14597, 14596])).
% 87.45/87.70 tff(14599,plain,
% 87.45/87.70 ($false),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14598, 283, 14546, 14592, 14573])).
% 87.45/87.70 tff(14600,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | node15(c_e_h_1, c_f, s10, s11) | (~node17(c_e_h_1, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.70 tff(14601,plain,
% 87.45/87.70 (m_c_h_element_v_in1(c_e_h_1, c_f, s10)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14600, 14572, 14546, 14565])).
% 87.45/87.70 tff(14602,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s10)), introduced(assumption)).
% 87.45/87.70 tff(14603,plain,
% 87.45/87.70 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14604,plain,
% 87.45/87.70 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14605,plain,
% 87.45/87.70 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10))))),
% 87.45/87.70 inference(monotonicity,[status(thm)],[14604])).
% 87.45/87.70 tff(14606,plain,
% 87.45/87.70 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))),
% 87.45/87.70 inference(transitivity,[status(thm)],[14605, 14603])).
% 87.45/87.70 tff(14607,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14608,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10))),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14607, 14606])).
% 87.45/87.70 tff(14609,plain,
% 87.45/87.70 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10))),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14608, 209, 14602])).
% 87.45/87.70 tff(14610,plain,
% 87.45/87.70 ($false),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14609, 14601, 14565])).
% 87.45/87.70 tff(14611,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | m_c_h_element_v_out(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.70 tff(14612,plain,
% 87.45/87.70 ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14611, 14545])).
% 87.45/87.70 tff(14613,plain,
% 87.45/87.70 (~m_c_h_element_v_out(c_e_h_1, c_f, s11)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14612, 14338])).
% 87.45/87.70 tff(14614,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s11)), introduced(assumption)).
% 87.45/87.70 tff(14615,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s11)), introduced(assumption)).
% 87.45/87.70 tff(14616,plain,
% 87.45/87.70 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14617,plain,
% 87.45/87.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14618,plain,
% 87.45/87.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14617, 14616])).
% 87.45/87.70 tff(14619,plain,
% 87.45/87.70 ($false),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14618, 1666, 14615, 14614])).
% 87.45/87.70 tff(14620,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.70 tff(14621,plain,
% 87.45/87.70 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14620, 14613])).
% 87.45/87.70 tff(14622,assumption,(node20(c_e_h_1, c_q, s11)), introduced(assumption)).
% 87.45/87.70 tff(14623,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)), introduced(assumption)).
% 87.45/87.70 tff(14624,plain,
% 87.45/87.70 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14625,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14626,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11)),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14625, 14624])).
% 87.45/87.70 tff(14627,plain,
% 87.45/87.70 ($false),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14626, 37, 14623, 14622])).
% 87.45/87.70 tff(14628,plain,((~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.70 tff(14629,plain,
% 87.45/87.70 (~node20(c_e_h_1, c_q, s11)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14628, 14621])).
% 87.45/87.70 tff(14630,assumption,(~node20(c_e_h_1, c_q, s11)), introduced(assumption)).
% 87.45/87.70 tff(14631,assumption,(node21(c_e_h_1, c_q, s11, s12)), introduced(assumption)).
% 87.45/87.70 tff(14632,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node21(c_e_h_1, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node21(c_e_h_1, c_q, s11, s12)))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14633,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node21(c_e_h_1, c_q, s11, s12)))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14634,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node21(c_e_h_1, c_q, s11, s12))),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14633, 14632])).
% 87.45/87.70 tff(14635,plain,
% 87.45/87.70 ($false),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14634, 51, 14538, 14631, 14630])).
% 87.45/87.70 tff(14636,plain,((~node21(c_e_h_1, c_q, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.70 tff(14637,plain,
% 87.45/87.70 ((~node21(c_e_h_1, c_q, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14636, 14629])).
% 87.45/87.70 tff(14638,plain,
% 87.45/87.70 (~node21(c_e_h_1, c_q, s11, s12)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14637, 14538])).
% 87.45/87.70 tff(14639,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s11)), introduced(assumption)).
% 87.45/87.70 tff(14640,assumption,(node22(c_e_h_1, c_q, s11, s12)), introduced(assumption)).
% 87.45/87.70 tff(14641,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14642,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14643,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14642, 14641])).
% 87.45/87.70 tff(14644,plain,
% 87.45/87.70 ($false),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14643, 107, 14639, 14538, 14640])).
% 87.45/87.70 tff(14645,plain,((~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.70 tff(14646,plain,
% 87.45/87.70 (~node22(c_e_h_1, c_q, s11, s12)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14645, 14538, 14639])).
% 87.45/87.70 tff(14647,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14648,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14649,plain,
% 87.45/87.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12)),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14648, 14647])).
% 87.45/87.70 tff(14650,plain,
% 87.45/87.70 (node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14649, 81, 4461])).
% 87.45/87.70 tff(14651,plain,
% 87.45/87.70 ($false),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14650, 14646, 14638])).
% 87.45/87.70 tff(14652,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.70 tff(14653,plain,
% 87.45/87.70 (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14652, 14378])).
% 87.45/87.70 tff(14654,plain,
% 87.45/87.70 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s12))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14655,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s12))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14656,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s12)),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14655, 14654])).
% 87.45/87.70 tff(14657,plain,
% 87.45/87.70 (node3(c_e_h_1, c_e_h_2, s12)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14656, 817, 814])).
% 87.45/87.70 tff(14658,plain,
% 87.45/87.70 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s12)) | (~node3(c_e_h_1, c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s12)) | (~node3(c_e_h_1, c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14659,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s12)) | (~node3(c_e_h_1, c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14660,plain,
% 87.45/87.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s12)) | (~node3(c_e_h_1, c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14659, 14658])).
% 87.45/87.70 tff(14661,plain,
% 87.45/87.70 ((~m_cell_v_ack(c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14660, 836, 14657])).
% 87.45/87.70 tff(14662,plain,
% 87.45/87.70 (~m_cell_v_ack(c_e_h_2, s12)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14661, 14653])).
% 87.45/87.70 tff(14663,plain,
% 87.45/87.70 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)) | m_cell_v_ack(c_e_h_2, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)) | m_cell_v_ack(c_e_h_2, s12))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14664,plain,
% 87.45/87.70 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)) | m_cell_v_ack(c_e_h_2, s12))),
% 87.45/87.70 inference(quant_inst,[status(thm)],[])).
% 87.45/87.70 tff(14665,plain,
% 87.45/87.70 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)) | m_cell_v_ack(c_e_h_2, s12)),
% 87.45/87.70 inference(modus_ponens,[status(thm)],[14664, 14663])).
% 87.45/87.70 tff(14666,plain,
% 87.45/87.70 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)),
% 87.45/87.70 inference(unit_resolution,[status(thm)],[14665, 848, 14662])).
% 87.45/87.70 tff(14667,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)), introduced(assumption)).
% 87.45/87.70 tff(14668,assumption,(node5(c_e_h_2, c_j, s12, s13)), introduced(assumption)).
% 87.45/87.70 tff(14669,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14670,plain,
% 87.45/87.70 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s12) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13))) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12))),
% 87.45/87.70 inference(rewrite,[status(thm)],[])).
% 87.45/87.70 tff(14671,plain,
% 87.45/87.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s12) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12)))),
% 87.45/87.71 inference(monotonicity,[status(thm)],[14670])).
% 87.45/87.71 tff(14672,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s12) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12))),
% 87.45/87.71 inference(transitivity,[status(thm)],[14671, 14669])).
% 87.45/87.71 tff(14673,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s12) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14674,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | (~node5(c_e_h_2, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14673, 14672])).
% 87.45/87.71 tff(14675,plain,
% 87.45/87.71 ($false),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14674, 862, 14526, 14668, 14667, 14537])).
% 87.45/87.71 tff(14676,plain,((~node5(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s12) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.71 tff(14677,plain,
% 87.45/87.71 ((~node5(c_e_h_2, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14676, 14666])).
% 87.45/87.71 tff(14678,plain,
% 87.45/87.71 (~node5(c_e_h_2, c_j, s12, s13)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14677, 14526, 14537])).
% 87.45/87.71 tff(14679,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s12, s13)) | node5(c_e_h_2, c_j, s12, s13) | node6(c_e_h_2, c_j, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node5(c_e_h_2, c_j, s12, s13) | node6(c_e_h_2, c_j, s12, s13))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14680,plain,
% 87.45/87.71 ((node6(c_e_h_2, c_j, s12, s13) | node5(c_e_h_2, c_j, s12, s13) | (~trans(s12, s13))) <=> ((~trans(s12, s13)) | node5(c_e_h_2, c_j, s12, s13) | node6(c_e_h_2, c_j, s12, s13))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14681,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s12, s13) | node5(c_e_h_2, c_j, s12, s13) | (~trans(s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s12, s13)) | node5(c_e_h_2, c_j, s12, s13) | node6(c_e_h_2, c_j, s12, s13)))),
% 87.45/87.71 inference(monotonicity,[status(thm)],[14680])).
% 87.45/87.71 tff(14682,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s12, s13) | node5(c_e_h_2, c_j, s12, s13) | (~trans(s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node5(c_e_h_2, c_j, s12, s13) | node6(c_e_h_2, c_j, s12, s13))),
% 87.45/87.71 inference(transitivity,[status(thm)],[14681, 14679])).
% 87.45/87.71 tff(14683,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s12, s13) | node5(c_e_h_2, c_j, s12, s13) | (~trans(s12, s13)))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14684,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node5(c_e_h_2, c_j, s12, s13) | node6(c_e_h_2, c_j, s12, s13)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14683, 14682])).
% 87.45/87.71 tff(14685,plain,
% 87.45/87.71 (node5(c_e_h_2, c_j, s12, s13) | node6(c_e_h_2, c_j, s12, s13)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14684, 881, 9599])).
% 87.45/87.71 tff(14686,plain,
% 87.45/87.71 ($false),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14685, 14678, 14536])).
% 87.45/87.71 tff(14687,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s13)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s12) | m_or_h_gate_v_out(c_e_h_2, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.71 tff(14688,plain,
% 87.45/87.71 (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14687, 14524, 14413])).
% 87.45/87.71 tff(14689,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s14)), introduced(assumption)).
% 87.45/87.71 tff(14690,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s14)), introduced(assumption)).
% 87.45/87.71 tff(14691,plain,
% 87.45/87.71 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14692,plain,
% 87.45/87.71 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14693,plain,
% 87.45/87.71 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14692, 14691])).
% 87.45/87.71 tff(14694,plain,
% 87.45/87.71 ($false),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14693, 365, 14690, 14689])).
% 87.45/87.71 tff(14695,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.71 tff(14696,plain,
% 87.45/87.71 (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14695, 14517])).
% 87.45/87.71 tff(14697,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s15)), introduced(assumption)).
% 87.45/87.71 tff(14698,assumption,(node18(c_e_h_2, c_e, s14, s15)), introduced(assumption)).
% 87.45/87.71 tff(14699,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14700,plain,
% 87.45/87.71 (((~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14701,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15))))),
% 87.45/87.71 inference(monotonicity,[status(thm)],[14700])).
% 87.45/87.71 tff(14702,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))),
% 87.45/87.71 inference(transitivity,[status(thm)],[14701, 14699])).
% 87.45/87.71 tff(14703,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14704,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~node18(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15))),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14703, 14702])).
% 87.45/87.71 tff(14705,plain,
% 87.45/87.71 ($false),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14704, 124, 14697, 10465, 14698])).
% 87.45/87.71 tff(14706,plain,((~node18(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.71 tff(14707,plain,
% 87.45/87.71 (~node18(c_e_h_2, c_e, s14, s15)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14706, 14697, 10465])).
% 87.45/87.71 tff(14708,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_2, c_e, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_2, c_e, s14, s15))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14709,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_2, c_e, s14, s15))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14710,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_2, c_e, s14, s15)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14709, 14708])).
% 87.45/87.71 tff(14711,plain,
% 87.45/87.71 (node19(c_e_h_2, c_e, s14, s15)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14710, 141, 10504])).
% 87.45/87.71 tff(14712,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node18(c_e_h_2, c_e, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node18(c_e_h_2, c_e, s14, s15))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14713,plain,
% 87.45/87.71 ((node17(c_e_h_2, c_e, s14) | node18(c_e_h_2, c_e, s14, s15) | (~node19(c_e_h_2, c_e, s14, s15))) <=> (node17(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node18(c_e_h_2, c_e, s14, s15))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14714,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s14) | node18(c_e_h_2, c_e, s14, s15) | (~node19(c_e_h_2, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node18(c_e_h_2, c_e, s14, s15)))),
% 87.45/87.71 inference(monotonicity,[status(thm)],[14713])).
% 87.45/87.71 tff(14715,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s14) | node18(c_e_h_2, c_e, s14, s15) | (~node19(c_e_h_2, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node18(c_e_h_2, c_e, s14, s15))),
% 87.45/87.71 inference(transitivity,[status(thm)],[14714, 14712])).
% 87.45/87.71 tff(14716,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s14) | node18(c_e_h_2, c_e, s14, s15) | (~node19(c_e_h_2, c_e, s14, s15)))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14717,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node18(c_e_h_2, c_e, s14, s15)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14716, 14715])).
% 87.45/87.71 tff(14718,plain,
% 87.45/87.71 (node17(c_e_h_2, c_e, s14) | node18(c_e_h_2, c_e, s14, s15)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14717, 156, 14711])).
% 87.45/87.71 tff(14719,plain,
% 87.45/87.71 (node17(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14718, 14707])).
% 87.45/87.71 tff(14720,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s14)), introduced(assumption)).
% 87.45/87.71 tff(14721,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14722,plain,
% 87.45/87.71 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14) | (~node17(c_e_h_2, c_e, s14))) <=> ((~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14723,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14) | (~node17(c_e_h_2, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14)))),
% 87.45/87.71 inference(monotonicity,[status(thm)],[14722])).
% 87.45/87.71 tff(14724,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14) | (~node17(c_e_h_2, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(transitivity,[status(thm)],[14723, 14721])).
% 87.45/87.71 tff(14725,plain,
% 87.45/87.71 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14) | (~node17(c_e_h_2, c_e, s14)))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14726,plain,
% 87.45/87.71 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14725, 14724])).
% 87.45/87.71 tff(14727,plain,
% 87.45/87.71 ((~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14726, 209, 14720])).
% 87.45/87.71 tff(14728,plain,
% 87.45/87.71 (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14727, 14719])).
% 87.45/87.71 tff(14729,assumption,(node15(c_e_h_2, c_e, s14, s15)), introduced(assumption)).
% 87.45/87.71 tff(14730,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | (~node15(c_e_h_2, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | (~node15(c_e_h_2, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14731,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | (~node15(c_e_h_2, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14732,plain,
% 87.45/87.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | (~node15(c_e_h_2, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14731, 14730])).
% 87.45/87.71 tff(14733,plain,
% 87.45/87.71 ($false),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14732, 173, 14697, 10465, 14729])).
% 87.45/87.71 tff(14734,plain,((~node15(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.71 tff(14735,plain,
% 87.45/87.71 (~node15(c_e_h_2, c_e, s14, s15)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14734, 14697, 10465])).
% 87.45/87.71 tff(14736,assumption,(node17(c_e_h_2, c_e, s14)), introduced(assumption)).
% 87.45/87.71 tff(14737,assumption,(node16(c_e_h_2, c_e, s14)), introduced(assumption)).
% 87.45/87.71 tff(14738,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s14)), introduced(assumption)).
% 87.45/87.71 tff(14739,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14740,plain,
% 87.45/87.71 ((m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~node17(c_e_h_2, c_e, s14))) <=> ((~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14741,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~node17(c_e_h_2, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14)))),
% 87.45/87.71 inference(monotonicity,[status(thm)],[14740])).
% 87.45/87.71 tff(14742,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~node17(c_e_h_2, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(transitivity,[status(thm)],[14741, 14739])).
% 87.45/87.71 tff(14743,plain,
% 87.45/87.71 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~node17(c_e_h_2, c_e, s14)))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14744,plain,
% 87.45/87.71 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14743, 14742])).
% 87.45/87.71 tff(14745,plain,
% 87.45/87.71 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14744, 245, 14736])).
% 87.45/87.71 tff(14746,plain,
% 87.45/87.71 (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14745, 14738])).
% 87.45/87.71 tff(14747,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | m_c_h_element_v_in2(c_e_h_2, c_e, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | m_c_h_element_v_in2(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14748,plain,
% 87.45/87.71 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | m_c_h_element_v_in2(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14749,plain,
% 87.45/87.71 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s14)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | m_c_h_element_v_in2(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14748, 14747])).
% 87.45/87.71 tff(14750,plain,
% 87.45/87.71 (m_c_h_element_v_in1(c_e_h_2, c_e, s14) | m_c_h_element_v_in2(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14749, 228, 14737])).
% 87.45/87.71 tff(14751,plain,
% 87.45/87.71 ($false),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14750, 14746, 14738])).
% 87.45/87.71 tff(14752,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~node16(c_e_h_2, c_e, s14)) | (~node17(c_e_h_2, c_e, s14))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.71 tff(14753,plain,
% 87.45/87.71 (m_c_h_element_v_in1(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14752, 14737, 14736])).
% 87.45/87.71 tff(14754,plain,
% 87.45/87.71 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14726, 209, 14736])).
% 87.45/87.71 tff(14755,plain,
% 87.45/87.71 (m_c_h_element_v_in2(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14754, 14753])).
% 87.45/87.71 tff(14756,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~node16(c_e_h_2, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~node16(c_e_h_2, c_e, s14)))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14757,plain,
% 87.45/87.71 (((~node16(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~node16(c_e_h_2, c_e, s14)))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14758,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~node16(c_e_h_2, c_e, s14))))),
% 87.45/87.71 inference(monotonicity,[status(thm)],[14757])).
% 87.45/87.71 tff(14759,plain,
% 87.45/87.71 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~node16(c_e_h_2, c_e, s14)))),
% 87.45/87.71 inference(transitivity,[status(thm)],[14758, 14756])).
% 87.45/87.71 tff(14760,plain,
% 87.45/87.71 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)))),
% 87.45/87.71 inference(quant_inst,[status(thm)],[])).
% 87.45/87.71 tff(14761,plain,
% 87.45/87.71 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14)) | (~node16(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(modus_ponens,[status(thm)],[14760, 14759])).
% 87.45/87.71 tff(14762,plain,
% 87.45/87.71 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s14))),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14761, 263, 14737])).
% 87.45/87.71 tff(14763,plain,
% 87.45/87.71 ($false),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14762, 14755, 14753])).
% 87.45/87.71 tff(14764,plain,((~node16(c_e_h_2, c_e, s14)) | (~node17(c_e_h_2, c_e, s14))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.71 tff(14765,plain,
% 87.45/87.71 (~node16(c_e_h_2, c_e, s14)),
% 87.45/87.71 inference(unit_resolution,[status(thm)],[14764, 14719])).
% 87.45/87.71 tff(14766,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14767,plain,
% 87.45/87.71 ((node16(c_e_h_2, c_e, s14) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15) | (~node19(c_e_h_2, c_e, s14, s15))) <=> (node16(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15))),
% 87.45/87.71 inference(rewrite,[status(thm)],[])).
% 87.45/87.71 tff(14768,plain,
% 87.45/87.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s14) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15) | (~node19(c_e_h_2, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15)))),
% 87.45/87.72 inference(monotonicity,[status(thm)],[14767])).
% 87.45/87.72 tff(14769,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s14) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15) | (~node19(c_e_h_2, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15))),
% 87.45/87.72 inference(transitivity,[status(thm)],[14768, 14766])).
% 87.45/87.72 tff(14770,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s14) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15) | (~node19(c_e_h_2, c_e, s14, s15)))),
% 87.45/87.72 inference(quant_inst,[status(thm)],[])).
% 87.45/87.72 tff(14771,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s14) | (~node19(c_e_h_2, c_e, s14, s15)) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15)),
% 87.45/87.72 inference(modus_ponens,[status(thm)],[14770, 14769])).
% 87.45/87.72 tff(14772,plain,
% 87.45/87.72 (node16(c_e_h_2, c_e, s14) | node14(c_e_h_2, c_e, s14, s15) | node15(c_e_h_2, c_e, s14, s15)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14771, 189, 14711])).
% 87.45/87.72 tff(14773,plain,
% 87.45/87.72 (node14(c_e_h_2, c_e, s14, s15)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14772, 14765, 14735])).
% 87.45/87.72 tff(14774,assumption,(node14(c_e_h_2, c_e, s14, s15)), introduced(assumption)).
% 87.45/87.72 tff(14775,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~node14(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~node14(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14776,plain,
% 87.45/87.72 (((~node14(c_e_h_2, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~node14(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14777,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~node14(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15))))),
% 87.45/87.72 inference(monotonicity,[status(thm)],[14776])).
% 87.45/87.72 tff(14778,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~node14(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))),
% 87.45/87.72 inference(transitivity,[status(thm)],[14777, 14775])).
% 87.45/87.72 tff(14779,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)))),
% 87.45/87.72 inference(quant_inst,[status(thm)],[])).
% 87.45/87.72 tff(14780,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s14) | (~node14(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15))),
% 87.45/87.72 inference(modus_ponens,[status(thm)],[14779, 14778])).
% 87.45/87.72 tff(14781,plain,
% 87.45/87.72 ($false),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14780, 283, 14697, 14774, 14738])).
% 87.45/87.72 tff(14782,plain,((~node14(c_e_h_2, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.72 tff(14783,plain,
% 87.45/87.72 ($false),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14782, 14773, 14728, 14697])).
% 87.45/87.72 tff(14784,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14) | m_c_h_element_v_out(c_e_h_2, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.72 tff(14785,plain,
% 87.45/87.72 (~m_c_h_element_v_out(c_e_h_2, c_e, s15)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14784, 14696, 10463])).
% 87.45/87.72 tff(14786,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s15)), introduced(assumption)).
% 87.45/87.72 tff(14787,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s13)), introduced(assumption)).
% 87.45/87.72 tff(14788,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s13)), introduced(assumption)).
% 87.45/87.72 tff(14789,plain,
% 87.45/87.72 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14790,plain,
% 87.45/87.72 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13))),
% 87.45/87.72 inference(quant_inst,[status(thm)],[])).
% 87.45/87.72 tff(14791,plain,
% 87.45/87.72 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13)),
% 87.45/87.72 inference(modus_ponens,[status(thm)],[14790, 14789])).
% 87.45/87.72 tff(14792,plain,
% 87.45/87.72 (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14791, 309, 14788])).
% 87.45/87.72 tff(14793,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s14)), introduced(assumption)).
% 87.45/87.72 tff(14794,assumption,(node18(c_e_h_2, c_h, s13, s14)), introduced(assumption)).
% 87.45/87.72 tff(14795,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node18(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node18(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14796,plain,
% 87.45/87.72 (((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~node18(c_e_h_2, c_h, s13, s14))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node18(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14797,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~node18(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node18(c_e_h_2, c_h, s13, s14))))),
% 87.45/87.72 inference(monotonicity,[status(thm)],[14796])).
% 87.45/87.72 tff(14798,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~node18(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node18(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(transitivity,[status(thm)],[14797, 14795])).
% 87.45/87.72 tff(14799,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~node18(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(quant_inst,[status(thm)],[])).
% 87.45/87.72 tff(14800,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node18(c_e_h_2, c_h, s13, s14))),
% 87.45/87.72 inference(modus_ponens,[status(thm)],[14799, 14798])).
% 87.45/87.72 tff(14801,plain,
% 87.45/87.72 ($false),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14800, 124, 14787, 14793, 14794])).
% 87.45/87.72 tff(14802,plain,((~node18(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 87.45/87.72 tff(14803,plain,
% 87.45/87.72 (~node18(c_e_h_2, c_h, s13, s14)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14802, 14793, 14787])).
% 87.45/87.72 tff(14804,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s13)), introduced(assumption)).
% 87.45/87.72 tff(14805,plain,
% 87.45/87.72 (~node18(c_e_h_2, c_h, s13, s14)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14802, 14787, 14793])).
% 87.45/87.72 tff(14806,assumption,(~node19(c_e_h_2, c_h, s13, s14)), introduced(assumption)).
% 87.45/87.72 tff(14807,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_2, c_h, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_2, c_h, s13, s14))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14808,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_2, c_h, s13, s14))),
% 87.45/87.72 inference(quant_inst,[status(thm)],[])).
% 87.45/87.72 tff(14809,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_2, c_h, s13, s14)),
% 87.45/87.72 inference(modus_ponens,[status(thm)],[14808, 14807])).
% 87.45/87.72 tff(14810,plain,
% 87.45/87.72 ($false),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14809, 141, 10040, 14806])).
% 87.45/87.72 tff(14811,plain,(node19(c_e_h_2, c_h, s13, s14)), inference(lemma,lemma(discharge,[]))).
% 87.45/87.72 tff(14812,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s13, s14) | node17(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s13, s14) | node17(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14813,plain,
% 87.45/87.72 ((node17(c_e_h_2, c_h, s13) | node18(c_e_h_2, c_h, s13, s14) | (~node19(c_e_h_2, c_h, s13, s14))) <=> (node18(c_e_h_2, c_h, s13, s14) | node17(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14814,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s13) | node18(c_e_h_2, c_h, s13, s14) | (~node19(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s13, s14) | node17(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14))))),
% 87.45/87.72 inference(monotonicity,[status(thm)],[14813])).
% 87.45/87.72 tff(14815,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s13) | node18(c_e_h_2, c_h, s13, s14) | (~node19(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s13, s14) | node17(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(transitivity,[status(thm)],[14814, 14812])).
% 87.45/87.72 tff(14816,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s13) | node18(c_e_h_2, c_h, s13, s14) | (~node19(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(quant_inst,[status(thm)],[])).
% 87.45/87.72 tff(14817,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s13, s14) | node17(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14))),
% 87.45/87.72 inference(modus_ponens,[status(thm)],[14816, 14815])).
% 87.45/87.72 tff(14818,plain,
% 87.45/87.72 (node18(c_e_h_2, c_h, s13, s14) | node17(c_e_h_2, c_h, s13)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14817, 156, 14811])).
% 87.45/87.72 tff(14819,plain,
% 87.45/87.72 (node17(c_e_h_2, c_h, s13)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14818, 14805])).
% 87.45/87.72 tff(14820,plain,
% 87.45/87.72 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14821,plain,
% 87.45/87.72 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13)))),
% 87.45/87.72 inference(quant_inst,[status(thm)],[])).
% 87.45/87.72 tff(14822,plain,
% 87.45/87.72 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13))),
% 87.45/87.72 inference(modus_ponens,[status(thm)],[14821, 14820])).
% 87.45/87.72 tff(14823,plain,
% 87.45/87.72 (m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s13))),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14822, 245, 14819])).
% 87.45/87.72 tff(14824,plain,
% 87.45/87.72 (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14823, 14804])).
% 87.45/87.72 tff(14825,assumption,(~node16(c_e_h_2, c_h, s13)), introduced(assumption)).
% 87.45/87.72 tff(14826,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~node14(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~node14(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14827,plain,
% 87.45/87.72 (((~node14(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~node14(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14828,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~node14(c_e_h_2, c_h, s13, s14))))),
% 87.45/87.72 inference(monotonicity,[status(thm)],[14827])).
% 87.45/87.72 tff(14829,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~node14(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(transitivity,[status(thm)],[14828, 14826])).
% 87.45/87.72 tff(14830,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)))),
% 87.45/87.72 inference(quant_inst,[status(thm)],[])).
% 87.45/87.72 tff(14831,plain,
% 87.45/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~node14(c_e_h_2, c_h, s13, s14))),
% 87.45/87.72 inference(modus_ponens,[status(thm)],[14830, 14829])).
% 87.45/87.72 tff(14832,plain,
% 87.45/87.72 ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~node14(c_e_h_2, c_h, s13, s14))),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14831, 283])).
% 87.45/87.72 tff(14833,plain,
% 87.45/87.72 (~node14(c_e_h_2, c_h, s13, s14)),
% 87.45/87.72 inference(unit_resolution,[status(thm)],[14832, 14793, 14804])).
% 87.45/87.72 tff(14834,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14835,plain,
% 87.45/87.72 ((node16(c_e_h_2, c_h, s13) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14) | (~node19(c_e_h_2, c_h, s13, s14))) <=> (node16(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14))),
% 87.45/87.72 inference(rewrite,[status(thm)],[])).
% 87.45/87.72 tff(14836,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s13) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14) | (~node19(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14)))),
% 87.45/87.72 inference(monotonicity,[status(thm)],[14835])).
% 87.45/87.72 tff(14837,plain,
% 87.45/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s13) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14) | (~node19(c_e_h_2, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14))),
% 87.54/87.72 inference(transitivity,[status(thm)],[14836, 14834])).
% 87.54/87.72 tff(14838,plain,
% 87.54/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s13) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14) | (~node19(c_e_h_2, c_h, s13, s14)))),
% 87.54/87.72 inference(quant_inst,[status(thm)],[])).
% 87.54/87.72 tff(14839,plain,
% 87.54/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s13) | (~node19(c_e_h_2, c_h, s13, s14)) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14)),
% 87.54/87.72 inference(modus_ponens,[status(thm)],[14838, 14837])).
% 87.54/87.72 tff(14840,plain,
% 87.54/87.72 (node16(c_e_h_2, c_h, s13) | node14(c_e_h_2, c_h, s13, s14) | node15(c_e_h_2, c_h, s13, s14)),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14839, 189, 14811])).
% 87.54/87.72 tff(14841,plain,
% 87.54/87.72 (node15(c_e_h_2, c_h, s13, s14)),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14840, 14833, 14825])).
% 87.54/87.72 tff(14842,plain,
% 87.54/87.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node15(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node15(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13))),
% 87.54/87.72 inference(rewrite,[status(thm)],[])).
% 87.54/87.72 tff(14843,plain,
% 87.54/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node15(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13))),
% 87.54/87.72 inference(quant_inst,[status(thm)],[])).
% 87.54/87.72 tff(14844,plain,
% 87.54/87.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | (~node15(c_e_h_2, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13)),
% 87.54/87.72 inference(modus_ponens,[status(thm)],[14843, 14842])).
% 87.54/87.72 tff(14845,plain,
% 87.54/87.72 ($false),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14844, 173, 14787, 14793, 14841])).
% 87.54/87.72 tff(14846,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | node16(c_e_h_2, c_h, s13) | m_c_h_element_v_in1(c_e_h_2, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.72 tff(14847,plain,
% 87.54/87.72 (node16(c_e_h_2, c_h, s13)),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14846, 14804, 14793, 14787])).
% 87.54/87.72 tff(14848,plain,
% 87.54/87.72 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | m_c_h_element_v_in2(c_e_h_2, c_h, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | m_c_h_element_v_in2(c_e_h_2, c_h, s13))),
% 87.54/87.72 inference(rewrite,[status(thm)],[])).
% 87.54/87.72 tff(14849,plain,
% 87.54/87.72 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | m_c_h_element_v_in2(c_e_h_2, c_h, s13))),
% 87.54/87.72 inference(quant_inst,[status(thm)],[])).
% 87.54/87.72 tff(14850,plain,
% 87.54/87.72 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s13)) | m_c_h_element_v_in1(c_e_h_2, c_h, s13) | m_c_h_element_v_in2(c_e_h_2, c_h, s13)),
% 87.54/87.72 inference(modus_ponens,[status(thm)],[14849, 14848])).
% 87.54/87.72 tff(14851,plain,
% 87.54/87.72 ($false),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14850, 228, 14804, 14847, 14824])).
% 87.54/87.72 tff(14852,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s13) | (~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.72 tff(14853,plain,
% 87.54/87.72 (m_c_h_element_v_in1(c_e_h_2, c_h, s13)),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14852, 14793, 14787])).
% 87.54/87.72 tff(14854,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s13)), introduced(assumption)).
% 87.54/87.72 tff(14855,plain,
% 87.54/87.72 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13)))),
% 87.54/87.72 inference(rewrite,[status(thm)],[])).
% 87.54/87.72 tff(14856,plain,
% 87.54/87.72 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~node17(c_e_h_2, c_h, s13))) <=> (m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13)))),
% 87.54/87.72 inference(rewrite,[status(thm)],[])).
% 87.54/87.72 tff(14857,plain,
% 87.54/87.72 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~node17(c_e_h_2, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13))))),
% 87.54/87.72 inference(monotonicity,[status(thm)],[14856])).
% 87.54/87.72 tff(14858,plain,
% 87.54/87.72 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~node17(c_e_h_2, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13)))),
% 87.54/87.72 inference(transitivity,[status(thm)],[14857, 14855])).
% 87.54/87.72 tff(14859,plain,
% 87.54/87.72 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~node17(c_e_h_2, c_h, s13)))),
% 87.54/87.72 inference(quant_inst,[status(thm)],[])).
% 87.54/87.72 tff(14860,plain,
% 87.54/87.72 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13))),
% 87.54/87.72 inference(modus_ponens,[status(thm)],[14859, 14858])).
% 87.54/87.72 tff(14861,plain,
% 87.54/87.72 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s13)) | (~node17(c_e_h_2, c_h, s13))),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14860, 209, 14854])).
% 87.54/87.72 tff(14862,plain,
% 87.54/87.72 (~node17(c_e_h_2, c_h, s13)),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14861, 14853])).
% 87.54/87.72 tff(14863,plain,
% 87.54/87.72 ($false),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14818, 14862, 14803])).
% 87.54/87.72 tff(14864,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s14)) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | m_c_h_element_v_out(c_e_h_2, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.72 tff(14865,plain,
% 87.54/87.72 (~m_c_h_element_v_out(c_e_h_2, c_h, s14)),
% 87.54/87.72 inference(unit_resolution,[status(thm)],[14864, 14792, 14787])).
% 87.54/87.72 tff(14866,plain,
% 87.54/87.72 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s14))),
% 87.54/87.72 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14867,plain,
% 87.54/87.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s14))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14868,plain,
% 87.54/87.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s14)) | m_c_h_element_v_out(c_e_h_2, c_h, s14)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14867, 14866])).
% 87.54/87.73 tff(14869,plain,
% 87.54/87.73 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s14)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14868, 23, 14865])).
% 87.54/87.73 tff(14870,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s14))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14871,plain,
% 87.54/87.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s14))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14872,plain,
% 87.54/87.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s14)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14871, 14870])).
% 87.54/87.73 tff(14873,plain,
% 87.54/87.73 (~node20(c_e_h_2, c_i, s14)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14872, 37, 14869])).
% 87.54/87.73 tff(14874,assumption,(~node20(c_e_h_2, c_i, s14)), introduced(assumption)).
% 87.54/87.73 tff(14875,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s15)), introduced(assumption)).
% 87.54/87.73 tff(14876,assumption,(node21(c_e_h_2, c_i, s14, s15)), introduced(assumption)).
% 87.54/87.73 tff(14877,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | (~node21(c_e_h_2, c_i, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | (~node21(c_e_h_2, c_i, s14, s15)))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14878,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | (~node21(c_e_h_2, c_i, s14, s15)))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14879,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | (~node21(c_e_h_2, c_i, s14, s15))),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14878, 14877])).
% 87.54/87.73 tff(14880,plain,
% 87.54/87.73 ($false),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14879, 51, 14875, 14874, 14876])).
% 87.54/87.73 tff(14881,plain,((~node21(c_e_h_2, c_i, s14, s15)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | node20(c_e_h_2, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.73 tff(14882,plain,
% 87.54/87.73 (~node21(c_e_h_2, c_i, s14, s15)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14881, 14875, 14874])).
% 87.54/87.73 tff(14883,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_2, c_i, s14, s15) | node22(c_e_h_2, c_i, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_2, c_i, s14, s15) | node22(c_e_h_2, c_i, s14, s15))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14884,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_2, c_i, s14, s15) | node22(c_e_h_2, c_i, s14, s15))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14885,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_2, c_i, s14, s15) | node22(c_e_h_2, c_i, s14, s15)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14884, 14883])).
% 87.54/87.73 tff(14886,plain,
% 87.54/87.73 (node21(c_e_h_2, c_i, s14, s15) | node22(c_e_h_2, c_i, s14, s15)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14885, 81, 10504])).
% 87.54/87.73 tff(14887,plain,
% 87.54/87.73 (node22(c_e_h_2, c_i, s14, s15)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14886, 14882])).
% 87.54/87.73 tff(14888,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | (~node22(c_e_h_2, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | (~node22(c_e_h_2, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14889,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | (~node22(c_e_h_2, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14890,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | (~node22(c_e_h_2, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14889, 14888])).
% 87.54/87.73 tff(14891,plain,
% 87.54/87.73 ($false),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14890, 107, 14690, 14875, 14887])).
% 87.54/87.73 tff(14892,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14) | node20(c_e_h_2, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.73 tff(14893,plain,
% 87.54/87.73 (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14892, 14690, 14873])).
% 87.54/87.73 tff(14894,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s15)), introduced(assumption)).
% 87.54/87.73 tff(14895,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s15)), introduced(assumption)).
% 87.54/87.73 tff(14896,plain,
% 87.54/87.73 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14897,plain,
% 87.54/87.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14898,plain,
% 87.54/87.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14897, 14896])).
% 87.54/87.73 tff(14899,plain,
% 87.54/87.73 ($false),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14898, 365, 14895, 14894])).
% 87.54/87.73 tff(14900,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.73 tff(14901,plain,
% 87.54/87.73 (~m_c_h_element_v_in2(c_e_h_2, c_e, s15)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14900, 14893])).
% 87.54/87.73 tff(14902,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s17)), introduced(assumption)).
% 87.54/87.73 tff(14903,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)), introduced(assumption)).
% 87.54/87.73 tff(14904,plain,
% 87.54/87.73 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14905,plain,
% 87.54/87.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14906,plain,
% 87.54/87.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14905, 14904])).
% 87.54/87.73 tff(14907,plain,
% 87.54/87.73 (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14906, 2218, 13656])).
% 87.54/87.73 tff(14908,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s12)), introduced(assumption)).
% 87.54/87.73 tff(14909,assumption,(node18(c_e_h_1, c_f, s11, s12)), introduced(assumption)).
% 87.54/87.73 tff(14910,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14911,plain,
% 87.54/87.73 (((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14912,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12))))),
% 87.54/87.73 inference(monotonicity,[status(thm)],[14911])).
% 87.54/87.73 tff(14913,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))),
% 87.54/87.73 inference(transitivity,[status(thm)],[14912, 14910])).
% 87.54/87.73 tff(14914,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14915,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14914, 14913])).
% 87.54/87.73 tff(14916,plain,
% 87.54/87.73 ($false),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14915, 124, 14615, 14908, 14909])).
% 87.54/87.73 tff(14917,plain,((~node18(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.73 tff(14918,plain,
% 87.54/87.73 (~node18(c_e_h_1, c_f, s11, s12)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14917, 14908, 14615])).
% 87.54/87.73 tff(14919,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_f, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_f, s11, s12))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14920,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_f, s11, s12))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14921,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_f, s11, s12)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14920, 14919])).
% 87.54/87.73 tff(14922,plain,
% 87.54/87.73 (node19(c_e_h_1, c_f, s11, s12)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14921, 141, 4461])).
% 87.54/87.73 tff(14923,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14924,plain,
% 87.54/87.73 ((node17(c_e_h_1, c_f, s11) | node18(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12))) <=> ((~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14925,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s11) | node18(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(monotonicity,[status(thm)],[14924])).
% 87.54/87.73 tff(14926,plain,
% 87.54/87.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s11) | node18(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(transitivity,[status(thm)],[14925, 14923])).
% 87.54/87.73 tff(14927,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s11) | node18(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14928,plain,
% 87.54/87.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14927, 14926])).
% 87.54/87.73 tff(14929,plain,
% 87.54/87.73 (node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14928, 156, 14922])).
% 87.54/87.73 tff(14930,plain,
% 87.54/87.73 (node17(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14929, 14918])).
% 87.54/87.73 tff(14931,assumption,(node17(c_e_h_1, c_f, s11)), introduced(assumption)).
% 87.54/87.73 tff(14932,assumption,(node16(c_e_h_1, c_f, s11)), introduced(assumption)).
% 87.54/87.73 tff(14933,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s11)), introduced(assumption)).
% 87.54/87.73 tff(14934,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14935,plain,
% 87.54/87.73 ((m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11))) <=> ((~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14936,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11))))),
% 87.54/87.73 inference(monotonicity,[status(thm)],[14935])).
% 87.54/87.73 tff(14937,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(transitivity,[status(thm)],[14936, 14934])).
% 87.54/87.73 tff(14938,plain,
% 87.54/87.73 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14939,plain,
% 87.54/87.73 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14938, 14937])).
% 87.54/87.73 tff(14940,plain,
% 87.54/87.73 (m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14939, 245, 14931])).
% 87.54/87.73 tff(14941,plain,
% 87.54/87.73 (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14940, 14933])).
% 87.54/87.73 tff(14942,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14943,plain,
% 87.54/87.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14944,plain,
% 87.54/87.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14943, 14942])).
% 87.54/87.73 tff(14945,plain,
% 87.54/87.73 (m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14944, 228, 14932])).
% 87.54/87.73 tff(14946,plain,
% 87.54/87.73 ($false),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14945, 14941, 14933])).
% 87.54/87.73 tff(14947,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~node16(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.73 tff(14948,plain,
% 87.54/87.73 (m_c_h_element_v_in1(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14947, 14932, 14931])).
% 87.54/87.73 tff(14949,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14950,plain,
% 87.54/87.73 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | (~node17(c_e_h_1, c_f, s11))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14951,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | (~node17(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(monotonicity,[status(thm)],[14950])).
% 87.54/87.73 tff(14952,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | (~node17(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 87.54/87.73 inference(transitivity,[status(thm)],[14951, 14949])).
% 87.54/87.73 tff(14953,plain,
% 87.54/87.73 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | (~node17(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(quant_inst,[status(thm)],[])).
% 87.54/87.73 tff(14954,plain,
% 87.54/87.73 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(modus_ponens,[status(thm)],[14953, 14952])).
% 87.54/87.73 tff(14955,plain,
% 87.54/87.73 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14954, 209, 14931])).
% 87.54/87.73 tff(14956,plain,
% 87.54/87.73 (m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 87.54/87.73 inference(unit_resolution,[status(thm)],[14955, 14948])).
% 87.54/87.73 tff(14957,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node16(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node16(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14958,plain,
% 87.54/87.73 (((~node16(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node16(c_e_h_1, c_f, s11)))),
% 87.54/87.73 inference(rewrite,[status(thm)],[])).
% 87.54/87.73 tff(14959,plain,
% 87.54/87.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node16(c_e_h_1, c_f, s11))))),
% 87.54/87.74 inference(monotonicity,[status(thm)],[14958])).
% 87.54/87.74 tff(14960,plain,
% 87.54/87.74 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node16(c_e_h_1, c_f, s11)))),
% 87.54/87.74 inference(transitivity,[status(thm)],[14959, 14957])).
% 87.54/87.74 tff(14961,plain,
% 87.54/87.74 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(14962,plain,
% 87.54/87.74 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node16(c_e_h_1, c_f, s11))),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[14961, 14960])).
% 87.54/87.74 tff(14963,plain,
% 87.54/87.74 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14962, 263, 14932])).
% 87.54/87.74 tff(14964,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14963, 14956, 14948])).
% 87.54/87.74 tff(14965,plain,((~node16(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(14966,plain,
% 87.54/87.74 (~node16(c_e_h_1, c_f, s11)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14965, 14930])).
% 87.54/87.74 tff(14967,assumption,(node15(c_e_h_1, c_f, s11, s12)), introduced(assumption)).
% 87.54/87.74 tff(14968,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(14969,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(14970,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[14969, 14968])).
% 87.54/87.74 tff(14971,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14970, 173, 14615, 14908, 14967])).
% 87.54/87.74 tff(14972,plain,((~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(14973,plain,
% 87.54/87.74 (~node15(c_e_h_1, c_f, s11, s12)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14972, 14908, 14615])).
% 87.54/87.74 tff(14974,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node14(c_e_h_1, c_f, s11, s12) | node16(c_e_h_1, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node14(c_e_h_1, c_f, s11, s12) | node16(c_e_h_1, c_f, s11))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(14975,plain,
% 87.54/87.74 ((node16(c_e_h_1, c_f, s11) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12))) <=> (node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node14(c_e_h_1, c_f, s11, s12) | node16(c_e_h_1, c_f, s11))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(14976,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s11) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node14(c_e_h_1, c_f, s11, s12) | node16(c_e_h_1, c_f, s11)))),
% 87.54/87.74 inference(monotonicity,[status(thm)],[14975])).
% 87.54/87.74 tff(14977,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s11) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node14(c_e_h_1, c_f, s11, s12) | node16(c_e_h_1, c_f, s11))),
% 87.54/87.74 inference(transitivity,[status(thm)],[14976, 14974])).
% 87.54/87.74 tff(14978,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s11) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(14979,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node14(c_e_h_1, c_f, s11, s12) | node16(c_e_h_1, c_f, s11)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[14978, 14977])).
% 87.54/87.74 tff(14980,plain,
% 87.54/87.74 (node15(c_e_h_1, c_f, s11, s12) | node14(c_e_h_1, c_f, s11, s12) | node16(c_e_h_1, c_f, s11)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14979, 189, 14922])).
% 87.54/87.74 tff(14981,plain,
% 87.54/87.74 (node14(c_e_h_1, c_f, s11, s12)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14980, 14973, 14966])).
% 87.54/87.74 tff(14982,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(14983,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(14984,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[14983, 14982])).
% 87.54/87.74 tff(14985,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14984, 283, 14908, 14933, 14981])).
% 87.54/87.74 tff(14986,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_out(c_e_h_1, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(14987,plain,
% 87.54/87.74 (m_c_h_element_v_in1(c_e_h_1, c_f, s11)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14986, 14908, 14615])).
% 87.54/87.74 tff(14988,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s11)), introduced(assumption)).
% 87.54/87.74 tff(14989,plain,
% 87.54/87.74 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11))),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14954, 209, 14988])).
% 87.54/87.74 tff(14990,plain,
% 87.54/87.74 (~node17(c_e_h_1, c_f, s11)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14989, 14987])).
% 87.54/87.74 tff(14991,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14929, 14990, 14918])).
% 87.54/87.74 tff(14992,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | m_c_h_element_v_out(c_e_h_1, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(14993,plain,
% 87.54/87.74 ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14992, 14907])).
% 87.54/87.74 tff(14994,plain,
% 87.54/87.74 (~m_c_h_element_v_out(c_e_h_1, c_f, s12)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14993, 14613])).
% 87.54/87.74 tff(14995,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s12)), introduced(assumption)).
% 87.54/87.74 tff(14996,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s12)), introduced(assumption)).
% 87.54/87.74 tff(14997,plain,
% 87.54/87.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(14998,plain,
% 87.54/87.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(14999,plain,
% 87.54/87.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[14998, 14997])).
% 87.54/87.74 tff(15000,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[14999, 1666, 14996, 14995])).
% 87.54/87.74 tff(15001,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(15002,plain,
% 87.54/87.74 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15001, 14994])).
% 87.54/87.74 tff(15003,assumption,(node20(c_e_h_1, c_q, s12)), introduced(assumption)).
% 87.54/87.74 tff(15004,plain,
% 87.54/87.74 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s12))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15005,plain,
% 87.54/87.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s12))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15006,plain,
% 87.54/87.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s12)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15005, 15004])).
% 87.54/87.74 tff(15007,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15006, 37, 15003, 15002])).
% 87.54/87.74 tff(15008,plain,(~node20(c_e_h_1, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(15009,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s12)), introduced(assumption)).
% 87.54/87.74 tff(15010,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s13)), introduced(assumption)).
% 87.54/87.74 tff(15011,assumption,(node22(c_e_h_1, c_q, s12, s13)), introduced(assumption)).
% 87.54/87.74 tff(15012,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15013,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15014,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15013, 15012])).
% 87.54/87.74 tff(15015,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15014, 107, 15009, 15010, 15011])).
% 87.54/87.74 tff(15016,plain,((~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(15017,plain,
% 87.54/87.74 (~node22(c_e_h_1, c_q, s12, s13)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15016, 15010, 15009])).
% 87.54/87.74 tff(15018,assumption,(~node20(c_e_h_1, c_q, s12)), introduced(assumption)).
% 87.54/87.74 tff(15019,assumption,(node21(c_e_h_1, c_q, s12, s13)), introduced(assumption)).
% 87.54/87.74 tff(15020,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node21(c_e_h_1, c_q, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node21(c_e_h_1, c_q, s12, s13)))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15021,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node21(c_e_h_1, c_q, s12, s13)))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15022,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node21(c_e_h_1, c_q, s12, s13))),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15021, 15020])).
% 87.54/87.74 tff(15023,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15022, 51, 15010, 15018, 15019])).
% 87.54/87.74 tff(15024,plain,((~node21(c_e_h_1, c_q, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(15025,plain,
% 87.54/87.74 (~node21(c_e_h_1, c_q, s12, s13)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15024, 15010, 15018])).
% 87.54/87.74 tff(15026,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15027,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15028,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15027, 15026])).
% 87.54/87.74 tff(15029,plain,
% 87.54/87.74 (node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15028, 81, 9599])).
% 87.54/87.74 tff(15030,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15029, 15025, 15017])).
% 87.54/87.74 tff(15031,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12) | m_and_h_gate_v_out(c_e_h_1, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(15032,plain,
% 87.54/87.74 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15031, 15008])).
% 87.54/87.74 tff(15033,plain,
% 87.54/87.74 (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15032, 14653])).
% 87.54/87.74 tff(15034,assumption,(~node3(c_e_h_1, c_e_h_2, s13)), introduced(assumption)).
% 87.54/87.74 tff(15035,plain,
% 87.54/87.74 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s13))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s13))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15036,plain,
% 87.54/87.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s13))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15037,plain,
% 87.54/87.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s13)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15036, 15035])).
% 87.54/87.74 tff(15038,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15037, 817, 814, 15034])).
% 87.54/87.74 tff(15039,plain,(node3(c_e_h_1, c_e_h_2, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(15040,plain,
% 87.54/87.74 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s13)) | (~node3(c_e_h_1, c_e_h_2, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s13)) | (~node3(c_e_h_1, c_e_h_2, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15041,plain,
% 87.54/87.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s13)) | (~node3(c_e_h_1, c_e_h_2, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15042,plain,
% 87.54/87.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s13)) | (~node3(c_e_h_1, c_e_h_2, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15041, 15040])).
% 87.54/87.74 tff(15043,plain,
% 87.54/87.74 ((~m_cell_v_ack(c_e_h_2, s13)) | (~node3(c_e_h_1, c_e_h_2, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15042, 836])).
% 87.54/87.74 tff(15044,plain,
% 87.54/87.74 ((~m_cell_v_ack(c_e_h_2, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15043, 15039])).
% 87.54/87.74 tff(15045,plain,
% 87.54/87.74 (~m_cell_v_ack(c_e_h_2, s13)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15044, 15033])).
% 87.54/87.74 tff(15046,plain,
% 87.54/87.74 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s13)) | m_cell_v_ack(c_e_h_2, s13))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s13)) | m_cell_v_ack(c_e_h_2, s13))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15047,plain,
% 87.54/87.74 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s13)) | m_cell_v_ack(c_e_h_2, s13))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15048,plain,
% 87.54/87.74 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s13)) | m_cell_v_ack(c_e_h_2, s13)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15047, 15046])).
% 87.54/87.74 tff(15049,plain,
% 87.54/87.74 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s13)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15048, 848, 15045])).
% 87.54/87.74 tff(15050,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s13)), introduced(assumption)).
% 87.54/87.74 tff(15051,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s14)), introduced(assumption)).
% 87.54/87.74 tff(15052,assumption,(node6(c_e_h_2, c_j, s13, s14)), introduced(assumption)).
% 87.54/87.74 tff(15053,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | (~node6(c_e_h_2, c_j, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | (~node6(c_e_h_2, c_j, s13, s14)))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15054,plain,
% 87.54/87.74 (((~node6(c_e_h_2, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | (~node6(c_e_h_2, c_j, s13, s14)))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15055,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | (~node6(c_e_h_2, c_j, s13, s14))))),
% 87.54/87.74 inference(monotonicity,[status(thm)],[15054])).
% 87.54/87.74 tff(15056,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | (~node6(c_e_h_2, c_j, s13, s14)))),
% 87.54/87.74 inference(transitivity,[status(thm)],[15055, 15053])).
% 87.54/87.74 tff(15057,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15058,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | (~node6(c_e_h_2, c_j, s13, s14))),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15057, 15056])).
% 87.54/87.74 tff(15059,plain,
% 87.54/87.74 ($false),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15058, 899, 14788, 15051, 15052])).
% 87.54/87.74 tff(15060,plain,((~node6(c_e_h_2, c_j, s13, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.74 tff(15061,plain,
% 87.54/87.74 (~node6(c_e_h_2, c_j, s13, s14)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15060, 15051, 14788])).
% 87.54/87.74 tff(15062,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s13, s14)) | node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s13, s14)) | node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15063,plain,
% 87.54/87.74 ((node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14) | (~trans(s13, s14))) <=> ((~trans(s13, s14)) | node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15064,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14) | (~trans(s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s13, s14)) | node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14)))),
% 87.54/87.74 inference(monotonicity,[status(thm)],[15063])).
% 87.54/87.74 tff(15065,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14) | (~trans(s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s13, s14)) | node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14))),
% 87.54/87.74 inference(transitivity,[status(thm)],[15064, 15062])).
% 87.54/87.74 tff(15066,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14) | (~trans(s13, s14)))),
% 87.54/87.74 inference(quant_inst,[status(thm)],[])).
% 87.54/87.74 tff(15067,plain,
% 87.54/87.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s13, s14)) | node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14)),
% 87.54/87.74 inference(modus_ponens,[status(thm)],[15066, 15065])).
% 87.54/87.74 tff(15068,plain,
% 87.54/87.74 (node6(c_e_h_2, c_j, s13, s14) | node5(c_e_h_2, c_j, s13, s14)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15067, 881, 10040])).
% 87.54/87.74 tff(15069,plain,
% 87.54/87.74 (node5(c_e_h_2, c_j, s13, s14)),
% 87.54/87.74 inference(unit_resolution,[status(thm)],[15068, 15061])).
% 87.54/87.74 tff(15070,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15071,plain,
% 87.54/87.74 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s13) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14))) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13))),
% 87.54/87.74 inference(rewrite,[status(thm)],[])).
% 87.54/87.74 tff(15072,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s13) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13)))),
% 87.54/87.74 inference(monotonicity,[status(thm)],[15071])).
% 87.54/87.74 tff(15073,plain,
% 87.54/87.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s13) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13))),
% 87.54/87.75 inference(transitivity,[status(thm)],[15072, 15070])).
% 87.54/87.75 tff(15074,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s13) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15075,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | (~node5(c_e_h_2, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13)),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15074, 15073])).
% 87.54/87.75 tff(15076,plain,
% 87.54/87.75 ($false),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15075, 862, 15051, 15069, 15050, 14903])).
% 87.54/87.75 tff(15077,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s13) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13) | m_or_h_gate_v_out(c_e_h_2, c_j, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.75 tff(15078,plain,
% 87.54/87.75 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s14)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13) | m_or_h_gate_v_out(c_e_h_2, c_j, s13)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15077, 15049])).
% 87.54/87.75 tff(15079,plain,
% 87.54/87.75 (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15078, 14788, 14903])).
% 87.54/87.75 tff(15080,assumption,(m_c_h_element_v_in2(c_e_h_2, c_h, s14)), introduced(assumption)).
% 87.54/87.75 tff(15081,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s14)), introduced(assumption)).
% 87.54/87.75 tff(15082,plain,
% 87.54/87.75 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15083,plain,
% 87.54/87.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15084,plain,
% 87.54/87.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s14)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14)),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15083, 15082])).
% 87.54/87.75 tff(15085,plain,
% 87.54/87.75 ($false),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15084, 309, 15081, 15080])).
% 87.54/87.75 tff(15086,plain,(m_or_h_gate_v_out(c_e_h_2, c_j, s14) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.75 tff(15087,plain,
% 87.54/87.75 (~m_c_h_element_v_in2(c_e_h_2, c_h, s14)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15086, 15079])).
% 87.54/87.75 tff(15088,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s14)), introduced(assumption)).
% 87.54/87.75 tff(15089,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s15)), introduced(assumption)).
% 87.54/87.75 tff(15090,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s14)), introduced(assumption)).
% 87.54/87.75 tff(15091,assumption,(node15(c_e_h_2, c_h, s14, s15)), introduced(assumption)).
% 87.54/87.75 tff(15092,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node15(c_e_h_2, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node15(c_e_h_2, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15093,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node15(c_e_h_2, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15094,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node15(c_e_h_2, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14)),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15093, 15092])).
% 87.54/87.75 tff(15095,plain,
% 87.54/87.75 ($false),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15094, 173, 15089, 15090, 15091])).
% 87.54/87.75 tff(15096,plain,((~node15(c_e_h_2, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.75 tff(15097,plain,
% 87.54/87.75 (~node15(c_e_h_2, c_h, s14, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15096, 15089, 15090])).
% 87.54/87.75 tff(15098,assumption,(~node15(c_e_h_2, c_h, s14, s15)), introduced(assumption)).
% 87.54/87.75 tff(15099,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s14)), introduced(assumption)).
% 87.54/87.75 tff(15100,plain,
% 87.54/87.75 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | m_c_h_element_v_in2(c_e_h_2, c_h, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | m_c_h_element_v_in2(c_e_h_2, c_h, s14))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15101,plain,
% 87.54/87.75 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | m_c_h_element_v_in2(c_e_h_2, c_h, s14))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15102,plain,
% 87.54/87.75 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | m_c_h_element_v_in2(c_e_h_2, c_h, s14)),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15101, 15100])).
% 87.54/87.75 tff(15103,plain,
% 87.54/87.75 ((~node16(c_e_h_2, c_h, s14)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15102, 228, 15088])).
% 87.54/87.75 tff(15104,plain,
% 87.54/87.75 (~node16(c_e_h_2, c_h, s14)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15103, 15099])).
% 87.54/87.75 tff(15105,assumption,(node14(c_e_h_2, c_h, s14, s15)), introduced(assumption)).
% 87.54/87.75 tff(15106,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~node14(c_e_h_2, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~node14(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15107,plain,
% 87.54/87.75 (((~node14(c_e_h_2, c_h, s14, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~node14(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15108,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s14, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~node14(c_e_h_2, c_h, s14, s15))))),
% 87.54/87.75 inference(monotonicity,[status(thm)],[15107])).
% 87.54/87.75 tff(15109,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s14, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~node14(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(transitivity,[status(thm)],[15108, 15106])).
% 87.54/87.75 tff(15110,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s14, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15111,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14) | (~node14(c_e_h_2, c_h, s14, s15))),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15110, 15109])).
% 87.54/87.75 tff(15112,plain,
% 87.54/87.75 ($false),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15111, 283, 15089, 15099, 15105])).
% 87.54/87.75 tff(15113,plain,((~node14(c_e_h_2, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.75 tff(15114,plain,
% 87.54/87.75 (~node14(c_e_h_2, c_h, s14, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15113, 15099, 15089])).
% 87.54/87.75 tff(15115,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_2, c_h, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_2, c_h, s14, s15))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15116,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_2, c_h, s14, s15))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15117,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_2, c_h, s14, s15)),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15116, 15115])).
% 87.54/87.75 tff(15118,plain,
% 87.54/87.75 (node19(c_e_h_2, c_h, s14, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15117, 141, 10504])).
% 87.54/87.75 tff(15119,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s14) | (~node19(c_e_h_2, c_h, s14, s15)) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s14) | (~node19(c_e_h_2, c_h, s14, s15)) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15120,plain,
% 87.54/87.75 ((node16(c_e_h_2, c_h, s14) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15) | (~node19(c_e_h_2, c_h, s14, s15))) <=> (node16(c_e_h_2, c_h, s14) | (~node19(c_e_h_2, c_h, s14, s15)) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15121,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s14) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15) | (~node19(c_e_h_2, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s14) | (~node19(c_e_h_2, c_h, s14, s15)) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(monotonicity,[status(thm)],[15120])).
% 87.54/87.75 tff(15122,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s14) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15) | (~node19(c_e_h_2, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s14) | (~node19(c_e_h_2, c_h, s14, s15)) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15))),
% 87.54/87.75 inference(transitivity,[status(thm)],[15121, 15119])).
% 87.54/87.75 tff(15123,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s14) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15) | (~node19(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15124,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s14) | (~node19(c_e_h_2, c_h, s14, s15)) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15)),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15123, 15122])).
% 87.54/87.75 tff(15125,plain,
% 87.54/87.75 (node16(c_e_h_2, c_h, s14) | node14(c_e_h_2, c_h, s14, s15) | node15(c_e_h_2, c_h, s14, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15124, 189, 15118])).
% 87.54/87.75 tff(15126,plain,
% 87.54/87.75 ($false),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15125, 15114, 15104, 15098])).
% 87.54/87.75 tff(15127,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s14) | node15(c_e_h_2, c_h, s14, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.75 tff(15128,plain,
% 87.54/87.75 (m_c_h_element_v_in1(c_e_h_2, c_h, s14)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15127, 15097, 15089, 15088])).
% 87.54/87.75 tff(15129,plain,
% 87.54/87.75 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s14)) | m_c_h_element_v_in2(c_e_h_2, c_h, s14) | (~node17(c_e_h_2, c_h, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s14)) | m_c_h_element_v_in2(c_e_h_2, c_h, s14) | (~node17(c_e_h_2, c_h, s14)))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15130,plain,
% 87.54/87.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s14)) | m_c_h_element_v_in2(c_e_h_2, c_h, s14) | (~node17(c_e_h_2, c_h, s14)))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15131,plain,
% 87.54/87.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s14)) | m_c_h_element_v_in2(c_e_h_2, c_h, s14) | (~node17(c_e_h_2, c_h, s14))),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15130, 15129])).
% 87.54/87.75 tff(15132,plain,
% 87.54/87.75 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s14)) | (~node17(c_e_h_2, c_h, s14))),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15131, 209, 15088])).
% 87.54/87.75 tff(15133,plain,
% 87.54/87.75 (~node17(c_e_h_2, c_h, s14)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15132, 15128])).
% 87.54/87.75 tff(15134,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s14) | node18(c_e_h_2, c_h, s14, s15) | (~node19(c_e_h_2, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s14) | node18(c_e_h_2, c_h, s14, s15) | (~node19(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15135,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s14) | node18(c_e_h_2, c_h, s14, s15) | (~node19(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15136,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s14) | node18(c_e_h_2, c_h, s14, s15) | (~node19(c_e_h_2, c_h, s14, s15))),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15135, 15134])).
% 87.54/87.75 tff(15137,plain,
% 87.54/87.75 (node17(c_e_h_2, c_h, s14) | node18(c_e_h_2, c_h, s14, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15136, 156, 15118])).
% 87.54/87.75 tff(15138,plain,
% 87.54/87.75 (node18(c_e_h_2, c_h, s14, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15137, 15133])).
% 87.54/87.75 tff(15139,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node18(c_e_h_2, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node18(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15140,plain,
% 87.54/87.75 (((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~node18(c_e_h_2, c_h, s14, s15))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node18(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15141,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~node18(c_e_h_2, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node18(c_e_h_2, c_h, s14, s15))))),
% 87.54/87.75 inference(monotonicity,[status(thm)],[15140])).
% 87.54/87.75 tff(15142,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~node18(c_e_h_2, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node18(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(transitivity,[status(thm)],[15141, 15139])).
% 87.54/87.75 tff(15143,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~node18(c_e_h_2, c_h, s14, s15)))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15144,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s14) | (~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | (~node18(c_e_h_2, c_h, s14, s15))),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15143, 15142])).
% 87.54/87.75 tff(15145,plain,
% 87.54/87.75 ($false),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15144, 124, 15089, 15090, 15138])).
% 87.54/87.75 tff(15146,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s14) | m_c_h_element_v_in2(c_e_h_2, c_h, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.75 tff(15147,plain,
% 87.54/87.75 (~m_c_h_element_v_out(c_e_h_2, c_h, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15146, 14865, 15087])).
% 87.54/87.75 tff(15148,plain,
% 87.54/87.75 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s15))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s15))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15149,plain,
% 87.54/87.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s15))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15150,plain,
% 87.54/87.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s15)) | m_c_h_element_v_out(c_e_h_2, c_h, s15)),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15149, 15148])).
% 87.54/87.75 tff(15151,plain,
% 87.54/87.75 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15150, 23, 15147])).
% 87.54/87.75 tff(15152,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s16)), introduced(assumption)).
% 87.54/87.75 tff(15153,plain,
% 87.54/87.75 (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[14892, 14873, 14690])).
% 87.54/87.75 tff(15154,assumption,(node22(c_e_h_2, c_i, s15, s16)), introduced(assumption)).
% 87.54/87.75 tff(15155,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | (~node22(c_e_h_2, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | (~node22(c_e_h_2, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15156,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | (~node22(c_e_h_2, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15))),
% 87.54/87.75 inference(quant_inst,[status(thm)],[])).
% 87.54/87.75 tff(15157,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | (~node22(c_e_h_2, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15)),
% 87.54/87.75 inference(modus_ponens,[status(thm)],[15156, 15155])).
% 87.54/87.75 tff(15158,plain,
% 87.54/87.75 ($false),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15157, 107, 15152, 14895, 15154])).
% 87.54/87.75 tff(15159,plain,((~node22(c_e_h_2, c_i, s15, s16)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.75 tff(15160,plain,
% 87.54/87.75 (~node22(c_e_h_2, c_i, s15, s16)),
% 87.54/87.75 inference(unit_resolution,[status(thm)],[15159, 15152, 14895])).
% 87.54/87.75 tff(15161,assumption,(~node20(c_e_h_2, c_i, s15)), introduced(assumption)).
% 87.54/87.75 tff(15162,assumption,(node21(c_e_h_2, c_i, s15, s16)), introduced(assumption)).
% 87.54/87.75 tff(15163,plain,
% 87.54/87.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | (~node21(c_e_h_2, c_i, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | (~node21(c_e_h_2, c_i, s15, s16)))),
% 87.54/87.75 inference(rewrite,[status(thm)],[])).
% 87.54/87.75 tff(15164,plain,
% 87.54/87.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | (~node21(c_e_h_2, c_i, s15, s16)))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15165,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | (~node21(c_e_h_2, c_i, s15, s16))),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15164, 15163])).
% 87.54/87.76 tff(15166,plain,
% 87.54/87.76 ($false),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15165, 51, 15152, 15161, 15162])).
% 87.54/87.76 tff(15167,plain,((~node21(c_e_h_2, c_i, s15, s16)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | node20(c_e_h_2, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.76 tff(15168,plain,
% 87.54/87.76 (~node21(c_e_h_2, c_i, s15, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15167, 15152, 15161])).
% 87.54/87.76 tff(15169,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_2, c_i, s15, s16) | node22(c_e_h_2, c_i, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_2, c_i, s15, s16) | node22(c_e_h_2, c_i, s15, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15170,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_2, c_i, s15, s16) | node22(c_e_h_2, c_i, s15, s16))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15171,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_2, c_i, s15, s16) | node22(c_e_h_2, c_i, s15, s16)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15170, 15169])).
% 87.54/87.76 tff(15172,plain,
% 87.54/87.76 (node21(c_e_h_2, c_i, s15, s16) | node22(c_e_h_2, c_i, s15, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15171, 81, 12879])).
% 87.54/87.76 tff(15173,plain,
% 87.54/87.76 ($false),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15172, 15168, 15160])).
% 87.54/87.76 tff(15174,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | node20(c_e_h_2, c_i, s15) | m_and_h_gate_v_out(c_e_h_2, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.76 tff(15175,plain,
% 87.54/87.76 (node20(c_e_h_2, c_i, s15)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15174, 15153, 15152])).
% 87.54/87.76 tff(15176,plain,
% 87.54/87.76 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s15)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s15)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s15))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15177,plain,
% 87.54/87.76 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s15)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s15))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15178,plain,
% 87.54/87.76 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s15)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s15)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15177, 15176])).
% 87.54/87.76 tff(15179,plain,
% 87.54/87.76 ($false),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15178, 37, 15175, 15151])).
% 87.54/87.76 tff(15180,plain,(m_or_h_gate_v_out(c_e_h_2, c_j, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s14) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.76 tff(15181,plain,
% 87.54/87.76 (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15180, 14690, 14788, 14787, 14903])).
% 87.54/87.76 tff(15182,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s16)), introduced(assumption)).
% 87.54/87.76 tff(15183,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s16)), introduced(assumption)).
% 87.54/87.76 tff(15184,plain,
% 87.54/87.76 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15185,plain,
% 87.54/87.76 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15186,plain,
% 87.54/87.76 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15185, 15184])).
% 87.54/87.76 tff(15187,plain,
% 87.54/87.76 ($false),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15186, 365, 15183, 15182])).
% 87.54/87.76 tff(15188,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s16)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.76 tff(15189,plain,
% 87.54/87.76 (~m_c_h_element_v_in2(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15188, 15181])).
% 87.54/87.76 tff(15190,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s16)), introduced(assumption)).
% 87.54/87.76 tff(15191,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s16)), introduced(assumption)).
% 87.54/87.76 tff(15192,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s16)), introduced(assumption)).
% 87.54/87.76 tff(15193,plain,
% 87.54/87.76 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16) | m_c_h_element_v_in2(c_e_h_2, c_e, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16) | m_c_h_element_v_in2(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15194,plain,
% 87.54/87.76 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16) | m_c_h_element_v_in2(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15195,plain,
% 87.54/87.76 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16) | m_c_h_element_v_in2(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15194, 15193])).
% 87.54/87.76 tff(15196,plain,
% 87.54/87.76 ((~node16(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15195, 228, 15191])).
% 87.54/87.76 tff(15197,plain,
% 87.54/87.76 (~node16(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15196, 15192])).
% 87.54/87.76 tff(15198,assumption,(~node16(c_e_h_2, c_e, s16)), introduced(assumption)).
% 87.54/87.76 tff(15199,assumption,(node14(c_e_h_2, c_e, s16, s17)), introduced(assumption)).
% 87.54/87.76 tff(15200,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s16, s17)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_e, s16, s17)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15201,plain,
% 87.54/87.76 (((~node14(c_e_h_2, c_e, s16, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17))) <=> ((~node14(c_e_h_2, c_e, s16, s17)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15202,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s16, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s16, s17)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16)))),
% 87.54/87.76 inference(monotonicity,[status(thm)],[15201])).
% 87.54/87.76 tff(15203,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s16, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_e, s16, s17)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(transitivity,[status(thm)],[15202, 15200])).
% 87.54/87.76 tff(15204,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s16, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15205,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_e, s16, s17)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15204, 15203])).
% 87.54/87.76 tff(15206,plain,
% 87.54/87.76 ($false),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15205, 283, 15199, 14902, 15192])).
% 87.54/87.76 tff(15207,plain,((~node14(c_e_h_2, c_e, s16, s17)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s16)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.76 tff(15208,plain,
% 87.54/87.76 (~node14(c_e_h_2, c_e, s16, s17)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15207, 14902, 15192])).
% 87.54/87.76 tff(15209,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_2, c_e, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_2, c_e, s16, s17))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15210,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_2, c_e, s16, s17))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15211,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_2, c_e, s16, s17)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15210, 15209])).
% 87.54/87.76 tff(15212,plain,
% 87.54/87.76 (node19(c_e_h_2, c_e, s16, s17)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15211, 141, 14096])).
% 87.54/87.76 tff(15213,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)) | node14(c_e_h_2, c_e, s16, s17) | node16(c_e_h_2, c_e, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)) | node14(c_e_h_2, c_e, s16, s17) | node16(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15214,plain,
% 87.54/87.76 ((node16(c_e_h_2, c_e, s16) | node14(c_e_h_2, c_e, s16, s17) | node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17))) <=> (node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)) | node14(c_e_h_2, c_e, s16, s17) | node16(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15215,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s16) | node14(c_e_h_2, c_e, s16, s17) | node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)) | node14(c_e_h_2, c_e, s16, s17) | node16(c_e_h_2, c_e, s16)))),
% 87.54/87.76 inference(monotonicity,[status(thm)],[15214])).
% 87.54/87.76 tff(15216,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s16) | node14(c_e_h_2, c_e, s16, s17) | node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)) | node14(c_e_h_2, c_e, s16, s17) | node16(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(transitivity,[status(thm)],[15215, 15213])).
% 87.54/87.76 tff(15217,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s16) | node14(c_e_h_2, c_e, s16, s17) | node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15218,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)) | node14(c_e_h_2, c_e, s16, s17) | node16(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15217, 15216])).
% 87.54/87.76 tff(15219,plain,
% 87.54/87.76 (node15(c_e_h_2, c_e, s16, s17) | node14(c_e_h_2, c_e, s16, s17) | node16(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15218, 189, 15212])).
% 87.54/87.76 tff(15220,plain,
% 87.54/87.76 (node15(c_e_h_2, c_e, s16, s17)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15219, 15208, 15198])).
% 87.54/87.76 tff(15221,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | (~node15(c_e_h_2, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | (~node15(c_e_h_2, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15222,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | (~node15(c_e_h_2, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15223,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | (~node15(c_e_h_2, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15222, 15221])).
% 87.54/87.76 tff(15224,plain,
% 87.54/87.76 ($false),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15223, 173, 15220, 14902, 15190])).
% 87.54/87.76 tff(15225,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16) | node16(c_e_h_2, c_e, s16) | m_c_h_element_v_in1(c_e_h_2, c_e, s16)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.76 tff(15226,plain,
% 87.54/87.76 ($false),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15225, 15197, 15192, 14902, 15190])).
% 87.54/87.76 tff(15227,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s16) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16) | m_c_h_element_v_in2(c_e_h_2, c_e, s16)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.76 tff(15228,plain,
% 87.54/87.76 (m_c_h_element_v_in1(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15227, 15190, 14902, 15191])).
% 87.54/87.76 tff(15229,plain,
% 87.54/87.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | (~node17(c_e_h_2, c_e, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | (~node17(c_e_h_2, c_e, s16)))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15230,plain,
% 87.54/87.76 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~node17(c_e_h_2, c_e, s16))) <=> (m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | (~node17(c_e_h_2, c_e, s16)))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15231,plain,
% 87.54/87.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~node17(c_e_h_2, c_e, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | (~node17(c_e_h_2, c_e, s16))))),
% 87.54/87.76 inference(monotonicity,[status(thm)],[15230])).
% 87.54/87.76 tff(15232,plain,
% 87.54/87.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~node17(c_e_h_2, c_e, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | (~node17(c_e_h_2, c_e, s16)))),
% 87.54/87.76 inference(transitivity,[status(thm)],[15231, 15229])).
% 87.54/87.76 tff(15233,plain,
% 87.54/87.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~node17(c_e_h_2, c_e, s16)))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15234,plain,
% 87.54/87.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_e, s16) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | (~node17(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15233, 15232])).
% 87.54/87.76 tff(15235,plain,
% 87.54/87.76 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s16)) | (~node17(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15234, 209, 15191])).
% 87.54/87.76 tff(15236,plain,
% 87.54/87.76 (~node17(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15235, 15228])).
% 87.54/87.76 tff(15237,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s16, s17)) | node18(c_e_h_2, c_e, s16, s17) | node17(c_e_h_2, c_e, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s16, s17)) | node18(c_e_h_2, c_e, s16, s17) | node17(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15238,plain,
% 87.54/87.76 ((node17(c_e_h_2, c_e, s16) | node18(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17))) <=> ((~node19(c_e_h_2, c_e, s16, s17)) | node18(c_e_h_2, c_e, s16, s17) | node17(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15239,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s16) | node18(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_e, s16, s17)) | node18(c_e_h_2, c_e, s16, s17) | node17(c_e_h_2, c_e, s16)))),
% 87.54/87.76 inference(monotonicity,[status(thm)],[15238])).
% 87.54/87.76 tff(15240,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s16) | node18(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s16, s17)) | node18(c_e_h_2, c_e, s16, s17) | node17(c_e_h_2, c_e, s16))),
% 87.54/87.76 inference(transitivity,[status(thm)],[15239, 15237])).
% 87.54/87.76 tff(15241,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s16) | node18(c_e_h_2, c_e, s16, s17) | (~node19(c_e_h_2, c_e, s16, s17)))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15242,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_e, s16, s17)) | node18(c_e_h_2, c_e, s16, s17) | node17(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15241, 15240])).
% 87.54/87.76 tff(15243,plain,
% 87.54/87.76 (node18(c_e_h_2, c_e, s16, s17) | node17(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15242, 156, 15212])).
% 87.54/87.76 tff(15244,plain,
% 87.54/87.76 (node18(c_e_h_2, c_e, s16, s17)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15243, 15236])).
% 87.54/87.76 tff(15245,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16) | (~node18(c_e_h_2, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16) | (~node18(c_e_h_2, c_e, s16, s17)))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15246,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16) | (~node18(c_e_h_2, c_e, s16, s17)))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15247,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s16) | (~node18(c_e_h_2, c_e, s16, s17))),
% 87.54/87.76 inference(modus_ponens,[status(thm)],[15246, 15245])).
% 87.54/87.76 tff(15248,plain,
% 87.54/87.76 ($false),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15247, 124, 15244, 14902, 15190])).
% 87.54/87.76 tff(15249,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s16) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s16)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.76 tff(15250,plain,
% 87.54/87.76 (m_c_h_element_v_out(c_e_h_2, c_e, s16)),
% 87.54/87.76 inference(unit_resolution,[status(thm)],[15249, 15189, 14902])).
% 87.54/87.76 tff(15251,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s16)), introduced(assumption)).
% 87.54/87.76 tff(15252,assumption,(node18(c_e_h_2, c_e, s15, s16)), introduced(assumption)).
% 87.54/87.76 tff(15253,plain,
% 87.54/87.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15) | (~node18(c_e_h_2, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15) | (~node18(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.76 inference(rewrite,[status(thm)],[])).
% 87.54/87.76 tff(15254,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15) | (~node18(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.76 inference(quant_inst,[status(thm)],[])).
% 87.54/87.76 tff(15255,plain,
% 87.54/87.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15) | (~node18(c_e_h_2, c_e, s15, s16))),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15254, 15253])).
% 87.54/87.77 tff(15256,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15255, 124, 14786, 15251, 15252])).
% 87.54/87.77 tff(15257,plain,((~node18(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15258,plain,
% 87.54/87.77 (~node18(c_e_h_2, c_e, s15, s16)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15257, 15251, 14786])).
% 87.54/87.77 tff(15259,assumption,(node15(c_e_h_2, c_e, s15, s16)), introduced(assumption)).
% 87.54/87.77 tff(15260,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | (~node15(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | (~node15(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15261,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | (~node15(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15262,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | (~node15(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15)),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15261, 15260])).
% 87.54/87.77 tff(15263,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15262, 173, 14786, 15251, 15259])).
% 87.54/87.77 tff(15264,plain,((~node15(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_e, s15) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15265,plain,
% 87.54/87.77 (~node15(c_e_h_2, c_e, s15, s16)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15264, 15251, 14786])).
% 87.54/87.77 tff(15266,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s15)), introduced(assumption)).
% 87.54/87.77 tff(15267,assumption,(node17(c_e_h_2, c_e, s15)), introduced(assumption)).
% 87.54/87.77 tff(15268,plain,
% 87.54/87.77 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s15)))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15269,plain,
% 87.54/87.77 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~node17(c_e_h_2, c_e, s15))) <=> ((~node17(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s15)))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15270,plain,
% 87.54/87.77 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~node17(c_e_h_2, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s15))))),
% 87.54/87.77 inference(monotonicity,[status(thm)],[15269])).
% 87.54/87.77 tff(15271,plain,
% 87.54/87.77 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~node17(c_e_h_2, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s15)))),
% 87.54/87.77 inference(transitivity,[status(thm)],[15270, 15268])).
% 87.54/87.77 tff(15272,plain,
% 87.54/87.77 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~node17(c_e_h_2, c_e, s15)))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15273,plain,
% 87.54/87.77 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s15)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s15))),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15272, 15271])).
% 87.54/87.77 tff(15274,plain,
% 87.54/87.77 (m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s15))),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15273, 209, 15267])).
% 87.54/87.77 tff(15275,plain,
% 87.54/87.77 (~m_c_h_element_v_in1(c_e_h_2, c_e, s15)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15274, 15266])).
% 87.54/87.77 tff(15276,assumption,(~node15(c_e_h_2, c_e, s15, s16)), introduced(assumption)).
% 87.54/87.77 tff(15277,plain,
% 87.54/87.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | m_c_h_element_v_in2(c_e_h_2, c_e, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | m_c_h_element_v_in2(c_e_h_2, c_e, s15))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15278,plain,
% 87.54/87.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | m_c_h_element_v_in2(c_e_h_2, c_e, s15))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15279,plain,
% 87.54/87.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s15)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | m_c_h_element_v_in2(c_e_h_2, c_e, s15)),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15278, 15277])).
% 87.54/87.77 tff(15280,plain,
% 87.54/87.77 (~node16(c_e_h_2, c_e, s15)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15279, 228, 15275, 15266])).
% 87.54/87.77 tff(15281,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_2, c_e, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_2, c_e, s15, s16))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15282,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_2, c_e, s15, s16))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15283,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_2, c_e, s15, s16)),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15282, 15281])).
% 87.54/87.77 tff(15284,plain,
% 87.54/87.77 (node19(c_e_h_2, c_e, s15, s16)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15283, 141, 12879])).
% 87.54/87.77 tff(15285,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s15) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)) | node14(c_e_h_2, c_e, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s15) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)) | node14(c_e_h_2, c_e, s15, s16))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15286,plain,
% 87.54/87.77 ((node16(c_e_h_2, c_e, s15) | node14(c_e_h_2, c_e, s15, s16) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16))) <=> (node16(c_e_h_2, c_e, s15) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)) | node14(c_e_h_2, c_e, s15, s16))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15287,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s15) | node14(c_e_h_2, c_e, s15, s16) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s15) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)) | node14(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.77 inference(monotonicity,[status(thm)],[15286])).
% 87.54/87.77 tff(15288,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s15) | node14(c_e_h_2, c_e, s15, s16) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s15) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)) | node14(c_e_h_2, c_e, s15, s16))),
% 87.54/87.77 inference(transitivity,[status(thm)],[15287, 15285])).
% 87.54/87.77 tff(15289,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s15) | node14(c_e_h_2, c_e, s15, s16) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15290,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s15) | node15(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)) | node14(c_e_h_2, c_e, s15, s16)),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15289, 15288])).
% 87.54/87.77 tff(15291,plain,
% 87.54/87.77 (node16(c_e_h_2, c_e, s15) | node15(c_e_h_2, c_e, s15, s16) | node14(c_e_h_2, c_e, s15, s16)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15290, 189, 15284])).
% 87.54/87.77 tff(15292,plain,
% 87.54/87.77 (node14(c_e_h_2, c_e, s15, s16)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15291, 15280, 15276])).
% 87.54/87.77 tff(15293,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~node14(c_e_h_2, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~node14(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15294,plain,
% 87.54/87.77 (((~node14(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~node14(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15295,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~node14(c_e_h_2, c_e, s15, s16))))),
% 87.54/87.77 inference(monotonicity,[status(thm)],[15294])).
% 87.54/87.77 tff(15296,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~node14(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.77 inference(transitivity,[status(thm)],[15295, 15293])).
% 87.54/87.77 tff(15297,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15298,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_in1(c_e_h_2, c_e, s15) | (~node14(c_e_h_2, c_e, s15, s16))),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15297, 15296])).
% 87.54/87.77 tff(15299,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15298, 283, 15251, 15292, 15275])).
% 87.54/87.77 tff(15300,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s15) | (~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | node15(c_e_h_2, c_e, s15, s16) | (~node17(c_e_h_2, c_e, s15))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15301,plain,
% 87.54/87.77 (~node17(c_e_h_2, c_e, s15)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15300, 15251, 15266, 15265])).
% 87.54/87.77 tff(15302,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s15) | node18(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s15) | node18(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15303,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s15) | node18(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16)))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15304,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s15) | node18(c_e_h_2, c_e, s15, s16) | (~node19(c_e_h_2, c_e, s15, s16))),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15303, 15302])).
% 87.54/87.77 tff(15305,plain,
% 87.54/87.77 (node17(c_e_h_2, c_e, s15) | node18(c_e_h_2, c_e, s15, s16)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15304, 156, 15284])).
% 87.54/87.77 tff(15306,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15305, 15301, 15258])).
% 87.54/87.77 tff(15307,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s16)) | m_c_h_element_v_in2(c_e_h_2, c_e, s15) | m_c_h_element_v_out(c_e_h_2, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15308,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15307, 15250, 14901, 14786])).
% 87.54/87.77 tff(15309,plain,(m_and_h_gate_v_out(c_e_h_2, c_i, s14) | m_c_h_element_v_out(c_e_h_2, c_e, s15) | (~m_c_h_element_v_out(c_e_h_2, c_e, s17)) | m_or_h_gate_v_out(c_e_h_2, c_j, s13) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | m_or_h_gate_v_in1(c_e_h_2, c_j, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15310,plain,
% 87.54/87.77 (~m_c_h_element_v_out(c_e_h_2, c_e, s17)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15309, 14785, 14688, 14486, 14517, 14245])).
% 87.54/87.77 tff(15311,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_l, s13)), introduced(assumption)).
% 87.54/87.77 tff(15312,plain,
% 87.54/87.77 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15313,plain,
% 87.54/87.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15314,plain,
% 87.54/87.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15313, 15312])).
% 87.54/87.77 tff(15315,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15314, 1638, 12686, 15311])).
% 87.54/87.77 tff(15316,plain,((~m_and_h_gate_v_in2(c_e_h_2, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15317,plain,
% 87.54/87.77 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15316, 12790])).
% 87.54/87.77 tff(15318,assumption,(~m_and_h_gate_v_in2(c_e_h_2, c_l, s13)), introduced(assumption)).
% 87.54/87.77 tff(15319,assumption,(node20(c_e_h_2, c_l, s13)), introduced(assumption)).
% 87.54/87.77 tff(15320,plain,
% 87.54/87.77 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s13))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15321,plain,
% 87.54/87.77 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s13))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15322,plain,
% 87.54/87.77 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s13)),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15321, 15320])).
% 87.54/87.77 tff(15323,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15322, 1535, 15319, 15318])).
% 87.54/87.77 tff(15324,plain,((~node20(c_e_h_2, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15325,plain,
% 87.54/87.77 (~node20(c_e_h_2, c_l, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15324, 15317])).
% 87.54/87.77 tff(15326,plain,
% 87.54/87.77 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s11)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14251, 14185])).
% 87.54/87.77 tff(15327,plain,
% 87.54/87.77 (~m_or_h_gate_v_out(c_e_h_2, c_j, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14412, 15326, 10262])).
% 87.54/87.77 tff(15328,plain,
% 87.54/87.77 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s11)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14142, 4433])).
% 87.54/87.77 tff(15329,plain,
% 87.54/87.77 (~node20(c_e_h_2, c_l, s11)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14150, 15328])).
% 87.54/87.77 tff(15330,plain,
% 87.54/87.77 (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14207, 14185, 15329])).
% 87.54/87.77 tff(15331,plain,
% 87.54/87.77 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14523, 15330])).
% 87.54/87.77 tff(15332,plain,
% 87.54/87.77 (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14687, 15331, 15327])).
% 87.54/87.77 tff(15333,plain,
% 87.54/87.77 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[12643, 12627, 4433])).
% 87.54/87.77 tff(15334,plain,
% 87.54/87.77 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14211, 1638, 15333])).
% 87.54/87.77 tff(15335,plain,
% 87.54/87.77 (~node20(c_e_h_2, c_l, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14215, 1535, 15334])).
% 87.54/87.77 tff(15336,plain,
% 87.54/87.77 (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14236, 15330, 15335])).
% 87.54/87.77 tff(15337,plain,
% 87.54/87.77 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14244, 15336])).
% 87.54/87.77 tff(15338,plain,
% 87.54/87.77 (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15078, 15337, 15332])).
% 87.54/87.77 tff(15339,plain,
% 87.54/87.77 (~m_c_h_element_v_in2(c_e_h_2, c_h, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15086, 15338])).
% 87.54/87.77 tff(15340,plain,
% 87.54/87.77 (~m_c_h_element_v_in2(c_e_h_2, c_h, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14416, 309, 15327])).
% 87.54/87.77 tff(15341,plain,
% 87.54/87.77 (~m_c_h_element_v_out(c_e_h_2, c_h, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14485, 15340, 14420])).
% 87.54/87.77 tff(15342,plain,
% 87.54/87.77 (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14791, 309, 15332])).
% 87.54/87.77 tff(15343,plain,
% 87.54/87.77 (~m_c_h_element_v_out(c_e_h_2, c_h, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14864, 15342, 15341])).
% 87.54/87.77 tff(15344,plain,
% 87.54/87.77 (~m_c_h_element_v_out(c_e_h_2, c_h, s15)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15146, 15343, 15339])).
% 87.54/87.77 tff(15345,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s17)), introduced(assumption)).
% 87.54/87.77 tff(15346,plain,
% 87.54/87.77 (~m_and_h_gate_v_out(c_e_h_2, c_l, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14207, 15329, 14185])).
% 87.54/87.77 tff(15347,plain,
% 87.54/87.77 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14523, 15346])).
% 87.54/87.77 tff(15348,plain,
% 87.54/87.77 (~m_or_h_gate_v_out(c_e_h_2, c_j, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14687, 15347, 14525])).
% 87.54/87.77 tff(15349,plain,
% 87.54/87.77 (~m_c_h_element_v_in2(c_e_h_2, c_h, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14791, 309, 15348])).
% 87.54/87.77 tff(15350,plain,
% 87.54/87.77 (~m_c_h_element_v_out(c_e_h_2, c_h, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14864, 15349, 14787])).
% 87.54/87.77 tff(15351,plain,
% 87.54/87.77 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[12643, 4433, 12627])).
% 87.54/87.77 tff(15352,plain,
% 87.54/87.77 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14211, 1638, 15351])).
% 87.54/87.77 tff(15353,plain,
% 87.54/87.77 (~node20(c_e_h_2, c_l, s12)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14215, 1535, 15352])).
% 87.54/87.77 tff(15354,plain,
% 87.54/87.77 (~m_and_h_gate_v_out(c_e_h_2, c_l, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14236, 15353, 15346])).
% 87.54/87.77 tff(15355,plain,
% 87.54/87.77 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14244, 15354])).
% 87.54/87.77 tff(15356,plain,
% 87.54/87.77 (~m_or_h_gate_v_out(c_e_h_2, c_j, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15078, 15355, 15348])).
% 87.54/87.77 tff(15357,plain,
% 87.54/87.77 (~m_c_h_element_v_in2(c_e_h_2, c_h, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15086, 15356])).
% 87.54/87.77 tff(15358,plain,
% 87.54/87.77 (~m_c_h_element_v_out(c_e_h_2, c_h, s15)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15146, 15357, 15350])).
% 87.54/87.77 tff(15359,plain,
% 87.54/87.77 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s15)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15150, 23, 15358])).
% 87.54/87.77 tff(15360,plain,
% 87.54/87.77 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14489, 23, 14787])).
% 87.54/87.77 tff(15361,plain,
% 87.54/87.77 (~node20(c_e_h_2, c_i, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14493, 37, 15360])).
% 87.54/87.77 tff(15362,plain,
% 87.54/87.77 (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14516, 15361, 10378])).
% 87.54/87.77 tff(15363,plain,
% 87.54/87.77 (node20(c_e_h_2, c_i, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14892, 15362, 14875])).
% 87.54/87.77 tff(15364,plain,
% 87.54/87.77 (m_and_h_gate_v_in1(c_e_h_2, c_i, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14872, 37, 15363])).
% 87.54/87.77 tff(15365,plain,
% 87.54/87.77 (m_c_h_element_v_out(c_e_h_2, c_h, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14868, 23, 15364])).
% 87.54/87.77 tff(15366,plain,
% 87.54/87.77 (~node18(c_e_h_2, c_h, s13, s14)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14802, 15365, 14787])).
% 87.54/87.77 tff(15367,plain,
% 87.54/87.77 (m_c_h_element_v_in1(c_e_h_2, c_h, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14852, 15365, 14787])).
% 87.54/87.77 tff(15368,plain,
% 87.54/87.77 (~node17(c_e_h_2, c_h, s13)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14861, 15367])).
% 87.54/87.77 tff(15369,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[14818, 15368, 15366])).
% 87.54/87.77 tff(15370,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s13) | m_c_h_element_v_in2(c_e_h_2, c_h, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)) | m_and_h_gate_v_out(c_e_h_2, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15371,plain,
% 87.54/87.77 (~m_and_h_gate_v_out(c_e_h_2, c_i, s15)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15370, 15349, 14787, 10378])).
% 87.54/87.77 tff(15372,plain,
% 87.54/87.77 (node20(c_e_h_2, c_i, s15)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15174, 15371, 15152])).
% 87.54/87.77 tff(15373,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15178, 37, 15372, 15359])).
% 87.54/87.77 tff(15374,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s13) | m_and_h_gate_v_out(c_e_h_2, c_i, s13) | m_or_h_gate_v_out(c_e_h_2, c_j, s12) | m_and_h_gate_v_out(c_e_h_2, c_l, s11) | node9(c_e_h_2, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15375,plain,
% 87.54/87.77 (~m_and_h_gate_v_out(c_e_h_2, c_i, s16)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15374, 15341, 4433, 12627, 14185, 15327, 10378])).
% 87.54/87.77 tff(15376,assumption,(node22(c_e_h_2, c_i, s16, s17)), introduced(assumption)).
% 87.54/87.77 tff(15377,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | (~node22(c_e_h_2, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | (~node22(c_e_h_2, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15378,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | (~node22(c_e_h_2, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15379,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | (~node22(c_e_h_2, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16)),
% 87.54/87.77 inference(modus_ponens,[status(thm)],[15378, 15377])).
% 87.54/87.77 tff(15380,plain,
% 87.54/87.77 ($false),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15379, 107, 15183, 15345, 15376])).
% 87.54/87.77 tff(15381,plain,((~node22(c_e_h_2, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.77 tff(15382,plain,
% 87.54/87.77 (~node22(c_e_h_2, c_i, s16, s17)),
% 87.54/87.77 inference(unit_resolution,[status(thm)],[15381, 15345, 15183])).
% 87.54/87.77 tff(15383,assumption,(~node20(c_e_h_2, c_i, s16)), introduced(assumption)).
% 87.54/87.77 tff(15384,assumption,(node21(c_e_h_2, c_i, s16, s17)), introduced(assumption)).
% 87.54/87.77 tff(15385,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | node20(c_e_h_2, c_i, s16) | (~node21(c_e_h_2, c_i, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | node20(c_e_h_2, c_i, s16) | (~node21(c_e_h_2, c_i, s16, s17)))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15386,plain,
% 87.54/87.77 ((node20(c_e_h_2, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | (~node21(c_e_h_2, c_i, s16, s17))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | node20(c_e_h_2, c_i, s16) | (~node21(c_e_h_2, c_i, s16, s17)))),
% 87.54/87.77 inference(rewrite,[status(thm)],[])).
% 87.54/87.77 tff(15387,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | (~node21(c_e_h_2, c_i, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | node20(c_e_h_2, c_i, s16) | (~node21(c_e_h_2, c_i, s16, s17))))),
% 87.54/87.77 inference(monotonicity,[status(thm)],[15386])).
% 87.54/87.77 tff(15388,plain,
% 87.54/87.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | (~node21(c_e_h_2, c_i, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | node20(c_e_h_2, c_i, s16) | (~node21(c_e_h_2, c_i, s16, s17)))),
% 87.54/87.77 inference(transitivity,[status(thm)],[15387, 15385])).
% 87.54/87.77 tff(15389,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | (~node21(c_e_h_2, c_i, s16, s17)))),
% 87.54/87.77 inference(quant_inst,[status(thm)],[])).
% 87.54/87.77 tff(15390,plain,
% 87.54/87.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | node20(c_e_h_2, c_i, s16) | (~node21(c_e_h_2, c_i, s16, s17))),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15389, 15388])).
% 87.54/87.78 tff(15391,plain,
% 87.54/87.78 ($false),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15390, 51, 15345, 15384, 15383])).
% 87.54/87.78 tff(15392,plain,((~node21(c_e_h_2, c_i, s16, s17)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | node20(c_e_h_2, c_i, s16)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.78 tff(15393,plain,
% 87.54/87.78 (~node21(c_e_h_2, c_i, s16, s17)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15392, 15345, 15383])).
% 87.54/87.78 tff(15394,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_2, c_i, s16, s17) | node22(c_e_h_2, c_i, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_2, c_i, s16, s17) | node22(c_e_h_2, c_i, s16, s17))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15395,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_2, c_i, s16, s17) | node22(c_e_h_2, c_i, s16, s17))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15396,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_2, c_i, s16, s17) | node22(c_e_h_2, c_i, s16, s17)),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15395, 15394])).
% 87.54/87.78 tff(15397,plain,
% 87.54/87.78 (node21(c_e_h_2, c_i, s16, s17) | node22(c_e_h_2, c_i, s16, s17)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15396, 81, 14096])).
% 87.54/87.78 tff(15398,plain,
% 87.54/87.78 ($false),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15397, 15393, 15382])).
% 87.54/87.78 tff(15399,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | node20(c_e_h_2, c_i, s16) | m_and_h_gate_v_out(c_e_h_2, c_i, s16)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.78 tff(15400,plain,
% 87.54/87.78 (node20(c_e_h_2, c_i, s16)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15399, 15375, 15345])).
% 87.54/87.78 tff(15401,plain,
% 87.54/87.78 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s16)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s16)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s16))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15402,plain,
% 87.54/87.78 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s16)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s16))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15403,plain,
% 87.54/87.78 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s16)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s16)),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15402, 15401])).
% 87.54/87.78 tff(15404,plain,
% 87.54/87.78 (m_and_h_gate_v_in1(c_e_h_2, c_i, s16)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15403, 37, 15400])).
% 87.54/87.78 tff(15405,plain,
% 87.54/87.78 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s16))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s16))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15406,plain,
% 87.54/87.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s16))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15407,plain,
% 87.54/87.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s16)),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15406, 15405])).
% 87.54/87.78 tff(15408,plain,
% 87.54/87.78 (m_c_h_element_v_out(c_e_h_2, c_h, s16)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15407, 23, 15404])).
% 87.54/87.78 tff(15409,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s16)), introduced(assumption)).
% 87.54/87.78 tff(15410,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s15)), introduced(assumption)).
% 87.54/87.78 tff(15411,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s15)), introduced(assumption)).
% 87.54/87.78 tff(15412,assumption,(node18(c_e_h_2, c_h, s15, s16)), introduced(assumption)).
% 87.54/87.78 tff(15413,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node18(c_e_h_2, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node18(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15414,plain,
% 87.54/87.78 (((~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~node18(c_e_h_2, c_h, s15, s16))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node18(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15415,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~node18(c_e_h_2, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node18(c_e_h_2, c_h, s15, s16))))),
% 87.54/87.78 inference(monotonicity,[status(thm)],[15414])).
% 87.54/87.78 tff(15416,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~node18(c_e_h_2, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node18(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(transitivity,[status(thm)],[15415, 15413])).
% 87.54/87.78 tff(15417,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~node18(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15418,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node18(c_e_h_2, c_h, s15, s16))),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15417, 15416])).
% 87.54/87.78 tff(15419,plain,
% 87.54/87.78 ($false),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15418, 124, 15410, 15409, 15412])).
% 87.54/87.78 tff(15420,plain,((~node18(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.78 tff(15421,plain,
% 87.54/87.78 (~node18(c_e_h_2, c_h, s15, s16)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15420, 15410, 15409])).
% 87.54/87.78 tff(15422,assumption,(~node19(c_e_h_2, c_h, s15, s16)), introduced(assumption)).
% 87.54/87.78 tff(15423,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_2, c_h, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_2, c_h, s15, s16))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15424,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_2, c_h, s15, s16))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15425,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_2, c_h, s15, s16)),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15424, 15423])).
% 87.54/87.78 tff(15426,plain,
% 87.54/87.78 ($false),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15425, 141, 12879, 15422])).
% 87.54/87.78 tff(15427,plain,(node19(c_e_h_2, c_h, s15, s16)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.78 tff(15428,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s15) | node18(c_e_h_2, c_h, s15, s16) | (~node19(c_e_h_2, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s15) | node18(c_e_h_2, c_h, s15, s16) | (~node19(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15429,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s15) | node18(c_e_h_2, c_h, s15, s16) | (~node19(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15430,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s15) | node18(c_e_h_2, c_h, s15, s16) | (~node19(c_e_h_2, c_h, s15, s16))),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15429, 15428])).
% 87.54/87.78 tff(15431,plain,
% 87.54/87.78 (node17(c_e_h_2, c_h, s15) | node18(c_e_h_2, c_h, s15, s16)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15430, 156, 15427])).
% 87.54/87.78 tff(15432,plain,
% 87.54/87.78 (node17(c_e_h_2, c_h, s15)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15431, 15421])).
% 87.54/87.78 tff(15433,plain,
% 87.54/87.78 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15434,plain,
% 87.54/87.78 ((m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)) | (~node17(c_e_h_2, c_h, s15))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15435,plain,
% 87.54/87.78 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)) | (~node17(c_e_h_2, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15))))),
% 87.54/87.78 inference(monotonicity,[status(thm)],[15434])).
% 87.54/87.78 tff(15436,plain,
% 87.54/87.78 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)) | (~node17(c_e_h_2, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)))),
% 87.54/87.78 inference(transitivity,[status(thm)],[15435, 15433])).
% 87.54/87.78 tff(15437,plain,
% 87.54/87.78 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)) | (~node17(c_e_h_2, c_h, s15)))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15438,plain,
% 87.54/87.78 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15))),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15437, 15436])).
% 87.54/87.78 tff(15439,plain,
% 87.54/87.78 ((~node17(c_e_h_2, c_h, s15)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15))),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15438, 245, 15411])).
% 87.54/87.78 tff(15440,plain,
% 87.54/87.78 (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15439, 15432])).
% 87.54/87.78 tff(15441,assumption,(~node15(c_e_h_2, c_h, s15, s16)), introduced(assumption)).
% 87.54/87.78 tff(15442,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node14(c_e_h_2, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node14(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15443,plain,
% 87.54/87.78 (((~node14(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node14(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15444,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node14(c_e_h_2, c_h, s15, s16))))),
% 87.54/87.78 inference(monotonicity,[status(thm)],[15443])).
% 87.54/87.78 tff(15445,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node14(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(transitivity,[status(thm)],[15444, 15442])).
% 87.54/87.78 tff(15446,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15447,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node14(c_e_h_2, c_h, s15, s16))),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15446, 15445])).
% 87.54/87.78 tff(15448,plain,
% 87.54/87.78 (m_c_h_element_v_in1(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node14(c_e_h_2, c_h, s15, s16))),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15447, 283])).
% 87.54/87.78 tff(15449,plain,
% 87.54/87.78 (~node14(c_e_h_2, c_h, s15, s16)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15448, 15411, 15409])).
% 87.54/87.78 tff(15450,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s15)), introduced(assumption)).
% 87.54/87.78 tff(15451,plain,
% 87.54/87.78 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | m_c_h_element_v_in2(c_e_h_2, c_h, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | m_c_h_element_v_in2(c_e_h_2, c_h, s15))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15452,plain,
% 87.54/87.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | m_c_h_element_v_in2(c_e_h_2, c_h, s15))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15453,plain,
% 87.54/87.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15) | m_c_h_element_v_in2(c_e_h_2, c_h, s15)),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15452, 15451])).
% 87.54/87.78 tff(15454,plain,
% 87.54/87.78 ((~node16(c_e_h_2, c_h, s15)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15453, 228, 15450])).
% 87.54/87.78 tff(15455,plain,
% 87.54/87.78 (~node16(c_e_h_2, c_h, s15)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15454, 15411])).
% 87.54/87.78 tff(15456,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s15) | node14(c_e_h_2, c_h, s15, s16) | node15(c_e_h_2, c_h, s15, s16) | (~node19(c_e_h_2, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s15) | node14(c_e_h_2, c_h, s15, s16) | node15(c_e_h_2, c_h, s15, s16) | (~node19(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15457,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s15) | node14(c_e_h_2, c_h, s15, s16) | node15(c_e_h_2, c_h, s15, s16) | (~node19(c_e_h_2, c_h, s15, s16)))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15458,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s15) | node14(c_e_h_2, c_h, s15, s16) | node15(c_e_h_2, c_h, s15, s16) | (~node19(c_e_h_2, c_h, s15, s16))),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15457, 15456])).
% 87.54/87.78 tff(15459,plain,
% 87.54/87.78 (node16(c_e_h_2, c_h, s15) | node14(c_e_h_2, c_h, s15, s16) | node15(c_e_h_2, c_h, s15, s16)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15458, 189, 15427])).
% 87.54/87.78 tff(15460,plain,
% 87.54/87.78 ($false),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15459, 15455, 15449, 15441])).
% 87.54/87.78 tff(15461,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s15) | node15(c_e_h_2, c_h, s15, s16) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.78 tff(15462,plain,
% 87.54/87.78 (node15(c_e_h_2, c_h, s15, s16)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15461, 15440, 15409, 15411])).
% 87.54/87.78 tff(15463,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node15(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node15(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15464,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node15(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15465,plain,
% 87.54/87.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | (~node15(c_e_h_2, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_2, c_h, s15)),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15464, 15463])).
% 87.54/87.78 tff(15466,plain,
% 87.54/87.78 ($false),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15465, 173, 15410, 15409, 15462])).
% 87.54/87.78 tff(15467,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16)) | m_c_h_element_v_in1(c_e_h_2, c_h, s15)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.78 tff(15468,plain,
% 87.54/87.78 (m_c_h_element_v_in1(c_e_h_2, c_h, s15)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15467, 15410, 15409])).
% 87.54/87.78 tff(15469,plain,
% 87.54/87.78 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s15)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15470,plain,
% 87.54/87.78 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15))) <=> ((~node17(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s15)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15471,plain,
% 87.54/87.78 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s15))))),
% 87.54/87.78 inference(monotonicity,[status(thm)],[15470])).
% 87.54/87.78 tff(15472,plain,
% 87.54/87.78 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s15)))),
% 87.54/87.78 inference(transitivity,[status(thm)],[15471, 15469])).
% 87.54/87.78 tff(15473,plain,
% 87.54/87.78 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~node17(c_e_h_2, c_h, s15)))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15474,plain,
% 87.54/87.78 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s15)) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s15))),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15473, 15472])).
% 87.54/87.78 tff(15475,plain,
% 87.54/87.78 ((~node17(c_e_h_2, c_h, s15)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s15))),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15474, 209, 15450])).
% 87.54/87.78 tff(15476,plain,
% 87.54/87.78 ($false),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15475, 15432, 15468])).
% 87.54/87.78 tff(15477,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s15) | m_c_h_element_v_in2(c_e_h_2, c_h, s15) | (~m_c_h_element_v_out(c_e_h_2, c_h, s16))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.78 tff(15478,plain,
% 87.54/87.78 (m_c_h_element_v_in2(c_e_h_2, c_h, s15)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15477, 15408, 15344])).
% 87.54/87.78 tff(15479,plain,
% 87.54/87.78 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s15))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s15))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15480,plain,
% 87.54/87.78 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s15))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15481,plain,
% 87.54/87.78 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s15)),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15480, 15479])).
% 87.54/87.78 tff(15482,plain,
% 87.54/87.78 (m_or_h_gate_v_out(c_e_h_2, c_j, s15)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15481, 309, 15478])).
% 87.54/87.78 tff(15483,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s14)), introduced(assumption)).
% 87.54/87.78 tff(15484,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s14)), introduced(assumption)).
% 87.54/87.78 tff(15485,plain,
% 87.54/87.78 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15486,plain,
% 87.54/87.78 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 87.54/87.78 inference(quant_inst,[status(thm)],[])).
% 87.54/87.78 tff(15487,plain,
% 87.54/87.78 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 87.54/87.78 inference(modus_ponens,[status(thm)],[15486, 15485])).
% 87.54/87.78 tff(15488,plain,
% 87.54/87.78 (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 87.54/87.78 inference(unit_resolution,[status(thm)],[15487, 2218, 13680])).
% 87.54/87.78 tff(15489,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s13)), introduced(assumption)).
% 87.54/87.78 tff(15490,assumption,(node18(c_e_h_1, c_f, s12, s13)), introduced(assumption)).
% 87.54/87.78 tff(15491,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15492,plain,
% 87.54/87.78 (((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))),
% 87.54/87.78 inference(rewrite,[status(thm)],[])).
% 87.54/87.78 tff(15493,plain,
% 87.54/87.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13))))),
% 87.54/87.79 inference(monotonicity,[status(thm)],[15492])).
% 87.54/87.79 tff(15494,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))),
% 87.54/87.79 inference(transitivity,[status(thm)],[15493, 15491])).
% 87.54/87.79 tff(15495,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15496,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15495, 15494])).
% 87.54/87.79 tff(15497,plain,
% 87.54/87.79 ($false),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15496, 124, 14996, 15490, 15489])).
% 87.54/87.79 tff(15498,plain,((~node18(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.79 tff(15499,plain,
% 87.54/87.79 (~node18(c_e_h_1, c_f, s12, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15498, 14996, 15489])).
% 87.54/87.79 tff(15500,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_f, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_f, s12, s13))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15501,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_f, s12, s13))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15502,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_f, s12, s13)),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15501, 15500])).
% 87.54/87.79 tff(15503,plain,
% 87.54/87.79 (node19(c_e_h_1, c_f, s12, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15502, 141, 9599])).
% 87.54/87.79 tff(15504,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s12, s13)) | node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s12, s13)) | node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15505,plain,
% 87.54/87.79 ((node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13))) <=> ((~node19(c_e_h_1, c_f, s12, s13)) | node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15506,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s12, s13)) | node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13)))),
% 87.54/87.79 inference(monotonicity,[status(thm)],[15505])).
% 87.54/87.79 tff(15507,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s12, s13)) | node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13))),
% 87.54/87.79 inference(transitivity,[status(thm)],[15506, 15504])).
% 87.54/87.79 tff(15508,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15509,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s12, s13)) | node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13)),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15508, 15507])).
% 87.54/87.79 tff(15510,plain,
% 87.54/87.79 (node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15509, 156, 15503])).
% 87.54/87.79 tff(15511,plain,
% 87.54/87.79 (node17(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15510, 15499])).
% 87.54/87.79 tff(15512,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s12)), introduced(assumption)).
% 87.54/87.79 tff(15513,plain,
% 87.54/87.79 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15514,plain,
% 87.54/87.79 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15515,plain,
% 87.54/87.79 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12))))),
% 87.54/87.79 inference(monotonicity,[status(thm)],[15514])).
% 87.54/87.79 tff(15516,plain,
% 87.54/87.79 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(transitivity,[status(thm)],[15515, 15513])).
% 87.54/87.79 tff(15517,plain,
% 87.54/87.79 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15518,plain,
% 87.54/87.79 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15517, 15516])).
% 87.54/87.79 tff(15519,plain,
% 87.54/87.79 ((~node17(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15518, 209, 15512])).
% 87.54/87.79 tff(15520,plain,
% 87.54/87.79 (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15519, 15511])).
% 87.54/87.79 tff(15521,assumption,(~node14(c_e_h_1, c_f, s12, s13)), introduced(assumption)).
% 87.54/87.79 tff(15522,plain,
% 87.54/87.79 (~node18(c_e_h_1, c_f, s12, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15498, 15489, 14996])).
% 87.54/87.79 tff(15523,plain,
% 87.54/87.79 (node17(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15510, 15522])).
% 87.54/87.79 tff(15524,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s12)), introduced(assumption)).
% 87.54/87.79 tff(15525,plain,
% 87.54/87.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15526,plain,
% 87.54/87.79 ((m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12))) <=> ((~node17(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15527,plain,
% 87.54/87.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12))))),
% 87.54/87.79 inference(monotonicity,[status(thm)],[15526])).
% 87.54/87.79 tff(15528,plain,
% 87.54/87.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(transitivity,[status(thm)],[15527, 15525])).
% 87.54/87.79 tff(15529,plain,
% 87.54/87.79 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15530,plain,
% 87.54/87.79 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15529, 15528])).
% 87.54/87.79 tff(15531,plain,
% 87.54/87.79 ((~node17(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15530, 245, 15524])).
% 87.54/87.79 tff(15532,plain,
% 87.54/87.79 (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15531, 15523])).
% 87.54/87.79 tff(15533,plain,
% 87.54/87.79 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15534,plain,
% 87.54/87.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15535,plain,
% 87.54/87.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15534, 15533])).
% 87.54/87.79 tff(15536,plain,
% 87.54/87.79 ((~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15535, 228, 15524])).
% 87.54/87.79 tff(15537,plain,
% 87.54/87.79 (~node16(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15536, 15532])).
% 87.54/87.79 tff(15538,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s12, s13)) | node15(c_e_h_1, c_f, s12, s13) | node14(c_e_h_1, c_f, s12, s13) | node16(c_e_h_1, c_f, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s12, s13)) | node15(c_e_h_1, c_f, s12, s13) | node14(c_e_h_1, c_f, s12, s13) | node16(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15539,plain,
% 87.54/87.79 ((node16(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13))) <=> ((~node19(c_e_h_1, c_f, s12, s13)) | node15(c_e_h_1, c_f, s12, s13) | node14(c_e_h_1, c_f, s12, s13) | node16(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15540,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s12, s13)) | node15(c_e_h_1, c_f, s12, s13) | node14(c_e_h_1, c_f, s12, s13) | node16(c_e_h_1, c_f, s12)))),
% 87.54/87.79 inference(monotonicity,[status(thm)],[15539])).
% 87.54/87.79 tff(15541,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s12, s13)) | node15(c_e_h_1, c_f, s12, s13) | node14(c_e_h_1, c_f, s12, s13) | node16(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(transitivity,[status(thm)],[15540, 15538])).
% 87.54/87.79 tff(15542,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15543,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s12, s13)) | node15(c_e_h_1, c_f, s12, s13) | node14(c_e_h_1, c_f, s12, s13) | node16(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15542, 15541])).
% 87.54/87.79 tff(15544,plain,
% 87.54/87.79 (node15(c_e_h_1, c_f, s12, s13) | node14(c_e_h_1, c_f, s12, s13) | node16(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15543, 189, 15503])).
% 87.54/87.79 tff(15545,plain,
% 87.54/87.79 (node15(c_e_h_1, c_f, s12, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15544, 15537, 15521])).
% 87.54/87.79 tff(15546,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15547,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15548,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12)),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15547, 15546])).
% 87.54/87.79 tff(15549,plain,
% 87.54/87.79 ($false),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15548, 173, 14996, 15545, 15489])).
% 87.54/87.79 tff(15550,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | m_c_h_element_v_in1(c_e_h_1, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.79 tff(15551,plain,
% 87.54/87.79 (node14(c_e_h_1, c_f, s12, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15550, 15520, 15489, 14996])).
% 87.54/87.79 tff(15552,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node14(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node14(c_e_h_1, c_f, s12, s13)))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15553,plain,
% 87.54/87.79 (((~node14(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node14(c_e_h_1, c_f, s12, s13)))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15554,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node14(c_e_h_1, c_f, s12, s13))))),
% 87.54/87.79 inference(monotonicity,[status(thm)],[15553])).
% 87.54/87.79 tff(15555,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node14(c_e_h_1, c_f, s12, s13)))),
% 87.54/87.79 inference(transitivity,[status(thm)],[15554, 15552])).
% 87.54/87.79 tff(15556,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15557,plain,
% 87.54/87.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node14(c_e_h_1, c_f, s12, s13))),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15556, 15555])).
% 87.54/87.79 tff(15558,plain,
% 87.54/87.79 ($false),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15557, 283, 15551, 15489, 15520])).
% 87.54/87.79 tff(15559,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.79 tff(15560,plain,
% 87.54/87.79 (m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15559, 15488])).
% 87.54/87.79 tff(15561,plain,
% 87.54/87.79 (~m_c_h_element_v_out(c_e_h_1, c_f, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15560, 14994])).
% 87.54/87.79 tff(15562,plain,
% 87.54/87.79 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15563,plain,
% 87.54/87.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15564,plain,
% 87.54/87.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13)),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15563, 15562])).
% 87.54/87.79 tff(15565,plain,
% 87.54/87.79 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15564, 1666, 15561])).
% 87.54/87.79 tff(15566,plain,
% 87.54/87.79 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15567,plain,
% 87.54/87.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13))),
% 87.54/87.79 inference(quant_inst,[status(thm)],[])).
% 87.54/87.79 tff(15568,plain,
% 87.54/87.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13)),
% 87.54/87.79 inference(modus_ponens,[status(thm)],[15567, 15566])).
% 87.54/87.79 tff(15569,plain,
% 87.54/87.79 (~node20(c_e_h_1, c_q, s13)),
% 87.54/87.79 inference(unit_resolution,[status(thm)],[15568, 37, 15565])).
% 87.54/87.79 tff(15570,assumption,(node21(c_e_h_1, c_q, s13, s14)), introduced(assumption)).
% 87.54/87.79 tff(15571,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14)))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15572,plain,
% 87.54/87.79 ((node20(c_e_h_1, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node21(c_e_h_1, c_q, s13, s14))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14)))),
% 87.54/87.79 inference(rewrite,[status(thm)],[])).
% 87.54/87.79 tff(15573,plain,
% 87.54/87.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node21(c_e_h_1, c_q, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14))))),
% 87.54/87.80 inference(monotonicity,[status(thm)],[15572])).
% 87.54/87.80 tff(15574,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node21(c_e_h_1, c_q, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14)))),
% 87.54/87.80 inference(transitivity,[status(thm)],[15573, 15571])).
% 87.54/87.80 tff(15575,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node21(c_e_h_1, c_q, s13, s14)))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15576,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14))),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15575, 15574])).
% 87.54/87.80 tff(15577,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15576, 51, 15484, 15570, 15569])).
% 87.54/87.80 tff(15578,plain,((~node21(c_e_h_1, c_q, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15579,plain,
% 87.54/87.80 (~node21(c_e_h_1, c_q, s13, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15578, 15484])).
% 87.54/87.80 tff(15580,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15581,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15582,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15581, 15580])).
% 87.54/87.80 tff(15583,plain,
% 87.54/87.80 (node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15582, 81, 10040])).
% 87.54/87.80 tff(15584,plain,
% 87.54/87.80 (node22(c_e_h_1, c_q, s13, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15583, 15579])).
% 87.54/87.80 tff(15585,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node22(c_e_h_1, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node22(c_e_h_1, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15586,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node22(c_e_h_1, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15587,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node22(c_e_h_1, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15586, 15585])).
% 87.54/87.80 tff(15588,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15587, 107, 15484, 15033, 15584])).
% 87.54/87.80 tff(15589,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15590,plain,
% 87.54/87.80 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s14))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s14))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15591,plain,
% 87.54/87.80 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s14))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15592,plain,
% 87.54/87.80 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s14)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15591, 15590])).
% 87.54/87.80 tff(15593,plain,
% 87.54/87.80 (node3(c_e_h_1, c_e_h_2, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15592, 817, 814])).
% 87.54/87.80 tff(15594,plain,
% 87.54/87.80 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s14)) | (~node3(c_e_h_1, c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s14)) | (~node3(c_e_h_1, c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15595,plain,
% 87.54/87.80 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s14)) | (~node3(c_e_h_1, c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15596,plain,
% 87.54/87.80 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s14)) | (~node3(c_e_h_1, c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15595, 15594])).
% 87.54/87.80 tff(15597,plain,
% 87.54/87.80 ((~m_cell_v_ack(c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15596, 836, 15593])).
% 87.54/87.80 tff(15598,plain,
% 87.54/87.80 (~m_cell_v_ack(c_e_h_2, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15597, 15589])).
% 87.54/87.80 tff(15599,plain,
% 87.54/87.80 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)) | m_cell_v_ack(c_e_h_2, s14))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)) | m_cell_v_ack(c_e_h_2, s14))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15600,plain,
% 87.54/87.80 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)) | m_cell_v_ack(c_e_h_2, s14))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15601,plain,
% 87.54/87.80 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)) | m_cell_v_ack(c_e_h_2, s14)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15600, 15599])).
% 87.54/87.80 tff(15602,plain,
% 87.54/87.80 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15601, 848, 15598])).
% 87.54/87.80 tff(15603,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s15)), introduced(assumption)).
% 87.54/87.80 tff(15604,assumption,(node6(c_e_h_2, c_j, s14, s15)), introduced(assumption)).
% 87.54/87.80 tff(15605,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | (~node6(c_e_h_2, c_j, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | (~node6(c_e_h_2, c_j, s14, s15)))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15606,plain,
% 87.54/87.80 (((~node6(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | (~node6(c_e_h_2, c_j, s14, s15)))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15607,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | (~node6(c_e_h_2, c_j, s14, s15))))),
% 87.54/87.80 inference(monotonicity,[status(thm)],[15606])).
% 87.54/87.80 tff(15608,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | (~node6(c_e_h_2, c_j, s14, s15)))),
% 87.54/87.80 inference(transitivity,[status(thm)],[15607, 15605])).
% 87.54/87.80 tff(15609,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15610,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | (~node6(c_e_h_2, c_j, s14, s15))),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15609, 15608])).
% 87.54/87.80 tff(15611,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15610, 899, 15603, 15081, 15604])).
% 87.54/87.80 tff(15612,plain,((~node6(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_out(c_e_h_2, c_j, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15613,plain,
% 87.54/87.80 (~node6(c_e_h_2, c_j, s14, s15)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15612, 15603, 15081])).
% 87.54/87.80 tff(15614,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s14, s15)) | node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s14, s15)) | node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15615,plain,
% 87.54/87.80 ((node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15) | (~trans(s14, s15))) <=> ((~trans(s14, s15)) | node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15616,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15) | (~trans(s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s14, s15)) | node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15)))),
% 87.54/87.80 inference(monotonicity,[status(thm)],[15615])).
% 87.54/87.80 tff(15617,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15) | (~trans(s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s14, s15)) | node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15))),
% 87.54/87.80 inference(transitivity,[status(thm)],[15616, 15614])).
% 87.54/87.80 tff(15618,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15) | (~trans(s14, s15)))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15619,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s14, s15)) | node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15618, 15617])).
% 87.54/87.80 tff(15620,plain,
% 87.54/87.80 (node6(c_e_h_2, c_j, s14, s15) | node5(c_e_h_2, c_j, s14, s15)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15619, 881, 10504])).
% 87.54/87.80 tff(15621,plain,
% 87.54/87.80 (node5(c_e_h_2, c_j, s14, s15)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15620, 15613])).
% 87.54/87.80 tff(15622,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15)))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15623,plain,
% 87.54/87.80 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15)))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15624,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15))))),
% 87.54/87.80 inference(monotonicity,[status(thm)],[15623])).
% 87.54/87.80 tff(15625,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15)))),
% 87.54/87.80 inference(transitivity,[status(thm)],[15624, 15622])).
% 87.54/87.80 tff(15626,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15627,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | (~node5(c_e_h_2, c_j, s14, s15))),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15626, 15625])).
% 87.54/87.80 tff(15628,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15627, 862, 15603, 15621, 15602, 15483])).
% 87.54/87.80 tff(15629,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s14) | m_or_h_gate_v_out(c_e_h_2, c_j, s14)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15630,plain,
% 87.54/87.80 (m_or_h_gate_v_in1(c_e_h_2, c_j, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15629, 15482, 15338])).
% 87.54/87.80 tff(15631,assumption,(~node20(c_e_h_2, c_l, s13)), introduced(assumption)).
% 87.54/87.80 tff(15632,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s14)), introduced(assumption)).
% 87.54/87.80 tff(15633,assumption,(node22(c_e_h_2, c_l, s13, s14)), introduced(assumption)).
% 87.54/87.80 tff(15634,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | (~node22(c_e_h_2, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | (~node22(c_e_h_2, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15635,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | (~node22(c_e_h_2, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15636,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | (~node22(c_e_h_2, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15635, 15634])).
% 87.54/87.80 tff(15637,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15636, 107, 14238, 15632, 15633])).
% 87.54/87.80 tff(15638,plain,((~node22(c_e_h_2, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s14))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15639,plain,
% 87.54/87.80 (~node22(c_e_h_2, c_l, s13, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15638, 15632, 14238])).
% 87.54/87.80 tff(15640,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_2, c_l, s13, s14) | node22(c_e_h_2, c_l, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_2, c_l, s13, s14) | node22(c_e_h_2, c_l, s13, s14))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15641,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_2, c_l, s13, s14) | node22(c_e_h_2, c_l, s13, s14))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15642,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_2, c_l, s13, s14) | node22(c_e_h_2, c_l, s13, s14)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15641, 15640])).
% 87.54/87.80 tff(15643,plain,
% 87.54/87.80 (node21(c_e_h_2, c_l, s13, s14) | node22(c_e_h_2, c_l, s13, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15642, 81, 10040])).
% 87.54/87.80 tff(15644,plain,
% 87.54/87.80 (node21(c_e_h_2, c_l, s13, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15643, 15639])).
% 87.54/87.80 tff(15645,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | (~node21(c_e_h_2, c_l, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | (~node21(c_e_h_2, c_l, s13, s14)))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15646,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | (~node21(c_e_h_2, c_l, s13, s14)))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15647,plain,
% 87.54/87.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | (~node21(c_e_h_2, c_l, s13, s14))),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15646, 15645])).
% 87.54/87.80 tff(15648,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15647, 51, 15632, 15631, 15644])).
% 87.54/87.80 tff(15649,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s14)) | node20(c_e_h_2, c_l, s13) | m_and_h_gate_v_out(c_e_h_2, c_l, s13)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15650,plain,
% 87.54/87.80 (~m_and_h_gate_v_out(c_e_h_2, c_l, s14)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15649, 15336, 15631])).
% 87.54/87.80 tff(15651,plain,
% 87.54/87.80 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s14))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s14))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15652,plain,
% 87.54/87.80 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s14))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15653,plain,
% 87.54/87.80 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s14)) | m_and_h_gate_v_out(c_e_h_2, c_l, s14)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15652, 15651])).
% 87.54/87.80 tff(15654,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15653, 801, 15650, 15630])).
% 87.54/87.80 tff(15655,plain,(m_and_h_gate_v_out(c_e_h_2, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11) | node9(c_e_h_2, c_m, s11) | m_and_h_gate_v_out(c_e_h_2, c_i, s13) | m_c_h_element_v_out(c_e_h_2, c_h, s12) | node20(c_e_h_2, c_l, s13) | m_or_h_gate_v_out(c_e_h_2, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15656,plain,
% 87.54/87.80 (~m_and_h_gate_v_out(c_e_h_2, c_i, s17)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15655, 15325, 10345, 4431, 14184, 10376, 12788, 10260])).
% 87.54/87.80 tff(15657,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s17)), introduced(assumption)).
% 87.54/87.80 tff(15658,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s17)), introduced(assumption)).
% 87.54/87.80 tff(15659,plain,
% 87.54/87.80 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s17))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s17))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15660,plain,
% 87.54/87.80 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s17))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15661,plain,
% 87.54/87.80 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s17)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15660, 15659])).
% 87.54/87.80 tff(15662,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15661, 365, 15658, 15657])).
% 87.54/87.80 tff(15663,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | m_and_h_gate_v_out(c_e_h_2, c_i, s17)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15664,plain,
% 87.54/87.80 (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15663, 15656])).
% 87.54/87.80 tff(15665,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s17)), introduced(assumption)).
% 87.54/87.80 tff(15666,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s19)), introduced(assumption)).
% 87.54/87.80 tff(15667,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s17)), introduced(assumption)).
% 87.54/87.80 tff(15668,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_r, s17)), introduced(assumption)).
% 87.54/87.80 tff(15669,plain,
% 87.54/87.80 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s17))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s17))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15670,plain,
% 87.54/87.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s17))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15671,plain,
% 87.54/87.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s17)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15670, 15669])).
% 87.54/87.80 tff(15672,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15671, 1884, 15665, 15668])).
% 87.54/87.80 tff(15673,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_r, s17)) | m_c_h_element_v_out(c_e_h_2, c_e, s17)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15674,plain,
% 87.54/87.80 (~m_and_h_gate_v_in1(c_e_h_2, c_r, s17)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15673, 15665])).
% 87.54/87.80 tff(15675,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_r, s17)), introduced(assumption)).
% 87.54/87.80 tff(15676,assumption,(node20(c_e_h_2, c_r, s17)), introduced(assumption)).
% 87.54/87.80 tff(15677,plain,
% 87.54/87.80 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s17))),
% 87.54/87.80 inference(rewrite,[status(thm)],[])).
% 87.54/87.80 tff(15678,plain,
% 87.54/87.80 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s17))),
% 87.54/87.80 inference(quant_inst,[status(thm)],[])).
% 87.54/87.80 tff(15679,plain,
% 87.54/87.80 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s17)),
% 87.54/87.80 inference(modus_ponens,[status(thm)],[15678, 15677])).
% 87.54/87.80 tff(15680,plain,
% 87.54/87.80 ($false),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15679, 37, 15676, 15675])).
% 87.54/87.80 tff(15681,plain,((~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.80 tff(15682,plain,
% 87.54/87.80 (~node20(c_e_h_2, c_r, s17)),
% 87.54/87.80 inference(unit_resolution,[status(thm)],[15681, 15674])).
% 87.54/87.80 tff(15683,assumption,(m_and_h_gate_v_out(c_e_h_2, c_r, s18)), introduced(assumption)).
% 87.54/87.80 tff(15684,assumption,(~node20(c_e_h_2, c_r, s17)), introduced(assumption)).
% 87.54/87.80 tff(15685,assumption,(node21(c_e_h_2, c_r, s17, s18)), introduced(assumption)).
% 87.54/87.80 tff(15686,plain,
% 87.54/87.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_2, c_r, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | node20(c_e_h_2, c_r, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_2, c_r, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | node20(c_e_h_2, c_r, s17))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15687,plain,
% 87.54/87.81 ((node20(c_e_h_2, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | (~node21(c_e_h_2, c_r, s17, s18))) <=> ((~node21(c_e_h_2, c_r, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | node20(c_e_h_2, c_r, s17))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15688,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | (~node21(c_e_h_2, c_r, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_2, c_r, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | node20(c_e_h_2, c_r, s17)))),
% 87.54/87.81 inference(monotonicity,[status(thm)],[15687])).
% 87.54/87.81 tff(15689,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | (~node21(c_e_h_2, c_r, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_2, c_r, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | node20(c_e_h_2, c_r, s17))),
% 87.54/87.81 inference(transitivity,[status(thm)],[15688, 15686])).
% 87.54/87.81 tff(15690,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | (~node21(c_e_h_2, c_r, s17, s18)))),
% 87.54/87.81 inference(quant_inst,[status(thm)],[])).
% 87.54/87.81 tff(15691,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_2, c_r, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | node20(c_e_h_2, c_r, s17)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15690, 15689])).
% 87.54/87.81 tff(15692,plain,
% 87.54/87.81 ($false),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15691, 51, 15685, 15684, 15683])).
% 87.54/87.81 tff(15693,plain,((~node21(c_e_h_2, c_r, s17, s18)) | node20(c_e_h_2, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.81 tff(15694,plain,
% 87.54/87.81 (~node21(c_e_h_2, c_r, s17, s18)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15693, 15683, 15684])).
% 87.54/87.81 tff(15695,plain,
% 87.54/87.81 (succ(s17, s18) <=> succ(s17, s18)),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15696,axiom,(succ(s17, s18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound18')).
% 87.54/87.81 tff(15697,plain,
% 87.54/87.81 (succ(s17, s18)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15696, 15695])).
% 87.54/87.81 tff(15698,plain,
% 87.54/87.81 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15699,plain,
% 87.54/87.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 87.54/87.81 inference(quant_inst,[status(thm)],[])).
% 87.54/87.81 tff(15700,plain,
% 87.54/87.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15699, 15698])).
% 87.54/87.81 tff(15701,plain,
% 87.54/87.81 (trans(s17, s18)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15700, 15697, 64])).
% 87.54/87.81 tff(15702,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_2, c_r, s17, s18) | node22(c_e_h_2, c_r, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_2, c_r, s17, s18) | node22(c_e_h_2, c_r, s17, s18))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15703,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_2, c_r, s17, s18) | node22(c_e_h_2, c_r, s17, s18))),
% 87.54/87.81 inference(quant_inst,[status(thm)],[])).
% 87.54/87.81 tff(15704,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_2, c_r, s17, s18) | node22(c_e_h_2, c_r, s17, s18)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15703, 15702])).
% 87.54/87.81 tff(15705,plain,
% 87.54/87.81 (node21(c_e_h_2, c_r, s17, s18) | node22(c_e_h_2, c_r, s17, s18)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15704, 81, 15701])).
% 87.54/87.81 tff(15706,plain,
% 87.54/87.81 (node22(c_e_h_2, c_r, s17, s18)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15705, 15694])).
% 87.54/87.81 tff(15707,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | (~node22(c_e_h_2, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | (~node22(c_e_h_2, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15708,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | (~node22(c_e_h_2, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17))),
% 87.54/87.81 inference(quant_inst,[status(thm)],[])).
% 87.54/87.81 tff(15709,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | (~node22(c_e_h_2, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15708, 15707])).
% 87.54/87.81 tff(15710,plain,
% 87.54/87.81 ($false),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15709, 107, 15706, 15683, 15667])).
% 87.54/87.81 tff(15711,plain,((~m_and_h_gate_v_out(c_e_h_2, c_r, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17) | node20(c_e_h_2, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 87.54/87.81 tff(15712,plain,
% 87.54/87.81 (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15711, 15682, 15667])).
% 87.54/87.81 tff(15713,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s18)), introduced(assumption)).
% 87.54/87.81 tff(15714,assumption,(node22(c_e_h_2, c_r, s18, s19)), introduced(assumption)).
% 87.54/87.81 tff(15715,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | (~node22(c_e_h_2, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | (~node22(c_e_h_2, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15716,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | (~node22(c_e_h_2, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18))),
% 87.54/87.81 inference(quant_inst,[status(thm)],[])).
% 87.54/87.81 tff(15717,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | (~node22(c_e_h_2, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15716, 15715])).
% 87.54/87.81 tff(15718,plain,
% 87.54/87.81 ($false),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15717, 107, 15714, 15713, 15666])).
% 87.54/87.81 tff(15719,plain,((~node22(c_e_h_2, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19))), inference(lemma,lemma(discharge,[]))).
% 87.54/87.81 tff(15720,plain,
% 87.54/87.81 (~node22(c_e_h_2, c_r, s18, s19)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15719, 15712, 15666])).
% 87.54/87.81 tff(15721,plain,
% 87.54/87.81 (succ(s18, s19) <=> succ(s18, s19)),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15722,axiom,(succ(s18, s19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound19')).
% 87.54/87.81 tff(15723,plain,
% 87.54/87.81 (succ(s18, s19)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15722, 15721])).
% 87.54/87.81 tff(15724,plain,
% 87.54/87.81 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15725,plain,
% 87.54/87.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 87.54/87.81 inference(quant_inst,[status(thm)],[])).
% 87.54/87.81 tff(15726,plain,
% 87.54/87.81 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15725, 15724])).
% 87.54/87.81 tff(15727,plain,
% 87.54/87.81 (trans(s18, s19)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15726, 15723, 64])).
% 87.54/87.81 tff(15728,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_2, c_r, s18, s19) | node22(c_e_h_2, c_r, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_2, c_r, s18, s19) | node22(c_e_h_2, c_r, s18, s19))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15729,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_2, c_r, s18, s19) | node22(c_e_h_2, c_r, s18, s19))),
% 87.54/87.81 inference(quant_inst,[status(thm)],[])).
% 87.54/87.81 tff(15730,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_2, c_r, s18, s19) | node22(c_e_h_2, c_r, s18, s19)),
% 87.54/87.81 inference(modus_ponens,[status(thm)],[15729, 15728])).
% 87.54/87.81 tff(15731,plain,
% 87.54/87.81 (node21(c_e_h_2, c_r, s18, s19) | node22(c_e_h_2, c_r, s18, s19)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15730, 81, 15727])).
% 87.54/87.81 tff(15732,plain,
% 87.54/87.81 (node21(c_e_h_2, c_r, s18, s19)),
% 87.54/87.81 inference(unit_resolution,[status(thm)],[15731, 15720])).
% 87.54/87.81 tff(15733,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | node20(c_e_h_2, c_r, s18) | (~node21(c_e_h_2, c_r, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | node20(c_e_h_2, c_r, s18) | (~node21(c_e_h_2, c_r, s18, s19)))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15734,plain,
% 87.54/87.81 ((node20(c_e_h_2, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | (~node21(c_e_h_2, c_r, s18, s19))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | node20(c_e_h_2, c_r, s18) | (~node21(c_e_h_2, c_r, s18, s19)))),
% 87.54/87.81 inference(rewrite,[status(thm)],[])).
% 87.54/87.81 tff(15735,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | (~node21(c_e_h_2, c_r, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | node20(c_e_h_2, c_r, s18) | (~node21(c_e_h_2, c_r, s18, s19))))),
% 87.54/87.81 inference(monotonicity,[status(thm)],[15734])).
% 87.54/87.81 tff(15736,plain,
% 87.54/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | (~node21(c_e_h_2, c_r, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | node20(c_e_h_2, c_r, s18) | (~node21(c_e_h_2, c_r, s18, s19)))),
% 87.54/87.81 inference(transitivity,[status(thm)],[15735, 15733])).
% 87.54/87.81 tff(15737,plain,
% 87.54/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | (~node21(c_e_h_2, c_r, s18, s19)))),
% 87.63/87.81 inference(quant_inst,[status(thm)],[])).
% 87.63/87.81 tff(15738,plain,
% 87.63/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | node20(c_e_h_2, c_r, s18) | (~node21(c_e_h_2, c_r, s18, s19))),
% 87.63/87.81 inference(modus_ponens,[status(thm)],[15737, 15736])).
% 87.63/87.81 tff(15739,plain,
% 87.63/87.81 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | node20(c_e_h_2, c_r, s18) | (~node21(c_e_h_2, c_r, s18, s19))),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15738, 51])).
% 87.63/87.81 tff(15740,plain,
% 87.63/87.81 (node20(c_e_h_2, c_r, s18)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15739, 15732, 15666])).
% 87.63/87.81 tff(15741,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s18)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s18)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s18))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15742,plain,
% 87.63/87.81 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s18)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s18))),
% 87.63/87.81 inference(quant_inst,[status(thm)],[])).
% 87.63/87.81 tff(15743,plain,
% 87.63/87.81 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_r, s18)) | m_and_h_gate_v_in1(c_e_h_2, c_r, s18)),
% 87.63/87.81 inference(modus_ponens,[status(thm)],[15742, 15741])).
% 87.63/87.81 tff(15744,plain,
% 87.63/87.81 (m_and_h_gate_v_in1(c_e_h_2, c_r, s18)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15743, 37, 15740])).
% 87.63/87.81 tff(15745,plain,
% 87.63/87.81 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s18))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s18))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15746,plain,
% 87.63/87.81 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_r, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s18))),
% 87.63/87.81 inference(quant_inst,[status(thm)],[])).
% 87.63/87.81 tff(15747,plain,
% 87.63/87.81 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_r, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s18)),
% 87.63/87.81 inference(modus_ponens,[status(thm)],[15746, 15745])).
% 87.63/87.81 tff(15748,plain,
% 87.63/87.81 (m_c_h_element_v_out(c_e_h_2, c_e, s18)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15747, 1884, 15744])).
% 87.63/87.81 tff(15749,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s18)), introduced(assumption)).
% 87.63/87.81 tff(15750,assumption,(node18(c_e_h_2, c_e, s17, s18)), introduced(assumption)).
% 87.63/87.81 tff(15751,plain,
% 87.63/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15752,plain,
% 87.63/87.81 (((~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15753,plain,
% 87.63/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18))))),
% 87.63/87.81 inference(monotonicity,[status(thm)],[15752])).
% 87.63/87.81 tff(15754,plain,
% 87.63/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))),
% 87.63/87.81 inference(transitivity,[status(thm)],[15753, 15751])).
% 87.63/87.81 tff(15755,plain,
% 87.63/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)))),
% 87.63/87.81 inference(quant_inst,[status(thm)],[])).
% 87.63/87.81 tff(15756,plain,
% 87.63/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~node18(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18))),
% 87.63/87.81 inference(modus_ponens,[status(thm)],[15755, 15754])).
% 87.63/87.81 tff(15757,plain,
% 87.63/87.81 ($false),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15756, 124, 15750, 15665, 15749])).
% 87.63/87.81 tff(15758,plain,((~node18(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.81 tff(15759,plain,
% 87.63/87.81 (~node18(c_e_h_2, c_e, s17, s18)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15758, 15748, 15665])).
% 87.63/87.81 tff(15760,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s17)), introduced(assumption)).
% 87.63/87.81 tff(15761,assumption,(node15(c_e_h_2, c_e, s17, s18)), introduced(assumption)).
% 87.63/87.81 tff(15762,plain,
% 87.63/87.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | (~node15(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | (~node15(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15763,plain,
% 87.63/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | (~node15(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(quant_inst,[status(thm)],[])).
% 87.63/87.81 tff(15764,plain,
% 87.63/87.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | (~node15(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(modus_ponens,[status(thm)],[15763, 15762])).
% 87.63/87.81 tff(15765,plain,
% 87.63/87.81 ($false),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15764, 173, 15761, 15665, 15749])).
% 87.63/87.81 tff(15766,plain,((~node15(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_2, c_e, s17) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.81 tff(15767,plain,
% 87.63/87.81 (~node15(c_e_h_2, c_e, s17, s18)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15766, 15748, 15665])).
% 87.63/87.81 tff(15768,assumption,(node17(c_e_h_2, c_e, s17)), introduced(assumption)).
% 87.63/87.81 tff(15769,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15770,plain,
% 87.63/87.81 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17) | (~node17(c_e_h_2, c_e, s17))) <=> ((~node17(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15771,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17) | (~node17(c_e_h_2, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17)))),
% 87.63/87.81 inference(monotonicity,[status(thm)],[15770])).
% 87.63/87.81 tff(15772,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17) | (~node17(c_e_h_2, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(transitivity,[status(thm)],[15771, 15769])).
% 87.63/87.81 tff(15773,plain,
% 87.63/87.81 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17) | (~node17(c_e_h_2, c_e, s17)))),
% 87.63/87.81 inference(quant_inst,[status(thm)],[])).
% 87.63/87.81 tff(15774,plain,
% 87.63/87.81 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(modus_ponens,[status(thm)],[15773, 15772])).
% 87.63/87.81 tff(15775,plain,
% 87.63/87.81 ((~node17(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15774, 209, 15760])).
% 87.63/87.81 tff(15776,plain,
% 87.63/87.81 (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15775, 15768])).
% 87.63/87.81 tff(15777,assumption,(~node15(c_e_h_2, c_e, s17, s18)), introduced(assumption)).
% 87.63/87.81 tff(15778,assumption,(node16(c_e_h_2, c_e, s17)), introduced(assumption)).
% 87.63/87.81 tff(15779,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s17)), introduced(assumption)).
% 87.63/87.81 tff(15780,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | m_c_h_element_v_in2(c_e_h_2, c_e, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | m_c_h_element_v_in2(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15781,plain,
% 87.63/87.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | m_c_h_element_v_in2(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(quant_inst,[status(thm)],[])).
% 87.63/87.81 tff(15782,plain,
% 87.63/87.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | m_c_h_element_v_in2(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(modus_ponens,[status(thm)],[15781, 15780])).
% 87.63/87.81 tff(15783,plain,
% 87.63/87.81 (m_c_h_element_v_in1(c_e_h_2, c_e, s17) | m_c_h_element_v_in2(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15782, 228, 15778])).
% 87.63/87.81 tff(15784,plain,
% 87.63/87.81 (m_c_h_element_v_in2(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15783, 15779])).
% 87.63/87.81 tff(15785,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15786,plain,
% 87.63/87.81 ((m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(rewrite,[status(thm)],[])).
% 87.63/87.81 tff(15787,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17)))),
% 87.63/87.81 inference(monotonicity,[status(thm)],[15786])).
% 87.63/87.81 tff(15788,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17))),
% 87.63/87.81 inference(transitivity,[status(thm)],[15787, 15785])).
% 87.63/87.81 tff(15789,plain,
% 87.63/87.81 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)))),
% 87.63/87.81 inference(quant_inst,[status(thm)],[])).
% 87.63/87.81 tff(15790,plain,
% 87.63/87.81 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~node17(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(modus_ponens,[status(thm)],[15789, 15788])).
% 87.63/87.81 tff(15791,plain,
% 87.63/87.81 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15790, 245, 15768])).
% 87.63/87.81 tff(15792,plain,
% 87.63/87.81 ($false),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15791, 15784, 15779])).
% 87.63/87.81 tff(15793,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~node17(c_e_h_2, c_e, s17)) | (~node16(c_e_h_2, c_e, s17))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.81 tff(15794,plain,
% 87.63/87.81 (m_c_h_element_v_in1(c_e_h_2, c_e, s17)),
% 87.63/87.81 inference(unit_resolution,[status(thm)],[15793, 15768, 15778])).
% 87.63/87.81 tff(15795,plain,
% 87.63/87.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15796,plain,
% 87.63/87.82 (((~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17))) <=> ((~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15797,plain,
% 87.63/87.82 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17))))),
% 87.63/87.82 inference(monotonicity,[status(thm)],[15796])).
% 87.63/87.82 tff(15798,plain,
% 87.63/87.82 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)))),
% 87.63/87.82 inference(transitivity,[status(thm)],[15797, 15795])).
% 87.63/87.82 tff(15799,plain,
% 87.63/87.82 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15800,plain,
% 87.63/87.82 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17))),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15799, 15798])).
% 87.63/87.82 tff(15801,plain,
% 87.63/87.82 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s17))),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15800, 263, 15778])).
% 87.63/87.82 tff(15802,plain,
% 87.63/87.82 (~m_c_h_element_v_in2(c_e_h_2, c_e, s17)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15801, 15794])).
% 87.63/87.82 tff(15803,plain,
% 87.63/87.82 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s17)) | m_c_h_element_v_in2(c_e_h_2, c_e, s17)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15774, 209, 15768])).
% 87.63/87.82 tff(15804,plain,
% 87.63/87.82 ($false),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15803, 15802, 15794])).
% 87.63/87.82 tff(15805,plain,((~node17(c_e_h_2, c_e, s17)) | (~node16(c_e_h_2, c_e, s17))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.82 tff(15806,plain,
% 87.63/87.82 (~node16(c_e_h_2, c_e, s17)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15805, 15768])).
% 87.63/87.82 tff(15807,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s17, s18)) | node19(c_e_h_2, c_e, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s17, s18)) | node19(c_e_h_2, c_e, s17, s18))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15808,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s17, s18)) | node19(c_e_h_2, c_e, s17, s18))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15809,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s17, s18)) | node19(c_e_h_2, c_e, s17, s18)),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15808, 15807])).
% 87.63/87.82 tff(15810,plain,
% 87.63/87.82 (node19(c_e_h_2, c_e, s17, s18)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15809, 141, 15701])).
% 87.63/87.82 tff(15811,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s17) | node15(c_e_h_2, c_e, s17, s18) | node14(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s17) | node15(c_e_h_2, c_e, s17, s18) | node14(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15812,plain,
% 87.63/87.82 ((node16(c_e_h_2, c_e, s17) | node14(c_e_h_2, c_e, s17, s18) | node15(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18))) <=> (node16(c_e_h_2, c_e, s17) | node15(c_e_h_2, c_e, s17, s18) | node14(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15813,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s17) | node14(c_e_h_2, c_e, s17, s18) | node15(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s17) | node15(c_e_h_2, c_e, s17, s18) | node14(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18))))),
% 87.63/87.82 inference(monotonicity,[status(thm)],[15812])).
% 87.63/87.82 tff(15814,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s17) | node14(c_e_h_2, c_e, s17, s18) | node15(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s17) | node15(c_e_h_2, c_e, s17, s18) | node14(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))),
% 87.63/87.82 inference(transitivity,[status(thm)],[15813, 15811])).
% 87.63/87.82 tff(15815,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s17) | node14(c_e_h_2, c_e, s17, s18) | node15(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15816,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s17) | node15(c_e_h_2, c_e, s17, s18) | node14(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18))),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15815, 15814])).
% 87.63/87.82 tff(15817,plain,
% 87.63/87.82 (node16(c_e_h_2, c_e, s17) | node15(c_e_h_2, c_e, s17, s18) | node14(c_e_h_2, c_e, s17, s18)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15816, 189, 15810])).
% 87.63/87.82 tff(15818,plain,
% 87.63/87.82 (node14(c_e_h_2, c_e, s17, s18)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15817, 15806, 15777])).
% 87.63/87.82 tff(15819,assumption,(node14(c_e_h_2, c_e, s17, s18)), introduced(assumption)).
% 87.63/87.82 tff(15820,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~node14(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~node14(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15821,plain,
% 87.63/87.82 (((~node14(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~node14(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15822,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~node14(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18))))),
% 87.63/87.82 inference(monotonicity,[status(thm)],[15821])).
% 87.63/87.82 tff(15823,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~node14(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))),
% 87.63/87.82 inference(transitivity,[status(thm)],[15822, 15820])).
% 87.63/87.82 tff(15824,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s17, s18)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15825,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s17) | (~node14(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18))),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15824, 15823])).
% 87.63/87.82 tff(15826,plain,
% 87.63/87.82 ($false),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15825, 283, 15819, 15749, 15779])).
% 87.63/87.82 tff(15827,plain,((~node14(c_e_h_2, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | m_c_h_element_v_in1(c_e_h_2, c_e, s17)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.82 tff(15828,plain,
% 87.63/87.82 ($false),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15827, 15818, 15776, 15749])).
% 87.63/87.82 tff(15829,plain,((~node17(c_e_h_2, c_e, s17)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s18)) | node15(c_e_h_2, c_e, s17, s18) | m_c_h_element_v_in2(c_e_h_2, c_e, s17)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.82 tff(15830,plain,
% 87.63/87.82 (~node17(c_e_h_2, c_e, s17)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15829, 15767, 15760, 15748])).
% 87.63/87.82 tff(15831,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s17) | node18(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s17) | node18(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15832,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s17) | node18(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18)))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15833,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s17) | node18(c_e_h_2, c_e, s17, s18) | (~node19(c_e_h_2, c_e, s17, s18))),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15832, 15831])).
% 87.63/87.82 tff(15834,plain,
% 87.63/87.82 (node17(c_e_h_2, c_e, s17) | node18(c_e_h_2, c_e, s17, s18)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15833, 156, 15810])).
% 87.63/87.82 tff(15835,plain,
% 87.63/87.82 ($false),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15834, 15830, 15759])).
% 87.63/87.82 tff(15836,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s17) | m_c_h_element_v_in2(c_e_h_2, c_e, s17) | (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.82 tff(15837,plain,
% 87.63/87.82 ((~m_and_h_gate_v_out(c_e_h_2, c_r, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15836, 15664, 15310])).
% 87.63/87.82 tff(15838,plain,
% 87.63/87.82 (~m_and_h_gate_v_out(c_e_h_2, c_r, s19)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15837, 14108])).
% 87.63/87.82 tff(15839,plain,
% 87.63/87.82 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s19))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s19))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15840,plain,
% 87.63/87.82 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s19))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15841,plain,
% 87.63/87.82 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s19)) | m_and_h_gate_v_out(c_e_h_2, c_r, s19)),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15840, 15839])).
% 87.63/87.82 tff(15842,plain,
% 87.63/87.82 (~m_user_v_ack(c_e_h_2, c_u, s19)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15841, 4481, 15838])).
% 87.63/87.82 tff(15843,plain,
% 87.63/87.82 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s19) | (~node25(s19)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s19) | (~node25(s19)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15844,plain,
% 87.63/87.82 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s19) | (~node25(s19)))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15845,plain,
% 87.63/87.82 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s19) | (~node25(s19))),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15844, 15843])).
% 87.63/87.82 tff(15846,plain,
% 87.63/87.82 (~node25(s19)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15845, 4492, 15842])).
% 87.63/87.82 tff(15847,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s12)), introduced(assumption)).
% 87.63/87.82 tff(15848,assumption,(node18(c_e_h_1, c_h, s11, s12)), introduced(assumption)).
% 87.63/87.82 tff(15849,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15850,plain,
% 87.63/87.82 (((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~node18(c_e_h_1, c_h, s11, s12))) <=> ((~node18(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15851,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~node18(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)))),
% 87.63/87.82 inference(monotonicity,[status(thm)],[15850])).
% 87.63/87.82 tff(15852,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~node18(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 87.63/87.82 inference(transitivity,[status(thm)],[15851, 15849])).
% 87.63/87.82 tff(15853,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~node18(c_e_h_1, c_h, s11, s12)))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15854,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15853, 15852])).
% 87.63/87.82 tff(15855,plain,
% 87.63/87.82 ($false),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15854, 124, 15847, 15848, 13638])).
% 87.63/87.82 tff(15856,plain,((~node18(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.82 tff(15857,plain,
% 87.63/87.82 ((~node18(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15856, 13636])).
% 87.63/87.82 tff(15858,plain,
% 87.63/87.82 (~node18(c_e_h_1, c_h, s11, s12)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15857, 15847])).
% 87.63/87.82 tff(15859,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s11)), introduced(assumption)).
% 87.63/87.82 tff(15860,plain,
% 87.63/87.82 (~node18(c_e_h_1, c_h, s11, s12)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15856, 13638, 15847])).
% 87.63/87.82 tff(15861,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_h, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_h, s11, s12))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15862,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_h, s11, s12))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15863,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_h, s11, s12)),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15862, 15861])).
% 87.63/87.82 tff(15864,plain,
% 87.63/87.82 (node19(c_e_h_1, c_h, s11, s12)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15863, 141, 4461])).
% 87.63/87.82 tff(15865,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s11, s12)) | node18(c_e_h_1, c_h, s11, s12) | node17(c_e_h_1, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s11, s12)) | node18(c_e_h_1, c_h, s11, s12) | node17(c_e_h_1, c_h, s11))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15866,plain,
% 87.63/87.82 ((node17(c_e_h_1, c_h, s11) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12))) <=> ((~node19(c_e_h_1, c_h, s11, s12)) | node18(c_e_h_1, c_h, s11, s12) | node17(c_e_h_1, c_h, s11))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15867,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s11) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s11, s12)) | node18(c_e_h_1, c_h, s11, s12) | node17(c_e_h_1, c_h, s11)))),
% 87.63/87.82 inference(monotonicity,[status(thm)],[15866])).
% 87.63/87.82 tff(15868,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s11) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s11, s12)) | node18(c_e_h_1, c_h, s11, s12) | node17(c_e_h_1, c_h, s11))),
% 87.63/87.82 inference(transitivity,[status(thm)],[15867, 15865])).
% 87.63/87.82 tff(15869,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s11) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15870,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s11, s12)) | node18(c_e_h_1, c_h, s11, s12) | node17(c_e_h_1, c_h, s11)),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15869, 15868])).
% 87.63/87.82 tff(15871,plain,
% 87.63/87.82 (node18(c_e_h_1, c_h, s11, s12) | node17(c_e_h_1, c_h, s11)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15870, 156, 15864])).
% 87.63/87.82 tff(15872,plain,
% 87.63/87.82 (node17(c_e_h_1, c_h, s11)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15871, 15860])).
% 87.63/87.82 tff(15873,assumption,(node14(c_e_h_1, c_h, s11, s12)), introduced(assumption)).
% 87.63/87.82 tff(15874,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15875,plain,
% 87.63/87.82 (((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12)))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15876,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12))))),
% 87.63/87.82 inference(monotonicity,[status(thm)],[15875])).
% 87.63/87.82 tff(15877,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12)))),
% 87.63/87.82 inference(transitivity,[status(thm)],[15876, 15874])).
% 87.63/87.82 tff(15878,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15879,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12))),
% 87.63/87.82 inference(modus_ponens,[status(thm)],[15878, 15877])).
% 87.63/87.82 tff(15880,plain,
% 87.63/87.82 ($false),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15879, 283, 15859, 15847, 15873])).
% 87.63/87.82 tff(15881,plain,((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.82 tff(15882,plain,
% 87.63/87.82 (~node14(c_e_h_1, c_h, s11, s12)),
% 87.63/87.82 inference(unit_resolution,[status(thm)],[15881, 15847, 15859])).
% 87.63/87.82 tff(15883,assumption,(node15(c_e_h_1, c_h, s11, s12)), introduced(assumption)).
% 87.63/87.82 tff(15884,plain,
% 87.63/87.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 87.63/87.82 inference(rewrite,[status(thm)],[])).
% 87.63/87.82 tff(15885,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 87.63/87.82 inference(quant_inst,[status(thm)],[])).
% 87.63/87.82 tff(15886,plain,
% 87.63/87.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15885, 15884])).
% 87.63/87.83 tff(15887,plain,
% 87.63/87.83 ($false),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15886, 173, 15847, 15883, 13638])).
% 87.63/87.83 tff(15888,plain,((~node15(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.83 tff(15889,plain,
% 87.63/87.83 (~node15(c_e_h_1, c_h, s11, s12)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15888, 13638, 15847])).
% 87.63/87.83 tff(15890,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s11) | (~node19(c_e_h_1, c_h, s11, s12)) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s11) | (~node19(c_e_h_1, c_h, s11, s12)) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15891,plain,
% 87.63/87.83 ((node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12))) <=> (node16(c_e_h_1, c_h, s11) | (~node19(c_e_h_1, c_h, s11, s12)) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15892,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s11) | (~node19(c_e_h_1, c_h, s11, s12)) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12)))),
% 87.63/87.83 inference(monotonicity,[status(thm)],[15891])).
% 87.63/87.83 tff(15893,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s11) | (~node19(c_e_h_1, c_h, s11, s12)) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12))),
% 87.63/87.83 inference(transitivity,[status(thm)],[15892, 15890])).
% 87.63/87.83 tff(15894,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15895,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s11) | (~node19(c_e_h_1, c_h, s11, s12)) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12)),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15894, 15893])).
% 87.63/87.83 tff(15896,plain,
% 87.63/87.83 (node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15895, 189, 15864])).
% 87.63/87.83 tff(15897,plain,
% 87.63/87.83 (node16(c_e_h_1, c_h, s11)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15896, 15889, 15882])).
% 87.63/87.83 tff(15898,assumption,(node16(c_e_h_1, c_h, s11)), introduced(assumption)).
% 87.63/87.83 tff(15899,plain,
% 87.63/87.83 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15900,plain,
% 87.63/87.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15901,plain,
% 87.63/87.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11)),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15900, 15899])).
% 87.63/87.83 tff(15902,plain,
% 87.63/87.83 (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15901, 228, 15898])).
% 87.63/87.83 tff(15903,plain,
% 87.63/87.83 (m_c_h_element_v_in2(c_e_h_1, c_h, s11)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15902, 15859])).
% 87.63/87.83 tff(15904,assumption,(node17(c_e_h_1, c_h, s11)), introduced(assumption)).
% 87.63/87.83 tff(15905,plain,
% 87.63/87.83 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11)))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15906,plain,
% 87.63/87.83 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11)))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15907,plain,
% 87.63/87.83 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11))),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15906, 15905])).
% 87.63/87.83 tff(15908,plain,
% 87.63/87.83 (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11))),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15907, 245, 15904])).
% 87.63/87.83 tff(15909,plain,
% 87.63/87.83 ($false),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15908, 15903, 15859])).
% 87.63/87.83 tff(15910,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11)) | (~node16(c_e_h_1, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.83 tff(15911,plain,
% 87.63/87.83 ($false),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15910, 15897, 15872, 15859])).
% 87.63/87.83 tff(15912,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s11) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.83 tff(15913,plain,
% 87.63/87.83 (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15912, 13636])).
% 87.63/87.83 tff(15914,plain,
% 87.63/87.83 (m_c_h_element_v_in1(c_e_h_1, c_h, s11)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15913, 15847])).
% 87.63/87.83 tff(15915,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s4)), introduced(assumption)).
% 87.63/87.83 tff(15916,assumption,(node6(c_e_h_3, c_j, s3, s4)), introduced(assumption)).
% 87.63/87.83 tff(15917,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4)))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15918,plain,
% 87.63/87.83 (((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4)))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15919,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4))))),
% 87.63/87.83 inference(monotonicity,[status(thm)],[15918])).
% 87.63/87.83 tff(15920,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4)))),
% 87.63/87.83 inference(transitivity,[status(thm)],[15919, 15917])).
% 87.63/87.83 tff(15921,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15922,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4))),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15921, 15920])).
% 87.63/87.83 tff(15923,plain,
% 87.63/87.83 ($false),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15922, 899, 13196, 15915, 15916])).
% 87.63/87.83 tff(15924,plain,((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.83 tff(15925,plain,
% 87.63/87.83 (~node6(c_e_h_3, c_j, s3, s4)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15924, 15915])).
% 87.63/87.83 tff(15926,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s3)), introduced(assumption)).
% 87.63/87.83 tff(15927,assumption,(node21(c_e_h_3, c_l, s2, s3)), introduced(assumption)).
% 87.63/87.83 tff(15928,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s2)), introduced(assumption)).
% 87.63/87.83 tff(15929,assumption,(node21(c_e_h_3, c_k, s1, s2)), introduced(assumption)).
% 87.63/87.83 tff(15930,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s1)), introduced(assumption)).
% 87.63/87.83 tff(15931,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s0)), introduced(assumption)).
% 87.63/87.83 tff(15932,plain,
% 87.63/87.83 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15933,plain,
% 87.63/87.83 ($false),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15932, 94, 15931])).
% 87.63/87.83 tff(15934,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.83 tff(15935,plain,
% 87.63/87.83 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X)))),
% 87.63/87.83 inference(bind,[status(th)],[])).
% 87.63/87.83 tff(15936,plain,
% 87.63/87.83 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 87.63/87.83 inference(quant_intro,[status(thm)],[15935])).
% 87.63/87.83 tff(15937,plain,
% 87.63/87.83 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15938,axiom,(![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_28')).
% 87.63/87.83 tff(15939,plain,
% 87.63/87.83 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15938, 15937])).
% 87.63/87.83 tff(15940,plain,(
% 87.63/87.83 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 87.63/87.83 inference(skolemize,[status(sab)],[15939])).
% 87.63/87.83 tff(15941,plain,
% 87.63/87.83 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15940, 15936])).
% 87.63/87.83 tff(15942,plain,
% 87.63/87.83 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15943,plain,
% 87.63/87.83 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15944,plain,
% 87.63/87.83 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15943, 15942])).
% 87.63/87.83 tff(15945,plain,
% 87.63/87.83 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15944, 15941, 15934])).
% 87.63/87.83 tff(15946,plain,
% 87.63/87.83 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)))),
% 87.63/87.83 inference(bind,[status(th)],[])).
% 87.63/87.83 tff(15947,plain,
% 87.63/87.83 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 87.63/87.83 inference(quant_intro,[status(thm)],[15946])).
% 87.63/87.83 tff(15948,plain,
% 87.63/87.83 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15949,axiom,(![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_30')).
% 87.63/87.83 tff(15950,plain,
% 87.63/87.83 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15949, 15948])).
% 87.63/87.83 tff(15951,plain,(
% 87.63/87.83 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 87.63/87.83 inference(skolemize,[status(sab)],[15950])).
% 87.63/87.83 tff(15952,plain,
% 87.63/87.83 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15951, 15947])).
% 87.63/87.83 tff(15953,plain,
% 87.63/87.83 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15954,plain,
% 87.63/87.83 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15955,plain,
% 87.63/87.83 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0)),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15954, 15953])).
% 87.63/87.83 tff(15956,plain,
% 87.63/87.83 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15955, 15952, 5824])).
% 87.63/87.83 tff(15957,assumption,(node5(c_e_h_3, c_g, s0, s1)), introduced(assumption)).
% 87.63/87.83 tff(15958,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node5(c_e_h_3, c_g, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node5(c_e_h_3, c_g, s0, s1)))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15959,plain,
% 87.63/87.83 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1))) <=> (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node5(c_e_h_3, c_g, s0, s1)))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15960,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node5(c_e_h_3, c_g, s0, s1))))),
% 87.63/87.83 inference(monotonicity,[status(thm)],[15959])).
% 87.63/87.83 tff(15961,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node5(c_e_h_3, c_g, s0, s1)))),
% 87.63/87.83 inference(transitivity,[status(thm)],[15960, 15958])).
% 87.63/87.83 tff(15962,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15963,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node5(c_e_h_3, c_g, s0, s1))),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15962, 15961])).
% 87.63/87.83 tff(15964,plain,
% 87.63/87.83 ($false),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15963, 862, 15930, 15957, 15956, 15945])).
% 87.63/87.83 tff(15965,plain,((~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.83 tff(15966,plain,
% 87.63/87.83 (~node5(c_e_h_3, c_g, s0, s1)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15965, 15930])).
% 87.63/87.83 tff(15967,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15968,plain,
% 87.63/87.83 ((node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15969,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1)))),
% 87.63/87.83 inference(monotonicity,[status(thm)],[15968])).
% 87.63/87.83 tff(15970,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1))),
% 87.63/87.83 inference(transitivity,[status(thm)],[15969, 15967])).
% 87.63/87.83 tff(15971,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1)))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15972,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1)),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15971, 15970])).
% 87.63/87.83 tff(15973,plain,
% 87.63/87.83 (node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15972, 881, 71])).
% 87.63/87.83 tff(15974,plain,
% 87.63/87.83 (node6(c_e_h_3, c_g, s0, s1)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15973, 15966])).
% 87.63/87.83 tff(15975,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~node6(c_e_h_3, c_g, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~node6(c_e_h_3, c_g, s0, s1)))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15976,plain,
% 87.63/87.83 (((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~node6(c_e_h_3, c_g, s0, s1)))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15977,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~node6(c_e_h_3, c_g, s0, s1))))),
% 87.63/87.83 inference(monotonicity,[status(thm)],[15976])).
% 87.63/87.83 tff(15978,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~node6(c_e_h_3, c_g, s0, s1)))),
% 87.63/87.83 inference(transitivity,[status(thm)],[15977, 15975])).
% 87.63/87.83 tff(15979,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15980,plain,
% 87.63/87.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~node6(c_e_h_3, c_g, s0, s1))),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15979, 15978])).
% 87.63/87.83 tff(15981,plain,
% 87.63/87.83 ($false),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15980, 899, 15930, 15974, 13107])).
% 87.63/87.83 tff(15982,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.83 tff(15983,plain,
% 87.63/87.83 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15984,plain,
% 87.63/87.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15985,plain,
% 87.63/87.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1)),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15984, 15983])).
% 87.63/87.83 tff(15986,plain,
% 87.63/87.83 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15985, 13114, 15982])).
% 87.63/87.83 tff(15987,plain,
% 87.63/87.83 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s1))),
% 87.63/87.83 inference(rewrite,[status(thm)],[])).
% 87.63/87.83 tff(15988,plain,
% 87.63/87.83 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s1))),
% 87.63/87.83 inference(quant_inst,[status(thm)],[])).
% 87.63/87.83 tff(15989,plain,
% 87.63/87.83 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s1)),
% 87.63/87.83 inference(modus_ponens,[status(thm)],[15988, 15987])).
% 87.63/87.83 tff(15990,plain,
% 87.63/87.83 (~node20(c_e_h_3, c_k, s1)),
% 87.63/87.83 inference(unit_resolution,[status(thm)],[15989, 37, 15986])).
% 87.63/87.83 tff(15991,plain,
% 87.63/87.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s1) | (~node21(c_e_h_3, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s1) | (~node21(c_e_h_3, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(15992,plain,
% 87.63/87.84 ((node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2))) <=> (node20(c_e_h_3, c_k, s1) | (~node21(c_e_h_3, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(15993,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s1) | (~node21(c_e_h_3, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2))))),
% 87.63/87.84 inference(monotonicity,[status(thm)],[15992])).
% 87.63/87.84 tff(15994,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s1) | (~node21(c_e_h_3, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)))),
% 87.63/87.84 inference(transitivity,[status(thm)],[15993, 15991])).
% 87.63/87.84 tff(15995,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2)))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(15996,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s1) | (~node21(c_e_h_3, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[15995, 15994])).
% 87.63/87.84 tff(15997,plain,
% 87.63/87.84 ($false),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[15996, 51, 15928, 15990, 15929])).
% 87.63/87.84 tff(15998,plain,((~node21(c_e_h_3, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.84 tff(15999,plain,
% 87.63/87.84 (~node21(c_e_h_3, c_k, s1, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[15998, 15928])).
% 87.63/87.84 tff(16000,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16001,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16002,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16001, 16000])).
% 87.63/87.84 tff(16003,plain,
% 87.63/87.84 (node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16002, 81, 344])).
% 87.63/87.84 tff(16004,plain,
% 87.63/87.84 (node22(c_e_h_3, c_k, s1, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16003, 15999])).
% 87.63/87.84 tff(16005,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16006,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16007,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16006, 16005])).
% 87.63/87.84 tff(16008,plain,
% 87.63/87.84 ($false),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16007, 107, 13142, 15928, 16004])).
% 87.63/87.84 tff(16009,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.84 tff(16010,plain,
% 87.63/87.84 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16011,plain,
% 87.63/87.84 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16012,plain,
% 87.63/87.84 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16011, 16010])).
% 87.63/87.84 tff(16013,plain,
% 87.63/87.84 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16012, 10554, 16009])).
% 87.63/87.84 tff(16014,plain,
% 87.63/87.84 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s2))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16015,plain,
% 87.63/87.84 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s2))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16016,plain,
% 87.63/87.84 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s2)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16015, 16014])).
% 87.63/87.84 tff(16017,plain,
% 87.63/87.84 (~node20(c_e_h_3, c_l, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16016, 37, 16013])).
% 87.63/87.84 tff(16018,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3)))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16019,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3)))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16020,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3))),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16019, 16018])).
% 87.63/87.84 tff(16021,plain,
% 87.63/87.84 ($false),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16020, 51, 15926, 16017, 15927])).
% 87.63/87.84 tff(16022,plain,((~node21(c_e_h_3, c_l, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.84 tff(16023,plain,
% 87.63/87.84 (~node21(c_e_h_3, c_l, s2, s3)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16022, 15926])).
% 87.63/87.84 tff(16024,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16025,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16026,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16025, 16024])).
% 87.63/87.84 tff(16027,plain,
% 87.63/87.84 (node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16026, 81, 582])).
% 87.63/87.84 tff(16028,plain,
% 87.63/87.84 (node22(c_e_h_3, c_l, s2, s3)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16027, 16023])).
% 87.63/87.84 tff(16029,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16030,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16031,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16030, 16029])).
% 87.63/87.84 tff(16032,plain,
% 87.63/87.84 ($false),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16031, 107, 15926, 13171, 16028])).
% 87.63/87.84 tff(16033,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.84 tff(16034,plain,
% 87.63/87.84 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16035,plain,
% 87.63/87.84 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16036,plain,
% 87.63/87.84 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16035, 16034])).
% 87.63/87.84 tff(16037,plain,
% 87.63/87.84 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16036, 801, 16033])).
% 87.63/87.84 tff(16038,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), introduced(assumption)).
% 87.63/87.84 tff(16039,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s2)), introduced(assumption)).
% 87.63/87.84 tff(16040,assumption,(node15(c_e_h_2, c_f, s1, s2)), introduced(assumption)).
% 87.63/87.84 tff(16041,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16042,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16043,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16042, 16041])).
% 87.63/87.84 tff(16044,plain,
% 87.63/87.84 ($false),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16043, 173, 16039, 13044, 16040])).
% 87.63/87.84 tff(16045,plain,((~node15(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.84 tff(16046,plain,
% 87.63/87.84 (~node15(c_e_h_2, c_f, s1, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16045, 16039])).
% 87.63/87.84 tff(16047,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s1)), introduced(assumption)).
% 87.63/87.84 tff(16048,plain,
% 87.63/87.84 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16049,plain,
% 87.63/87.84 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16050,plain,
% 87.63/87.84 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16049, 16048])).
% 87.63/87.84 tff(16051,plain,
% 87.63/87.84 (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16050, 2218, 112])).
% 87.63/87.84 tff(16052,plain,
% 87.63/87.84 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16053,plain,
% 87.63/87.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16054,plain,
% 87.63/87.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16053, 16052])).
% 87.63/87.84 tff(16055,plain,
% 87.63/87.84 ((~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16054, 228, 16051])).
% 87.63/87.84 tff(16056,plain,
% 87.63/87.84 (~node16(c_e_h_2, c_f, s1)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16055, 16047])).
% 87.63/87.84 tff(16057,assumption,(node14(c_e_h_2, c_f, s1, s2)), introduced(assumption)).
% 87.63/87.84 tff(16058,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16059,plain,
% 87.63/87.84 (((~node14(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16060,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))))),
% 87.63/87.84 inference(monotonicity,[status(thm)],[16059])).
% 87.63/87.84 tff(16061,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))),
% 87.63/87.84 inference(transitivity,[status(thm)],[16060, 16058])).
% 87.63/87.84 tff(16062,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16063,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16062, 16061])).
% 87.63/87.84 tff(16064,plain,
% 87.63/87.84 ($false),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16063, 283, 16039, 16047, 16057])).
% 87.63/87.84 tff(16065,plain,((~node14(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.84 tff(16066,plain,
% 87.63/87.84 (~node14(c_e_h_2, c_f, s1, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16065, 16047, 16039])).
% 87.63/87.84 tff(16067,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_f, s1, s2))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16068,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_f, s1, s2))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16069,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_f, s1, s2)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16068, 16067])).
% 87.63/87.84 tff(16070,plain,
% 87.63/87.84 (node19(c_e_h_2, c_f, s1, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16069, 141, 344])).
% 87.63/87.84 tff(16071,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s1, s2)) | node16(c_e_h_2, c_f, s1) | node15(c_e_h_2, c_f, s1, s2) | node14(c_e_h_2, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node16(c_e_h_2, c_f, s1) | node15(c_e_h_2, c_f, s1, s2) | node14(c_e_h_2, c_f, s1, s2))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16072,plain,
% 87.63/87.84 ((node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2) | node15(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2))) <=> ((~node19(c_e_h_2, c_f, s1, s2)) | node16(c_e_h_2, c_f, s1) | node15(c_e_h_2, c_f, s1, s2) | node14(c_e_h_2, c_f, s1, s2))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16073,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2) | node15(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s1, s2)) | node16(c_e_h_2, c_f, s1) | node15(c_e_h_2, c_f, s1, s2) | node14(c_e_h_2, c_f, s1, s2)))),
% 87.63/87.84 inference(monotonicity,[status(thm)],[16072])).
% 87.63/87.84 tff(16074,plain,
% 87.63/87.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2) | node15(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node16(c_e_h_2, c_f, s1) | node15(c_e_h_2, c_f, s1, s2) | node14(c_e_h_2, c_f, s1, s2))),
% 87.63/87.84 inference(transitivity,[status(thm)],[16073, 16071])).
% 87.63/87.84 tff(16075,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2) | node15(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))),
% 87.63/87.84 inference(quant_inst,[status(thm)],[])).
% 87.63/87.84 tff(16076,plain,
% 87.63/87.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node16(c_e_h_2, c_f, s1) | node15(c_e_h_2, c_f, s1, s2) | node14(c_e_h_2, c_f, s1, s2)),
% 87.63/87.84 inference(modus_ponens,[status(thm)],[16075, 16074])).
% 87.63/87.84 tff(16077,plain,
% 87.63/87.84 (node16(c_e_h_2, c_f, s1) | node15(c_e_h_2, c_f, s1, s2) | node14(c_e_h_2, c_f, s1, s2)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16076, 189, 16070])).
% 87.63/87.84 tff(16078,plain,
% 87.63/87.84 ($false),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16077, 16066, 16056, 16046])).
% 87.63/87.84 tff(16079,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.84 tff(16080,plain,
% 87.63/87.84 (m_c_h_element_v_in1(c_e_h_2, c_f, s1)),
% 87.63/87.84 inference(unit_resolution,[status(thm)],[16079, 16039])).
% 87.63/87.84 tff(16081,plain,
% 87.63/87.84 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 87.63/87.84 inference(rewrite,[status(thm)],[])).
% 87.63/87.84 tff(16082,plain,
% 87.63/87.84 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1))) <=> ((~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16083,plain,
% 87.63/87.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1)))),
% 87.63/87.85 inference(monotonicity,[status(thm)],[16082])).
% 87.63/87.85 tff(16084,plain,
% 87.63/87.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 87.63/87.85 inference(transitivity,[status(thm)],[16083, 16081])).
% 87.63/87.85 tff(16085,plain,
% 87.63/87.85 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16086,plain,
% 87.63/87.85 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16085, 16084])).
% 87.63/87.85 tff(16087,plain,
% 87.63/87.85 ((~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16086, 209, 16051])).
% 87.63/87.85 tff(16088,plain,
% 87.63/87.85 (~node17(c_e_h_2, c_f, s1)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16087, 16080])).
% 87.63/87.85 tff(16089,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s1, s2)) | node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16090,plain,
% 87.63/87.85 ((node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2))) <=> ((~node19(c_e_h_2, c_f, s1, s2)) | node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16091,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s1, s2)) | node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2)))),
% 87.63/87.85 inference(monotonicity,[status(thm)],[16090])).
% 87.63/87.85 tff(16092,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2))),
% 87.63/87.85 inference(transitivity,[status(thm)],[16091, 16089])).
% 87.63/87.85 tff(16093,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16094,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16093, 16092])).
% 87.63/87.85 tff(16095,plain,
% 87.63/87.85 (node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16094, 156, 16070])).
% 87.63/87.85 tff(16096,plain,
% 87.63/87.85 (node18(c_e_h_2, c_f, s1, s2)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16095, 16088])).
% 87.63/87.85 tff(16097,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node18(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node18(c_e_h_2, c_f, s1, s2)))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16098,plain,
% 87.63/87.85 (((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node18(c_e_h_2, c_f, s1, s2)))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16099,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node18(c_e_h_2, c_f, s1, s2))))),
% 87.63/87.85 inference(monotonicity,[status(thm)],[16098])).
% 87.63/87.85 tff(16100,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node18(c_e_h_2, c_f, s1, s2)))),
% 87.63/87.85 inference(transitivity,[status(thm)],[16099, 16097])).
% 87.63/87.85 tff(16101,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2)))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16102,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node18(c_e_h_2, c_f, s1, s2))),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16101, 16100])).
% 87.63/87.85 tff(16103,plain,
% 87.63/87.85 ($false),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16102, 124, 16039, 13044, 16096])).
% 87.63/87.85 tff(16104,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.85 tff(16105,plain,
% 87.63/87.85 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16106,plain,
% 87.63/87.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16107,plain,
% 87.63/87.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16106, 16105])).
% 87.63/87.85 tff(16108,plain,
% 87.63/87.85 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16107, 1666, 16104])).
% 87.63/87.85 tff(16109,plain,
% 87.63/87.85 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s2))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16110,plain,
% 87.63/87.85 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s2))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16111,plain,
% 87.63/87.85 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s2)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16110, 16109])).
% 87.63/87.85 tff(16112,plain,
% 87.63/87.85 (~node20(c_e_h_2, c_q, s2)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16111, 37, 16108])).
% 87.63/87.85 tff(16113,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s2)), introduced(assumption)).
% 87.63/87.85 tff(16114,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s3)), introduced(assumption)).
% 87.63/87.85 tff(16115,assumption,(node22(c_e_h_2, c_q, s2, s3)), introduced(assumption)).
% 87.63/87.85 tff(16116,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16117,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16118,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16117, 16116])).
% 87.63/87.85 tff(16119,plain,
% 87.63/87.85 ($false),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16118, 107, 16114, 16113, 16115])).
% 87.63/87.85 tff(16120,plain,((~node22(c_e_h_2, c_q, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.85 tff(16121,plain,
% 87.63/87.85 (~node22(c_e_h_2, c_q, s2, s3)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16120, 16114, 16113])).
% 87.63/87.85 tff(16122,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16123,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16124,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16123, 16122])).
% 87.63/87.85 tff(16125,plain,
% 87.63/87.85 (node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16124, 81, 582])).
% 87.63/87.85 tff(16126,plain,
% 87.63/87.85 (node21(c_e_h_2, c_q, s2, s3)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16125, 16121])).
% 87.63/87.85 tff(16127,assumption,(~node20(c_e_h_2, c_q, s2)), introduced(assumption)).
% 87.63/87.85 tff(16128,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2) | (~node21(c_e_h_2, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2) | (~node21(c_e_h_2, c_q, s2, s3)))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16129,plain,
% 87.63/87.85 ((node20(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2) | (~node21(c_e_h_2, c_q, s2, s3)))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16130,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2) | (~node21(c_e_h_2, c_q, s2, s3))))),
% 87.63/87.85 inference(monotonicity,[status(thm)],[16129])).
% 87.63/87.85 tff(16131,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2) | (~node21(c_e_h_2, c_q, s2, s3)))),
% 87.63/87.85 inference(transitivity,[status(thm)],[16130, 16128])).
% 87.63/87.85 tff(16132,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3)))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16133,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2) | (~node21(c_e_h_2, c_q, s2, s3))),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16132, 16131])).
% 87.63/87.85 tff(16134,plain,
% 87.63/87.85 ($false),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16133, 51, 16114, 16127, 16126])).
% 87.63/87.85 tff(16135,plain,((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.85 tff(16136,plain,
% 87.63/87.85 ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16135, 13077])).
% 87.63/87.85 tff(16137,plain,
% 87.63/87.85 (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16136, 16112])).
% 87.63/87.85 tff(16138,assumption,(~node3(c_e_h_2, c_e_h_3, s3)), introduced(assumption)).
% 87.63/87.85 tff(16139,plain,
% 87.63/87.85 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s3))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16140,plain,
% 87.63/87.85 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s3))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16141,plain,
% 87.63/87.85 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s3)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16140, 16139])).
% 87.63/87.85 tff(16142,plain,
% 87.63/87.85 ($false),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16141, 7448, 814, 16138])).
% 87.63/87.85 tff(16143,plain,(node3(c_e_h_2, c_e_h_3, s3)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.85 tff(16144,plain,
% 87.63/87.85 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16145,plain,
% 87.63/87.85 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16146,plain,
% 87.63/87.85 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16145, 16144])).
% 87.63/87.85 tff(16147,plain,
% 87.63/87.85 ((~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16146, 836])).
% 87.63/87.85 tff(16148,plain,
% 87.63/87.85 ((~m_cell_v_ack(c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16147, 16143])).
% 87.63/87.85 tff(16149,plain,
% 87.63/87.85 (~m_cell_v_ack(c_e_h_3, s3)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16148, 16137])).
% 87.63/87.85 tff(16150,plain,
% 87.63/87.85 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)) | m_cell_v_ack(c_e_h_3, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)) | m_cell_v_ack(c_e_h_3, s3))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16151,plain,
% 87.63/87.85 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)) | m_cell_v_ack(c_e_h_3, s3))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16152,plain,
% 87.63/87.85 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)) | m_cell_v_ack(c_e_h_3, s3)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16151, 16150])).
% 87.63/87.85 tff(16153,plain,
% 87.63/87.85 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16152, 848, 16149])).
% 87.63/87.85 tff(16154,assumption,(node5(c_e_h_3, c_j, s3, s4)), introduced(assumption)).
% 87.63/87.85 tff(16155,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16156,plain,
% 87.63/87.85 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16157,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)))),
% 87.63/87.85 inference(monotonicity,[status(thm)],[16156])).
% 87.63/87.85 tff(16158,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))),
% 87.63/87.85 inference(transitivity,[status(thm)],[16157, 16155])).
% 87.63/87.85 tff(16159,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16160,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16159, 16158])).
% 87.63/87.85 tff(16161,plain,
% 87.63/87.85 ($false),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16160, 862, 15915, 16154, 16153, 16038])).
% 87.63/87.85 tff(16162,plain,((~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.85 tff(16163,plain,
% 87.63/87.85 ((~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16162, 16037])).
% 87.63/87.85 tff(16164,plain,
% 87.63/87.85 (~node5(c_e_h_3, c_j, s3, s4)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16163, 15915])).
% 87.63/87.85 tff(16165,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16166,plain,
% 87.63/87.85 ((node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16167,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4)))),
% 87.63/87.85 inference(monotonicity,[status(thm)],[16166])).
% 87.63/87.85 tff(16168,plain,
% 87.63/87.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4))),
% 87.63/87.85 inference(transitivity,[status(thm)],[16167, 16165])).
% 87.63/87.85 tff(16169,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4)))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16170,plain,
% 87.63/87.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16169, 16168])).
% 87.63/87.85 tff(16171,plain,
% 87.63/87.85 (node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4)),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16170, 881, 679])).
% 87.63/87.85 tff(16172,plain,
% 87.63/87.85 ($false),
% 87.63/87.85 inference(unit_resolution,[status(thm)],[16171, 16164, 15925])).
% 87.63/87.85 tff(16173,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.85 tff(16174,plain,
% 87.63/87.85 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 87.63/87.85 inference(rewrite,[status(thm)],[])).
% 87.63/87.85 tff(16175,plain,
% 87.63/87.85 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 87.63/87.85 inference(quant_inst,[status(thm)],[])).
% 87.63/87.85 tff(16176,plain,
% 87.63/87.85 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4)),
% 87.63/87.85 inference(modus_ponens,[status(thm)],[16175, 16174])).
% 87.63/87.86 tff(16177,plain,
% 87.63/87.86 (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16176, 309, 16173])).
% 87.63/87.86 tff(16178,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s5)), introduced(assumption)).
% 87.63/87.86 tff(16179,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s4)), introduced(assumption)).
% 87.63/87.86 tff(16180,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s4)), introduced(assumption)).
% 87.63/87.86 tff(16181,assumption,(node14(c_e_h_3, c_h, s4, s5)), introduced(assumption)).
% 87.63/87.86 tff(16182,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node14(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node14(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16183,plain,
% 87.63/87.86 (((~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node14(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16184,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node14(c_e_h_3, c_h, s4, s5))))),
% 87.63/87.86 inference(monotonicity,[status(thm)],[16183])).
% 87.63/87.86 tff(16185,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node14(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(transitivity,[status(thm)],[16184, 16182])).
% 87.63/87.86 tff(16186,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16187,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node14(c_e_h_3, c_h, s4, s5))),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16186, 16185])).
% 87.63/87.86 tff(16188,plain,
% 87.63/87.86 ($false),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16187, 283, 16178, 16181, 16180])).
% 87.63/87.86 tff(16189,plain,((~node14(c_e_h_3, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.86 tff(16190,plain,
% 87.63/87.86 (~node14(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16189, 16178, 16180])).
% 87.63/87.86 tff(16191,assumption,(node15(c_e_h_3, c_h, s4, s5)), introduced(assumption)).
% 87.63/87.86 tff(16192,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16193,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16194,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16193, 16192])).
% 87.63/87.86 tff(16195,plain,
% 87.63/87.86 ($false),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16194, 173, 16178, 16179, 16191])).
% 87.63/87.86 tff(16196,plain,((~node15(c_e_h_3, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.86 tff(16197,plain,
% 87.63/87.86 (~node15(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16196, 16179, 16178])).
% 87.63/87.86 tff(16198,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16199,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16200,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16199, 16198])).
% 87.63/87.86 tff(16201,plain,
% 87.63/87.86 (node19(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16200, 141, 1432])).
% 87.63/87.86 tff(16202,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s4) | (~node19(c_e_h_3, c_h, s4, s5)) | node15(c_e_h_3, c_h, s4, s5) | node14(c_e_h_3, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s4) | (~node19(c_e_h_3, c_h, s4, s5)) | node15(c_e_h_3, c_h, s4, s5) | node14(c_e_h_3, c_h, s4, s5))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16203,plain,
% 87.63/87.86 ((node16(c_e_h_3, c_h, s4) | node14(c_e_h_3, c_h, s4, s5) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5))) <=> (node16(c_e_h_3, c_h, s4) | (~node19(c_e_h_3, c_h, s4, s5)) | node15(c_e_h_3, c_h, s4, s5) | node14(c_e_h_3, c_h, s4, s5))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16204,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s4) | node14(c_e_h_3, c_h, s4, s5) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s4) | (~node19(c_e_h_3, c_h, s4, s5)) | node15(c_e_h_3, c_h, s4, s5) | node14(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(monotonicity,[status(thm)],[16203])).
% 87.63/87.86 tff(16205,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s4) | node14(c_e_h_3, c_h, s4, s5) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s4) | (~node19(c_e_h_3, c_h, s4, s5)) | node15(c_e_h_3, c_h, s4, s5) | node14(c_e_h_3, c_h, s4, s5))),
% 87.63/87.86 inference(transitivity,[status(thm)],[16204, 16202])).
% 87.63/87.86 tff(16206,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s4) | node14(c_e_h_3, c_h, s4, s5) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16207,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s4) | (~node19(c_e_h_3, c_h, s4, s5)) | node15(c_e_h_3, c_h, s4, s5) | node14(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16206, 16205])).
% 87.63/87.86 tff(16208,plain,
% 87.63/87.86 (node16(c_e_h_3, c_h, s4) | node15(c_e_h_3, c_h, s4, s5) | node14(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16207, 189, 16201])).
% 87.63/87.86 tff(16209,plain,
% 87.63/87.86 (node16(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16208, 16197, 16190])).
% 87.63/87.86 tff(16210,plain,
% 87.63/87.86 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16211,plain,
% 87.63/87.86 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16212,plain,
% 87.63/87.86 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16211, 16210])).
% 87.63/87.86 tff(16213,plain,
% 87.63/87.86 ((~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16212, 228, 16180])).
% 87.63/87.86 tff(16214,plain,
% 87.63/87.86 (m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16213, 16209])).
% 87.63/87.86 tff(16215,plain,
% 87.63/87.86 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16216,plain,
% 87.63/87.86 ((m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16217,plain,
% 87.63/87.86 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)))),
% 87.63/87.86 inference(monotonicity,[status(thm)],[16216])).
% 87.63/87.86 tff(16218,plain,
% 87.63/87.86 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(transitivity,[status(thm)],[16217, 16215])).
% 87.63/87.86 tff(16219,plain,
% 87.63/87.86 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16220,plain,
% 87.63/87.86 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16219, 16218])).
% 87.63/87.86 tff(16221,plain,
% 87.63/87.86 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16220, 245, 16180])).
% 87.63/87.86 tff(16222,plain,
% 87.63/87.86 (~node17(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16221, 16214])).
% 87.63/87.86 tff(16223,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16224,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16225,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5))),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16224, 16223])).
% 87.63/87.86 tff(16226,plain,
% 87.63/87.86 (node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16225, 156, 16201])).
% 87.63/87.86 tff(16227,plain,
% 87.63/87.86 (node18(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16226, 16222])).
% 87.63/87.86 tff(16228,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node18(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node18(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16229,plain,
% 87.63/87.86 (((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~node18(c_e_h_3, c_h, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node18(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16230,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~node18(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node18(c_e_h_3, c_h, s4, s5))))),
% 87.63/87.86 inference(monotonicity,[status(thm)],[16229])).
% 87.63/87.86 tff(16231,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~node18(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node18(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(transitivity,[status(thm)],[16230, 16228])).
% 87.63/87.86 tff(16232,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~node18(c_e_h_3, c_h, s4, s5)))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16233,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node18(c_e_h_3, c_h, s4, s5))),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16232, 16231])).
% 87.63/87.86 tff(16234,plain,
% 87.63/87.86 ($false),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16233, 124, 16178, 16179, 16227])).
% 87.63/87.86 tff(16235,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.86 tff(16236,plain,
% 87.63/87.86 (m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16235, 16179, 16178])).
% 87.63/87.86 tff(16237,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s4)), introduced(assumption)).
% 87.63/87.86 tff(16238,plain,
% 87.63/87.86 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16239,plain,
% 87.63/87.86 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16240,plain,
% 87.63/87.86 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)))),
% 87.63/87.86 inference(monotonicity,[status(thm)],[16239])).
% 87.63/87.86 tff(16241,plain,
% 87.63/87.86 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(transitivity,[status(thm)],[16240, 16238])).
% 87.63/87.86 tff(16242,plain,
% 87.63/87.86 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16243,plain,
% 87.63/87.86 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16242, 16241])).
% 87.63/87.86 tff(16244,plain,
% 87.63/87.86 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4))),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16243, 209, 16237])).
% 87.63/87.86 tff(16245,plain,
% 87.63/87.86 (~node17(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16244, 16236])).
% 87.63/87.86 tff(16246,plain,
% 87.63/87.86 (node18(c_e_h_3, c_h, s4, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16226, 16245])).
% 87.63/87.86 tff(16247,plain,
% 87.63/87.86 ($false),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16233, 124, 16178, 16179, 16246])).
% 87.63/87.86 tff(16248,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.86 tff(16249,plain,
% 87.63/87.86 ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16248, 13281])).
% 87.63/87.86 tff(16250,plain,
% 87.63/87.86 (~m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16249, 16177])).
% 87.63/87.86 tff(16251,plain,
% 87.63/87.86 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16252,plain,
% 87.63/87.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16253,plain,
% 87.63/87.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16252, 16251])).
% 87.63/87.86 tff(16254,plain,
% 87.63/87.86 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16253, 23, 16250])).
% 87.63/87.86 tff(16255,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)), introduced(assumption)).
% 87.63/87.86 tff(16256,assumption,(node20(c_e_h_3, c_i, s5)), introduced(assumption)).
% 87.63/87.86 tff(16257,plain,
% 87.63/87.86 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16258,plain,
% 87.63/87.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16259,plain,
% 87.63/87.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16258, 16257])).
% 87.63/87.86 tff(16260,plain,
% 87.63/87.86 ($false),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16259, 37, 16256, 16255])).
% 87.63/87.86 tff(16261,plain,(m_and_h_gate_v_in1(c_e_h_3, c_i, s5) | (~node20(c_e_h_3, c_i, s5))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.86 tff(16262,plain,
% 87.63/87.86 (~node20(c_e_h_3, c_i, s5)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16261, 16254])).
% 87.63/87.86 tff(16263,assumption,(~node20(c_e_h_3, c_i, s5)), introduced(assumption)).
% 87.63/87.86 tff(16264,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s6)), introduced(assumption)).
% 87.63/87.86 tff(16265,assumption,(node21(c_e_h_3, c_i, s5, s6)), introduced(assumption)).
% 87.63/87.86 tff(16266,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6)))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16267,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6)))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16268,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6))),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16267, 16266])).
% 87.63/87.86 tff(16269,plain,
% 87.63/87.86 ($false),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16268, 51, 16264, 16265, 16263])).
% 87.63/87.86 tff(16270,plain,((~node21(c_e_h_3, c_i, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.86 tff(16271,plain,
% 87.63/87.86 (~node21(c_e_h_3, c_i, s5, s6)),
% 87.63/87.86 inference(unit_resolution,[status(thm)],[16270, 16264, 16263])).
% 87.63/87.86 tff(16272,plain,
% 87.63/87.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6))),
% 87.63/87.86 inference(rewrite,[status(thm)],[])).
% 87.63/87.86 tff(16273,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6))),
% 87.63/87.86 inference(quant_inst,[status(thm)],[])).
% 87.63/87.86 tff(16274,plain,
% 87.63/87.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6)),
% 87.63/87.86 inference(modus_ponens,[status(thm)],[16273, 16272])).
% 87.63/87.87 tff(16275,plain,
% 87.63/87.87 (node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16274, 81, 1499])).
% 87.63/87.87 tff(16276,plain,
% 87.63/87.87 (node22(c_e_h_3, c_i, s5, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16275, 16271])).
% 87.63/87.87 tff(16277,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16278,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16279,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16278, 16277])).
% 87.63/87.87 tff(16280,plain,
% 87.63/87.87 ($false),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16279, 107, 16264, 13312, 16276])).
% 87.63/87.87 tff(16281,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5) | node20(c_e_h_3, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.87 tff(16282,plain,
% 87.63/87.87 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16281, 13310])).
% 87.63/87.87 tff(16283,plain,
% 87.63/87.87 (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16282, 16262])).
% 87.63/87.87 tff(16284,plain,
% 87.63/87.87 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16285,plain,
% 87.63/87.87 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16286,plain,
% 87.63/87.87 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16285, 16284])).
% 87.63/87.87 tff(16287,plain,
% 87.63/87.87 (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16286, 2218, 16283])).
% 87.63/87.87 tff(16288,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s7)), introduced(assumption)).
% 87.63/87.87 tff(16289,assumption,(node18(c_e_h_3, c_f, s6, s7)), introduced(assumption)).
% 87.63/87.87 tff(16290,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16291,plain,
% 87.63/87.87 (((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16292,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7))))),
% 87.63/87.87 inference(monotonicity,[status(thm)],[16291])).
% 87.63/87.87 tff(16293,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))),
% 87.63/87.87 inference(transitivity,[status(thm)],[16292, 16290])).
% 87.63/87.87 tff(16294,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16295,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16294, 16293])).
% 87.63/87.87 tff(16296,plain,
% 87.63/87.87 ($false),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16295, 124, 16288, 13405, 16289])).
% 87.63/87.87 tff(16297,plain,((~node18(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.87 tff(16298,plain,
% 87.63/87.87 (~node18(c_e_h_3, c_f, s6, s7)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16297, 16288, 13405])).
% 87.63/87.87 tff(16299,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_f, s6, s7))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16300,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_f, s6, s7))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16301,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_f, s6, s7)),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16300, 16299])).
% 87.63/87.87 tff(16302,plain,
% 87.63/87.87 (node19(c_e_h_3, c_f, s6, s7)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16301, 141, 1552])).
% 87.63/87.87 tff(16303,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7) | node17(c_e_h_3, c_f, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7) | node17(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16304,plain,
% 87.63/87.87 ((node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7))) <=> ((~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7) | node17(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16305,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7) | node17(c_e_h_3, c_f, s6)))),
% 87.63/87.87 inference(monotonicity,[status(thm)],[16304])).
% 87.63/87.87 tff(16306,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7) | node17(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(transitivity,[status(thm)],[16305, 16303])).
% 87.63/87.87 tff(16307,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16308,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7) | node17(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16307, 16306])).
% 87.63/87.87 tff(16309,plain,
% 87.63/87.87 (node18(c_e_h_3, c_f, s6, s7) | node17(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16308, 156, 16302])).
% 87.63/87.87 tff(16310,plain,
% 87.63/87.87 (node17(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16309, 16298])).
% 87.63/87.87 tff(16311,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s6)), introduced(assumption)).
% 87.63/87.87 tff(16312,plain,
% 87.63/87.87 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~node17(c_e_h_3, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~node17(c_e_h_3, c_f, s6)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16313,plain,
% 87.63/87.87 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~node17(c_e_h_3, c_f, s6)))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16314,plain,
% 87.63/87.87 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~node17(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16313, 16312])).
% 87.63/87.87 tff(16315,plain,
% 87.63/87.87 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | (~node17(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16314, 209, 16311])).
% 87.63/87.87 tff(16316,plain,
% 87.63/87.87 (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16315, 16310])).
% 87.63/87.87 tff(16317,assumption,(node15(c_e_h_3, c_f, s6, s7)), introduced(assumption)).
% 87.63/87.87 tff(16318,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | (~node15(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | (~node15(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16319,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | (~node15(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16320,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | (~node15(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16319, 16318])).
% 87.63/87.87 tff(16321,plain,
% 87.63/87.87 ($false),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16320, 173, 16288, 13405, 16317])).
% 87.63/87.87 tff(16322,plain,((~node15(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.87 tff(16323,plain,
% 87.63/87.87 (~node15(c_e_h_3, c_f, s6, s7)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16322, 16288, 13405])).
% 87.63/87.87 tff(16324,assumption,(node17(c_e_h_3, c_f, s6)), introduced(assumption)).
% 87.63/87.87 tff(16325,assumption,(node16(c_e_h_3, c_f, s6)), introduced(assumption)).
% 87.63/87.87 tff(16326,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s6)), introduced(assumption)).
% 87.63/87.87 tff(16327,plain,
% 87.63/87.87 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | (~node17(c_e_h_3, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | (~node17(c_e_h_3, c_f, s6)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16328,plain,
% 87.63/87.87 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | (~node17(c_e_h_3, c_f, s6)))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16329,plain,
% 87.63/87.87 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | (~node17(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16328, 16327])).
% 87.63/87.87 tff(16330,plain,
% 87.63/87.87 (m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16329, 245, 16324])).
% 87.63/87.87 tff(16331,plain,
% 87.63/87.87 (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16330, 16326])).
% 87.63/87.87 tff(16332,plain,
% 87.63/87.87 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16333,plain,
% 87.63/87.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16334,plain,
% 87.63/87.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16333, 16332])).
% 87.63/87.87 tff(16335,plain,
% 87.63/87.87 (m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16334, 228, 16325])).
% 87.63/87.87 tff(16336,plain,
% 87.63/87.87 ($false),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16335, 16331, 16326])).
% 87.63/87.87 tff(16337,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node16(c_e_h_3, c_f, s6)) | (~node17(c_e_h_3, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.87 tff(16338,plain,
% 87.63/87.87 (m_c_h_element_v_in1(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16337, 16325, 16324])).
% 87.63/87.87 tff(16339,plain,
% 87.63/87.87 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16314, 209, 16324])).
% 87.63/87.87 tff(16340,plain,
% 87.63/87.87 (m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16339, 16338])).
% 87.63/87.87 tff(16341,plain,
% 87.63/87.87 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16342,plain,
% 87.63/87.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16343,plain,
% 87.63/87.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16342, 16341])).
% 87.63/87.87 tff(16344,plain,
% 87.63/87.87 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16343, 263, 16325])).
% 87.63/87.87 tff(16345,plain,
% 87.63/87.87 ($false),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16344, 16340, 16338])).
% 87.63/87.87 tff(16346,plain,((~node16(c_e_h_3, c_f, s6)) | (~node17(c_e_h_3, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.87 tff(16347,plain,
% 87.63/87.87 (~node16(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16346, 16310])).
% 87.63/87.87 tff(16348,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s6, s7)) | node15(c_e_h_3, c_f, s6, s7) | node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s6, s7)) | node15(c_e_h_3, c_f, s6, s7) | node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16349,plain,
% 87.63/87.87 ((node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7))) <=> ((~node19(c_e_h_3, c_f, s6, s7)) | node15(c_e_h_3, c_f, s6, s7) | node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16350,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s6, s7)) | node15(c_e_h_3, c_f, s6, s7) | node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7)))),
% 87.63/87.87 inference(monotonicity,[status(thm)],[16349])).
% 87.63/87.87 tff(16351,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s6, s7)) | node15(c_e_h_3, c_f, s6, s7) | node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7))),
% 87.63/87.87 inference(transitivity,[status(thm)],[16350, 16348])).
% 87.63/87.87 tff(16352,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16353,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s6, s7)) | node15(c_e_h_3, c_f, s6, s7) | node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7)),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16352, 16351])).
% 87.63/87.87 tff(16354,plain,
% 87.63/87.87 (node15(c_e_h_3, c_f, s6, s7) | node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16353, 189, 16302])).
% 87.63/87.87 tff(16355,plain,
% 87.63/87.87 (node14(c_e_h_3, c_f, s6, s7)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16354, 16347, 16323])).
% 87.63/87.87 tff(16356,assumption,(node14(c_e_h_3, c_f, s6, s7)), introduced(assumption)).
% 87.63/87.87 tff(16357,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16358,plain,
% 87.63/87.87 (((~node14(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16359,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7))))),
% 87.63/87.87 inference(monotonicity,[status(thm)],[16358])).
% 87.63/87.87 tff(16360,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7)))),
% 87.63/87.87 inference(transitivity,[status(thm)],[16359, 16357])).
% 87.63/87.87 tff(16361,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16362,plain,
% 87.63/87.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7))),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16361, 16360])).
% 87.63/87.87 tff(16363,plain,
% 87.63/87.87 ($false),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16362, 283, 16288, 16356, 16326])).
% 87.63/87.87 tff(16364,plain,((~node14(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.87 tff(16365,plain,
% 87.63/87.87 ($false),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16364, 16355, 16316, 16288])).
% 87.63/87.87 tff(16366,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.87 tff(16367,plain,
% 87.63/87.87 ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16366, 13403])).
% 87.63/87.87 tff(16368,plain,
% 87.63/87.87 (~m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16367, 16287])).
% 87.63/87.87 tff(16369,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)), introduced(assumption)).
% 87.63/87.87 tff(16370,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s7)), introduced(assumption)).
% 87.63/87.87 tff(16371,plain,
% 87.63/87.87 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16372,plain,
% 87.63/87.87 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 87.63/87.87 inference(quant_inst,[status(thm)],[])).
% 87.63/87.87 tff(16373,plain,
% 87.63/87.87 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 87.63/87.87 inference(modus_ponens,[status(thm)],[16372, 16371])).
% 87.63/87.87 tff(16374,plain,
% 87.63/87.87 ($false),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16373, 6389, 16370, 16369])).
% 87.63/87.87 tff(16375,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.87 tff(16376,plain,
% 87.63/87.87 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[16375, 16368])).
% 87.63/87.87 tff(16377,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)), introduced(assumption)).
% 87.63/87.87 tff(16378,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)), introduced(assumption)).
% 87.63/87.87 tff(16379,plain,
% 87.63/87.87 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[13417, 12002])).
% 87.63/87.87 tff(16380,plain,
% 87.63/87.87 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)),
% 87.63/87.87 inference(unit_resolution,[status(thm)],[13444, 16379, 11986, 13420])).
% 87.63/87.87 tff(16381,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)), introduced(assumption)).
% 87.63/87.87 tff(16382,assumption,(node10(c_e_h_3, c_m, s7, s8)), introduced(assumption)).
% 87.63/87.87 tff(16383,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16384,plain,
% 87.63/87.87 (((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8)))),
% 87.63/87.87 inference(rewrite,[status(thm)],[])).
% 87.63/87.87 tff(16385,plain,
% 87.63/87.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8))))),
% 87.63/87.88 inference(monotonicity,[status(thm)],[16384])).
% 87.63/87.88 tff(16386,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8)))),
% 87.63/87.88 inference(transitivity,[status(thm)],[16385, 16383])).
% 87.63/87.88 tff(16387,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16388,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8))),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16387, 16386])).
% 87.63/87.88 tff(16389,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16388, 1191, 16377, 16382, 16378, 16381])).
% 87.63/87.88 tff(16390,plain,((~node10(c_e_h_3, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16391,plain,
% 87.63/87.88 (~node10(c_e_h_3, c_m, s7, s8)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16390, 16377, 16378, 16381])).
% 87.63/87.88 tff(16392,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)), introduced(assumption)).
% 87.63/87.88 tff(16393,assumption,(node11(c_e_h_3, c_m, s7, s8)), introduced(assumption)).
% 87.63/87.88 tff(16394,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | (~node11(c_e_h_3, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | (~node11(c_e_h_3, c_m, s7, s8)))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16395,plain,
% 87.63/87.88 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | (~node11(c_e_h_3, c_m, s7, s8)))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16396,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | (~node11(c_e_h_3, c_m, s7, s8))))),
% 87.63/87.88 inference(monotonicity,[status(thm)],[16395])).
% 87.63/87.88 tff(16397,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | (~node11(c_e_h_3, c_m, s7, s8)))),
% 87.63/87.88 inference(transitivity,[status(thm)],[16396, 16394])).
% 87.63/87.88 tff(16398,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16399,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | (~node11(c_e_h_3, c_m, s7, s8))),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16398, 16397])).
% 87.63/87.88 tff(16400,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16399, 1161, 16392, 16377, 16393])).
% 87.63/87.88 tff(16401,plain,((~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16402,plain,
% 87.63/87.88 (~node11(c_e_h_3, c_m, s7, s8)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16401, 16377, 16392])).
% 87.63/87.88 tff(16403,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16404,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16405,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8)),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16404, 16403])).
% 87.63/87.88 tff(16406,plain,
% 87.63/87.88 (node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16405, 1092, 2152])).
% 87.63/87.88 tff(16407,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16406, 16402, 16391])).
% 87.63/87.88 tff(16408,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16409,plain,
% 87.63/87.88 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16408, 16380, 16378, 16377])).
% 87.63/87.88 tff(16410,plain,
% 87.63/87.88 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[12023, 12002, 12001])).
% 87.63/87.88 tff(16411,plain,
% 87.63/87.88 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16412,plain,
% 87.63/87.88 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16413,plain,
% 87.63/87.88 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16412, 16411])).
% 87.63/87.88 tff(16414,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16413, 6378, 16410, 16409])).
% 87.63/87.88 tff(16415,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | node9(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16416,plain,
% 87.63/87.88 ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | node9(c_e_h_3, c_n, s6)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16415, 11479])).
% 87.63/87.88 tff(16417,plain,
% 87.63/87.88 ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16416, 11984, 12000])).
% 87.63/87.88 tff(16418,plain,
% 87.63/87.88 ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16417, 13411])).
% 87.63/87.88 tff(16419,plain,
% 87.63/87.88 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16418, 16376])).
% 87.63/87.88 tff(16420,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)), introduced(assumption)).
% 87.63/87.88 tff(16421,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)), introduced(assumption)).
% 87.63/87.88 tff(16422,plain,
% 87.63/87.88 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16423,plain,
% 87.63/87.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16424,plain,
% 87.63/87.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16423, 16422])).
% 87.63/87.88 tff(16425,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16424, 6442, 16421, 16420])).
% 87.63/87.88 tff(16426,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16427,plain,
% 87.63/87.88 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16426, 16419])).
% 87.63/87.88 tff(16428,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)), introduced(assumption)).
% 87.63/87.88 tff(16429,assumption,(node9(c_e_h_3, c_n, s8)), introduced(assumption)).
% 87.63/87.88 tff(16430,plain,
% 87.63/87.88 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16431,plain,
% 87.63/87.88 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16432,plain,
% 87.63/87.88 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16431, 16430])).
% 87.63/87.88 tff(16433,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16432, 1062, 16429, 16428])).
% 87.63/87.88 tff(16434,plain,((~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16435,plain,
% 87.63/87.88 (~node9(c_e_h_3, c_n, s8)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16434, 16427])).
% 87.63/87.88 tff(16436,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)), introduced(assumption)).
% 87.63/87.88 tff(16437,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)), introduced(assumption)).
% 87.63/87.88 tff(16438,assumption,(node11(c_e_h_3, c_n, s8, s9)), introduced(assumption)).
% 87.63/87.88 tff(16439,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16440,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16441,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16440, 16439])).
% 87.63/87.88 tff(16442,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16441, 1130, 16438, 16437, 16436])).
% 87.63/87.88 tff(16443,plain,((~node11(c_e_h_3, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16444,plain,
% 87.63/87.88 (~node11(c_e_h_3, c_n, s8, s9)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16443, 16437, 16436])).
% 87.63/87.88 tff(16445,assumption,(~node9(c_e_h_3, c_n, s8)), introduced(assumption)).
% 87.63/87.88 tff(16446,assumption,(node10(c_e_h_3, c_n, s8, s9)), introduced(assumption)).
% 87.63/87.88 tff(16447,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9)))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16448,plain,
% 87.63/87.88 ((node9(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node10(c_e_h_3, c_n, s8, s9))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9)))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16449,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node10(c_e_h_3, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9))))),
% 87.63/87.88 inference(monotonicity,[status(thm)],[16448])).
% 87.63/87.88 tff(16450,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node10(c_e_h_3, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9)))),
% 87.63/87.88 inference(transitivity,[status(thm)],[16449, 16447])).
% 87.63/87.88 tff(16451,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node10(c_e_h_3, c_n, s8, s9)))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16452,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9))),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16451, 16450])).
% 87.63/87.88 tff(16453,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16452, 1076, 16446, 16437, 16445])).
% 87.63/87.88 tff(16454,plain,((~node10(c_e_h_3, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16455,plain,
% 87.63/87.88 (~node10(c_e_h_3, c_n, s8, s9)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16454, 16437, 16445])).
% 87.63/87.88 tff(16456,plain,
% 87.63/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9))),
% 87.63/87.88 inference(rewrite,[status(thm)],[])).
% 87.63/87.88 tff(16457,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9))),
% 87.63/87.88 inference(quant_inst,[status(thm)],[])).
% 87.63/87.88 tff(16458,plain,
% 87.63/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9)),
% 87.63/87.88 inference(modus_ponens,[status(thm)],[16457, 16456])).
% 87.63/87.88 tff(16459,plain,
% 87.63/87.88 (node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16458, 1092, 2636])).
% 87.63/87.88 tff(16460,plain,
% 87.63/87.88 ($false),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16459, 16455, 16444])).
% 87.63/87.88 tff(16461,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)), inference(lemma,lemma(discharge,[]))).
% 87.63/87.88 tff(16462,plain,
% 87.63/87.88 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16461, 13480])).
% 87.63/87.88 tff(16463,plain,
% 87.63/87.88 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 87.63/87.88 inference(unit_resolution,[status(thm)],[16462, 16435])).
% 87.63/87.88 tff(16464,plain,
% 87.63/87.88 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 87.71/87.88 inference(rewrite,[status(thm)],[])).
% 87.71/87.88 tff(16465,plain,
% 87.71/87.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 87.71/87.88 inference(quant_inst,[status(thm)],[])).
% 87.71/87.88 tff(16466,plain,
% 87.71/87.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 87.71/87.88 inference(modus_ponens,[status(thm)],[16465, 16464])).
% 87.71/87.88 tff(16467,plain,
% 87.71/87.88 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16466, 6513, 16463])).
% 87.71/87.88 tff(16468,plain,
% 87.71/87.88 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s9))),
% 87.71/87.88 inference(rewrite,[status(thm)],[])).
% 87.71/87.88 tff(16469,plain,
% 87.71/87.88 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s9))),
% 87.71/87.88 inference(quant_inst,[status(thm)],[])).
% 87.71/87.88 tff(16470,plain,
% 87.71/87.88 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s9)),
% 87.71/87.88 inference(modus_ponens,[status(thm)],[16469, 16468])).
% 87.71/87.88 tff(16471,plain,
% 87.71/87.88 (~node20(c_e_h_3, c_q, s9)),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16470, 1535, 16467])).
% 87.71/87.88 tff(16472,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s10)), introduced(assumption)).
% 87.71/87.88 tff(16473,assumption,(node22(c_e_h_3, c_q, s9, s10)), introduced(assumption)).
% 87.71/87.88 tff(16474,plain,
% 87.71/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))),
% 87.71/87.88 inference(rewrite,[status(thm)],[])).
% 87.71/87.88 tff(16475,plain,
% 87.71/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))),
% 87.71/87.88 inference(quant_inst,[status(thm)],[])).
% 87.71/87.88 tff(16476,plain,
% 87.71/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 87.71/87.88 inference(modus_ponens,[status(thm)],[16475, 16474])).
% 87.71/87.88 tff(16477,plain,
% 87.71/87.88 ($false),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16476, 107, 16472, 13513, 16473])).
% 87.71/87.88 tff(16478,plain,((~node22(c_e_h_3, c_q, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.88 tff(16479,plain,
% 87.71/87.88 (~node22(c_e_h_3, c_q, s9, s10)),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16478, 16472])).
% 87.71/87.88 tff(16480,assumption,(~node20(c_e_h_3, c_q, s9)), introduced(assumption)).
% 87.71/87.88 tff(16481,assumption,(node21(c_e_h_3, c_q, s9, s10)), introduced(assumption)).
% 87.71/87.88 tff(16482,plain,
% 87.71/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node21(c_e_h_3, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node21(c_e_h_3, c_q, s9, s10)))),
% 87.71/87.88 inference(rewrite,[status(thm)],[])).
% 87.71/87.88 tff(16483,plain,
% 87.71/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node21(c_e_h_3, c_q, s9, s10)))),
% 87.71/87.88 inference(quant_inst,[status(thm)],[])).
% 87.71/87.88 tff(16484,plain,
% 87.71/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node21(c_e_h_3, c_q, s9, s10))),
% 87.71/87.88 inference(modus_ponens,[status(thm)],[16483, 16482])).
% 87.71/87.88 tff(16485,plain,
% 87.71/87.88 ($false),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16484, 51, 16472, 16481, 16480])).
% 87.71/87.88 tff(16486,plain,((~node21(c_e_h_3, c_q, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.88 tff(16487,plain,
% 87.71/87.88 (~node21(c_e_h_3, c_q, s9, s10)),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16486, 16472, 16480])).
% 87.71/87.88 tff(16488,plain,
% 87.71/87.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10))),
% 87.71/87.88 inference(rewrite,[status(thm)],[])).
% 87.71/87.88 tff(16489,plain,
% 87.71/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10))),
% 87.71/87.88 inference(quant_inst,[status(thm)],[])).
% 87.71/87.88 tff(16490,plain,
% 87.71/87.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10)),
% 87.71/87.88 inference(modus_ponens,[status(thm)],[16489, 16488])).
% 87.71/87.88 tff(16491,plain,
% 87.71/87.88 (node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10)),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16490, 81, 3175])).
% 87.71/87.88 tff(16492,plain,
% 87.71/87.88 ($false),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16491, 16487, 16479])).
% 87.71/87.88 tff(16493,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.88 tff(16494,plain,
% 87.71/87.88 (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16493, 16471])).
% 87.71/87.88 tff(16495,plain,
% 87.71/87.88 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s10))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s10))),
% 87.71/87.88 inference(rewrite,[status(thm)],[])).
% 87.71/87.88 tff(16496,plain,
% 87.71/87.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s10))),
% 87.71/87.88 inference(quant_inst,[status(thm)],[])).
% 87.71/87.88 tff(16497,plain,
% 87.71/87.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s10)),
% 87.71/87.88 inference(modus_ponens,[status(thm)],[16496, 16495])).
% 87.71/87.88 tff(16498,plain,
% 87.71/87.88 (node3(c_e_h_3, c_e_h_1, s10)),
% 87.71/87.88 inference(unit_resolution,[status(thm)],[16497, 3860, 814])).
% 87.71/87.88 tff(16499,plain,
% 87.71/87.88 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s10)) | (~node3(c_e_h_3, c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s10)) | (~node3(c_e_h_3, c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))),
% 87.71/87.88 inference(rewrite,[status(thm)],[])).
% 87.71/87.88 tff(16500,plain,
% 87.71/87.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s10)) | (~node3(c_e_h_3, c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16501,plain,
% 87.71/87.89 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s10)) | (~node3(c_e_h_3, c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16500, 16499])).
% 87.71/87.89 tff(16502,plain,
% 87.71/87.89 ((~m_cell_v_ack(c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16501, 836, 16498])).
% 87.71/87.89 tff(16503,plain,
% 87.71/87.89 (~m_cell_v_ack(c_e_h_1, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16502, 16494])).
% 87.71/87.89 tff(16504,plain,
% 87.71/87.89 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)) | m_cell_v_ack(c_e_h_1, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)) | m_cell_v_ack(c_e_h_1, s10))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16505,plain,
% 87.71/87.89 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)) | m_cell_v_ack(c_e_h_1, s10))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16506,plain,
% 87.71/87.89 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)) | m_cell_v_ack(c_e_h_1, s10)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16505, 16504])).
% 87.71/87.89 tff(16507,plain,
% 87.71/87.89 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16506, 848, 16503])).
% 87.71/87.89 tff(16508,plain,
% 87.71/87.89 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16509,plain,
% 87.71/87.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16510,plain,
% 87.71/87.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16509, 16508])).
% 87.71/87.89 tff(16511,plain,
% 87.71/87.89 ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16510, 1638])).
% 87.71/87.89 tff(16512,plain,
% 87.71/87.89 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16511, 6887])).
% 87.71/87.89 tff(16513,plain,
% 87.71/87.89 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s9))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16514,plain,
% 87.71/87.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s9))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16515,plain,
% 87.71/87.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s9)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16514, 16513])).
% 87.71/87.89 tff(16516,plain,
% 87.71/87.89 (~node20(c_e_h_1, c_l, s9)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16515, 1535, 16512])).
% 87.71/87.89 tff(16517,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s10)), introduced(assumption)).
% 87.71/87.89 tff(16518,assumption,(node22(c_e_h_1, c_l, s9, s10)), introduced(assumption)).
% 87.71/87.89 tff(16519,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node22(c_e_h_1, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node22(c_e_h_1, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16520,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node22(c_e_h_1, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16521,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node22(c_e_h_1, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16520, 16519])).
% 87.71/87.89 tff(16522,plain,
% 87.71/87.89 ($false),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16521, 107, 12952, 16518, 16517])).
% 87.71/87.89 tff(16523,plain,((~node22(c_e_h_1, c_l, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.89 tff(16524,plain,
% 87.71/87.89 (~node22(c_e_h_1, c_l, s9, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16523, 16517])).
% 87.71/87.89 tff(16525,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16526,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16527,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16526, 16525])).
% 87.71/87.89 tff(16528,plain,
% 87.71/87.89 (node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16527, 81, 3175])).
% 87.71/87.89 tff(16529,plain,
% 87.71/87.89 (node21(c_e_h_1, c_l, s9, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16528, 16524])).
% 87.71/87.89 tff(16530,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node21(c_e_h_1, c_l, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node21(c_e_h_1, c_l, s9, s10)))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16531,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node21(c_e_h_1, c_l, s9, s10)))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16532,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node21(c_e_h_1, c_l, s9, s10))),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16531, 16530])).
% 87.71/87.89 tff(16533,plain,
% 87.71/87.89 ($false),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16532, 51, 16529, 16517, 16516])).
% 87.71/87.89 tff(16534,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.89 tff(16535,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s10)), introduced(assumption)).
% 87.71/87.89 tff(16536,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s10)), introduced(assumption)).
% 87.71/87.89 tff(16537,plain,
% 87.71/87.89 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16538,plain,
% 87.71/87.89 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16539,plain,
% 87.71/87.89 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16538, 16537])).
% 87.71/87.89 tff(16540,plain,
% 87.71/87.89 ($false),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16539, 801, 16536, 16535])).
% 87.71/87.89 tff(16541,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.89 tff(16542,plain,
% 87.71/87.89 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16541, 16534])).
% 87.71/87.89 tff(16543,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)), introduced(assumption)).
% 87.71/87.89 tff(16544,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)), introduced(assumption)).
% 87.71/87.89 tff(16545,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s11)), introduced(assumption)).
% 87.71/87.89 tff(16546,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s10)), introduced(assumption)).
% 87.71/87.89 tff(16547,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16548,plain,
% 87.71/87.89 (((~node6(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16549,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)))),
% 87.71/87.89 inference(monotonicity,[status(thm)],[16548])).
% 87.71/87.89 tff(16550,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 87.71/87.89 inference(transitivity,[status(thm)],[16549, 16547])).
% 87.71/87.89 tff(16551,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16552,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16551, 16550])).
% 87.71/87.89 tff(16553,plain,
% 87.71/87.89 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16552, 899])).
% 87.71/87.89 tff(16554,plain,
% 87.71/87.89 (~node6(c_e_h_1, c_j, s10, s11)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16553, 16545, 16546])).
% 87.71/87.89 tff(16555,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16556,plain,
% 87.71/87.89 ((node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11) | (~trans(s10, s11))) <=> ((~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16557,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11)))),
% 87.71/87.89 inference(monotonicity,[status(thm)],[16556])).
% 87.71/87.89 tff(16558,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11))),
% 87.71/87.89 inference(transitivity,[status(thm)],[16557, 16555])).
% 87.71/87.89 tff(16559,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11) | (~trans(s10, s11)))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16560,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16559, 16558])).
% 87.71/87.89 tff(16561,plain,
% 87.71/87.89 (node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16560, 881, 3778])).
% 87.71/87.89 tff(16562,plain,
% 87.71/87.89 (node5(c_e_h_1, c_j, s10, s11)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16561, 16554])).
% 87.71/87.89 tff(16563,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16564,plain,
% 87.71/87.89 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16565,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11))))),
% 87.71/87.89 inference(monotonicity,[status(thm)],[16564])).
% 87.71/87.89 tff(16566,plain,
% 87.71/87.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)))),
% 87.71/87.89 inference(transitivity,[status(thm)],[16565, 16563])).
% 87.71/87.89 tff(16567,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16568,plain,
% 87.71/87.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11))),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16567, 16566])).
% 87.71/87.89 tff(16569,plain,
% 87.71/87.89 ($false),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16568, 862, 16562, 16545, 16544, 16543])).
% 87.71/87.89 tff(16570,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.89 tff(16571,plain,
% 87.71/87.89 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16570, 13534])).
% 87.71/87.89 tff(16572,plain,
% 87.71/87.89 (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16571, 16542, 16507])).
% 87.71/87.89 tff(16573,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s11)), introduced(assumption)).
% 87.71/87.89 tff(16574,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s11)), introduced(assumption)).
% 87.71/87.89 tff(16575,plain,
% 87.71/87.89 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16576,plain,
% 87.71/87.89 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16577,plain,
% 87.71/87.89 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11)),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16576, 16575])).
% 87.71/87.89 tff(16578,plain,
% 87.71/87.89 ($false),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16577, 309, 16574, 16573])).
% 87.71/87.89 tff(16579,plain,((~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.89 tff(16580,plain,
% 87.71/87.89 (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16579, 16572])).
% 87.71/87.89 tff(16581,plain,
% 87.71/87.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11)))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16582,plain,
% 87.71/87.89 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11)))),
% 87.71/87.89 inference(rewrite,[status(thm)],[])).
% 87.71/87.89 tff(16583,plain,
% 87.71/87.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11))))),
% 87.71/87.89 inference(monotonicity,[status(thm)],[16582])).
% 87.71/87.89 tff(16584,plain,
% 87.71/87.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11)))),
% 87.71/87.89 inference(transitivity,[status(thm)],[16583, 16581])).
% 87.71/87.89 tff(16585,plain,
% 87.71/87.89 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11)))),
% 87.71/87.89 inference(quant_inst,[status(thm)],[])).
% 87.71/87.89 tff(16586,plain,
% 87.71/87.89 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11))),
% 87.71/87.89 inference(modus_ponens,[status(thm)],[16585, 16584])).
% 87.71/87.89 tff(16587,plain,
% 87.71/87.89 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11))),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16586, 209, 16580])).
% 87.71/87.89 tff(16588,plain,
% 87.71/87.89 (~node17(c_e_h_1, c_h, s11)),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[16587, 15914])).
% 87.71/87.89 tff(16589,plain,
% 87.71/87.89 ($false),
% 87.71/87.89 inference(unit_resolution,[status(thm)],[15871, 16588, 15858])).
% 87.71/87.89 tff(16590,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.89 tff(16591,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s4)), introduced(assumption)).
% 87.71/87.89 tff(16592,assumption,(node21(c_e_h_3, c_l, s3, s4)), introduced(assumption)).
% 87.71/87.89 tff(16593,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s3)), introduced(assumption)).
% 87.71/87.89 tff(16594,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s1)), introduced(assumption)).
% 87.71/87.89 tff(16595,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s1)), introduced(assumption)).
% 87.71/87.89 tff(16596,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), introduced(assumption)).
% 87.71/87.89 tff(16597,plain,
% 87.71/87.89 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16598,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16597, 465, 16596])).
% 87.71/87.90 tff(16599,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16600,plain,
% 87.71/87.90 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16601,plain,
% 87.71/87.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16602,plain,
% 87.71/87.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16601, 16600])).
% 87.71/87.90 tff(16603,plain,
% 87.71/87.90 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16602, 477, 16599])).
% 87.71/87.90 tff(16604,plain,
% 87.71/87.90 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16605,plain,
% 87.71/87.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16606,plain,
% 87.71/87.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16605, 16604])).
% 87.71/87.90 tff(16607,plain,
% 87.71/87.90 (~node20(c_e_h_3, c_c, s0)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16606, 37, 16603])).
% 87.71/87.90 tff(16608,assumption,(node21(c_e_h_3, c_c, s0, s1)), introduced(assumption)).
% 87.71/87.90 tff(16609,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1)))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16610,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1)))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16611,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1))),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16610, 16609])).
% 87.71/87.90 tff(16612,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16611, 51, 16608, 16595, 16607])).
% 87.71/87.90 tff(16613,plain,((~node21(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16614,plain,
% 87.71/87.90 (~node21(c_e_h_3, c_c, s0, s1)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16613, 16595])).
% 87.71/87.90 tff(16615,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s0)), introduced(assumption)).
% 87.71/87.90 tff(16616,assumption,(node22(c_e_h_3, c_c, s0, s1)), introduced(assumption)).
% 87.71/87.90 tff(16617,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16618,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16619,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16618, 16617])).
% 87.71/87.90 tff(16620,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16619, 107, 16616, 16615, 16595])).
% 87.71/87.90 tff(16621,plain,((~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16622,plain,
% 87.71/87.90 ((~node22(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16621, 15934])).
% 87.71/87.90 tff(16623,plain,
% 87.71/87.90 (~node22(c_e_h_3, c_c, s0, s1)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16622, 16595])).
% 87.71/87.90 tff(16624,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16625,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16626,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16625, 16624])).
% 87.71/87.90 tff(16627,plain,
% 87.71/87.90 (node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16626, 81, 71])).
% 87.71/87.90 tff(16628,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16627, 16623, 16614])).
% 87.71/87.90 tff(16629,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16630,plain,
% 87.71/87.90 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16631,plain,
% 87.71/87.90 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16632,plain,
% 87.71/87.90 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16631, 16630])).
% 87.71/87.90 tff(16633,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16632, 15941, 16629, 16594])).
% 87.71/87.90 tff(16634,plain,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16635,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)), introduced(assumption)).
% 87.71/87.90 tff(16636,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s2)), introduced(assumption)).
% 87.71/87.90 tff(16637,plain,
% 87.71/87.90 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16638,plain,
% 87.71/87.90 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16639,plain,
% 87.71/87.90 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16638, 16637])).
% 87.71/87.90 tff(16640,plain,
% 87.71/87.90 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16639, 15952, 7769])).
% 87.71/87.90 tff(16641,assumption,(node5(c_e_h_3, c_g, s1, s2)), introduced(assumption)).
% 87.71/87.90 tff(16642,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16643,plain,
% 87.71/87.90 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2))) <=> (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16644,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2))))),
% 87.71/87.90 inference(monotonicity,[status(thm)],[16643])).
% 87.71/87.90 tff(16645,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)))),
% 87.71/87.90 inference(transitivity,[status(thm)],[16644, 16642])).
% 87.71/87.90 tff(16646,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16647,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2))),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16646, 16645])).
% 87.71/87.90 tff(16648,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16647, 862, 16641, 16636, 16640, 16635])).
% 87.71/87.90 tff(16649,plain,((~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16650,plain,
% 87.71/87.90 (~node5(c_e_h_3, c_g, s1, s2)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16649, 16636, 16635])).
% 87.71/87.90 tff(16651,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s1)), introduced(assumption)).
% 87.71/87.90 tff(16652,assumption,(node6(c_e_h_3, c_g, s1, s2)), introduced(assumption)).
% 87.71/87.90 tff(16653,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | (~node6(c_e_h_3, c_g, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | (~node6(c_e_h_3, c_g, s1, s2)))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16654,plain,
% 87.71/87.90 (((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | (~node6(c_e_h_3, c_g, s1, s2)))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16655,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | (~node6(c_e_h_3, c_g, s1, s2))))),
% 87.71/87.90 inference(monotonicity,[status(thm)],[16654])).
% 87.71/87.90 tff(16656,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | (~node6(c_e_h_3, c_g, s1, s2)))),
% 87.71/87.90 inference(transitivity,[status(thm)],[16655, 16653])).
% 87.71/87.90 tff(16657,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16658,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | (~node6(c_e_h_3, c_g, s1, s2))),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16657, 16656])).
% 87.71/87.90 tff(16659,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16658, 899, 16652, 16651, 16636])).
% 87.71/87.90 tff(16660,plain,((~node6(c_e_h_3, c_g, s1, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16661,plain,
% 87.71/87.90 ((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2))),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16660, 15982])).
% 87.71/87.90 tff(16662,plain,
% 87.71/87.90 (~node6(c_e_h_3, c_g, s1, s2)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16661, 16636])).
% 87.71/87.90 tff(16663,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16664,plain,
% 87.71/87.90 ((node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16665,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2)))),
% 87.71/87.90 inference(monotonicity,[status(thm)],[16664])).
% 87.71/87.90 tff(16666,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2))),
% 87.71/87.90 inference(transitivity,[status(thm)],[16665, 16663])).
% 87.71/87.90 tff(16667,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2) | (~trans(s1, s2)))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16668,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16667, 16666])).
% 87.71/87.90 tff(16669,plain,
% 87.71/87.90 (node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16668, 881, 344])).
% 87.71/87.90 tff(16670,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16669, 16662, 16650])).
% 87.71/87.90 tff(16671,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16672,plain,
% 87.71/87.90 (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16671, 16634])).
% 87.71/87.90 tff(16673,plain,
% 87.71/87.90 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16674,plain,
% 87.71/87.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16675,plain,
% 87.71/87.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16674, 16673])).
% 87.71/87.90 tff(16676,plain,
% 87.71/87.90 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16675, 13114, 16672])).
% 87.71/87.90 tff(16677,plain,
% 87.71/87.90 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s2))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16678,plain,
% 87.71/87.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s2))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16679,plain,
% 87.71/87.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s2)),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16678, 16677])).
% 87.71/87.90 tff(16680,plain,
% 87.71/87.90 (~node20(c_e_h_3, c_k, s2)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16679, 37, 16676])).
% 87.71/87.90 tff(16681,assumption,(node21(c_e_h_3, c_k, s2, s3)), introduced(assumption)).
% 87.71/87.90 tff(16682,assumption,(~node20(c_e_h_3, c_k, s2)), introduced(assumption)).
% 87.71/87.90 tff(16683,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s2) | (~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s2) | (~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16684,plain,
% 87.71/87.90 ((node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3))) <=> (node20(c_e_h_3, c_k, s2) | (~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)))),
% 87.71/87.90 inference(rewrite,[status(thm)],[])).
% 87.71/87.90 tff(16685,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s2) | (~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3))))),
% 87.71/87.90 inference(monotonicity,[status(thm)],[16684])).
% 87.71/87.90 tff(16686,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s2) | (~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)))),
% 87.71/87.90 inference(transitivity,[status(thm)],[16685, 16683])).
% 87.71/87.90 tff(16687,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3)))),
% 87.71/87.90 inference(quant_inst,[status(thm)],[])).
% 87.71/87.90 tff(16688,plain,
% 87.71/87.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s2) | (~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 87.71/87.90 inference(modus_ponens,[status(thm)],[16687, 16686])).
% 87.71/87.90 tff(16689,plain,
% 87.71/87.90 ($false),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16688, 51, 16593, 16682, 16681])).
% 87.71/87.90 tff(16690,plain,((~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | node20(c_e_h_3, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.90 tff(16691,plain,
% 87.71/87.90 ((~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16690, 16680])).
% 87.71/87.90 tff(16692,plain,
% 87.71/87.90 (~node21(c_e_h_3, c_k, s2, s3)),
% 87.71/87.90 inference(unit_resolution,[status(thm)],[16691, 16593])).
% 87.71/87.90 tff(16693,assumption,(node22(c_e_h_3, c_k, s2, s3)), introduced(assumption)).
% 87.71/87.90 tff(16694,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s2)), introduced(assumption)).
% 87.71/87.90 tff(16695,plain,
% 87.71/87.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16696,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16697,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16696, 16695])).
% 87.71/87.91 tff(16698,plain,
% 87.71/87.91 ($false),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16697, 107, 16593, 16694, 16693])).
% 87.71/87.91 tff(16699,plain,((~node22(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.91 tff(16700,plain,
% 87.71/87.91 ((~node22(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16699, 16009])).
% 87.71/87.91 tff(16701,plain,
% 87.71/87.91 (~node22(c_e_h_3, c_k, s2, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16700, 16593])).
% 87.71/87.91 tff(16702,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16703,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16704,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16703, 16702])).
% 87.71/87.91 tff(16705,plain,
% 87.71/87.91 (node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16704, 81, 582])).
% 87.71/87.91 tff(16706,plain,
% 87.71/87.91 ($false),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16705, 16701, 16692])).
% 87.71/87.91 tff(16707,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s3)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.91 tff(16708,plain,
% 87.71/87.91 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16709,plain,
% 87.71/87.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16710,plain,
% 87.71/87.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16709, 16708])).
% 87.71/87.91 tff(16711,plain,
% 87.71/87.91 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16710, 10554, 16707])).
% 87.71/87.91 tff(16712,plain,
% 87.71/87.91 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s3))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16713,plain,
% 87.71/87.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s3))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16714,plain,
% 87.71/87.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s3)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16713, 16712])).
% 87.71/87.91 tff(16715,plain,
% 87.71/87.91 (~node20(c_e_h_3, c_l, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16714, 37, 16711])).
% 87.71/87.91 tff(16716,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16717,plain,
% 87.71/87.91 ((node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16718,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4))))),
% 87.71/87.91 inference(monotonicity,[status(thm)],[16717])).
% 87.71/87.91 tff(16719,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)))),
% 87.71/87.91 inference(transitivity,[status(thm)],[16718, 16716])).
% 87.71/87.91 tff(16720,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4)))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16721,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4))),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16720, 16719])).
% 87.71/87.91 tff(16722,plain,
% 87.71/87.91 ($false),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16721, 51, 16591, 16715, 16592])).
% 87.71/87.91 tff(16723,plain,((~node21(c_e_h_3, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.91 tff(16724,plain,
% 87.71/87.91 (~node21(c_e_h_3, c_l, s3, s4)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16723, 16591])).
% 87.71/87.91 tff(16725,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16726,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16727,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16726, 16725])).
% 87.71/87.91 tff(16728,plain,
% 87.71/87.91 (node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16727, 81, 679])).
% 87.71/87.91 tff(16729,plain,
% 87.71/87.91 (node22(c_e_h_3, c_l, s3, s4)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16728, 16724])).
% 87.71/87.91 tff(16730,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16731,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16732,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16731, 16730])).
% 87.71/87.91 tff(16733,plain,
% 87.71/87.91 ($false),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16732, 107, 16591, 16033, 16729])).
% 87.71/87.91 tff(16734,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.91 tff(16735,plain,
% 87.71/87.91 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16736,plain,
% 87.71/87.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16737,plain,
% 87.71/87.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16736, 16735])).
% 87.71/87.91 tff(16738,plain,
% 87.71/87.91 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16737, 801, 16734])).
% 87.71/87.91 tff(16739,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s4)), introduced(assumption)).
% 87.71/87.91 tff(16740,assumption,(node22(c_e_h_2, c_q, s3, s4)), introduced(assumption)).
% 87.71/87.91 tff(16741,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16742,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16743,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16742, 16741])).
% 87.71/87.91 tff(16744,plain,
% 87.71/87.91 ($false),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16743, 107, 16137, 16739, 16740])).
% 87.71/87.91 tff(16745,plain,((~node22(c_e_h_2, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.91 tff(16746,plain,
% 87.71/87.91 (~node22(c_e_h_2, c_q, s3, s4)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16745, 16739])).
% 87.71/87.91 tff(16747,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s3)), introduced(assumption)).
% 87.71/87.91 tff(16748,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s2)), introduced(assumption)).
% 87.71/87.91 tff(16749,assumption,(m_c_h_element_v_in2(c_e_h_2, c_f, s2)), introduced(assumption)).
% 87.71/87.91 tff(16750,plain,
% 87.71/87.91 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16751,plain,
% 87.71/87.91 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16752,plain,
% 87.71/87.91 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16751, 16750])).
% 87.71/87.91 tff(16753,plain,
% 87.71/87.91 ($false),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16752, 2218, 358, 16749])).
% 87.71/87.91 tff(16754,plain,((~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.91 tff(16755,plain,
% 87.71/87.91 (~m_c_h_element_v_in2(c_e_h_2, c_f, s2)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16754, 356])).
% 87.71/87.91 tff(16756,assumption,(~node15(c_e_h_2, c_f, s2, s3)), introduced(assumption)).
% 87.71/87.91 tff(16757,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s2)), introduced(assumption)).
% 87.71/87.91 tff(16758,plain,
% 87.71/87.91 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16759,plain,
% 87.71/87.91 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16760,plain,
% 87.71/87.91 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | m_c_h_element_v_in2(c_e_h_2, c_f, s2)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16759, 16758])).
% 87.71/87.91 tff(16761,plain,
% 87.71/87.91 ((~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16760, 228, 16757])).
% 87.71/87.91 tff(16762,plain,
% 87.71/87.91 (~node16(c_e_h_2, c_f, s2)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16761, 16748])).
% 87.71/87.91 tff(16763,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_f, s2, s3))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16764,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_f, s2, s3))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16765,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_f, s2, s3)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16764, 16763])).
% 87.71/87.91 tff(16766,plain,
% 87.71/87.91 (node19(c_e_h_2, c_f, s2, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16765, 141, 582])).
% 87.71/87.91 tff(16767,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node15(c_e_h_2, c_f, s2, s3) | node14(c_e_h_2, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node15(c_e_h_2, c_f, s2, s3) | node14(c_e_h_2, c_f, s2, s3))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16768,plain,
% 87.71/87.91 ((node16(c_e_h_2, c_f, s2) | node14(c_e_h_2, c_f, s2, s3) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3))) <=> (node16(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node15(c_e_h_2, c_f, s2, s3) | node14(c_e_h_2, c_f, s2, s3))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16769,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | node14(c_e_h_2, c_f, s2, s3) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node15(c_e_h_2, c_f, s2, s3) | node14(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.91 inference(monotonicity,[status(thm)],[16768])).
% 87.71/87.91 tff(16770,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | node14(c_e_h_2, c_f, s2, s3) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node15(c_e_h_2, c_f, s2, s3) | node14(c_e_h_2, c_f, s2, s3))),
% 87.71/87.91 inference(transitivity,[status(thm)],[16769, 16767])).
% 87.71/87.91 tff(16771,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | node14(c_e_h_2, c_f, s2, s3) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16772,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node15(c_e_h_2, c_f, s2, s3) | node14(c_e_h_2, c_f, s2, s3)),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16771, 16770])).
% 87.71/87.91 tff(16773,plain,
% 87.71/87.91 (node16(c_e_h_2, c_f, s2) | node15(c_e_h_2, c_f, s2, s3) | node14(c_e_h_2, c_f, s2, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16772, 189, 16766])).
% 87.71/87.91 tff(16774,plain,
% 87.71/87.91 (node14(c_e_h_2, c_f, s2, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16773, 16762, 16756])).
% 87.71/87.91 tff(16775,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node14(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node14(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16776,plain,
% 87.71/87.91 (((~node14(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node14(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16777,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node14(c_e_h_2, c_f, s2, s3))))),
% 87.71/87.91 inference(monotonicity,[status(thm)],[16776])).
% 87.71/87.91 tff(16778,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node14(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.91 inference(transitivity,[status(thm)],[16777, 16775])).
% 87.71/87.91 tff(16779,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16780,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node14(c_e_h_2, c_f, s2, s3))),
% 87.71/87.91 inference(modus_ponens,[status(thm)],[16779, 16778])).
% 87.71/87.91 tff(16781,plain,
% 87.71/87.91 ($false),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16780, 283, 16747, 16748, 16774])).
% 87.71/87.91 tff(16782,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | node15(c_e_h_2, c_f, s2, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.91 tff(16783,plain,
% 87.71/87.91 (m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | node15(c_e_h_2, c_f, s2, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16782, 16755])).
% 87.71/87.91 tff(16784,plain,
% 87.71/87.91 (node15(c_e_h_2, c_f, s2, s3)),
% 87.71/87.91 inference(unit_resolution,[status(thm)],[16783, 16747, 16748])).
% 87.71/87.91 tff(16785,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s2)), introduced(assumption)).
% 87.71/87.91 tff(16786,plain,
% 87.71/87.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 87.71/87.91 inference(rewrite,[status(thm)],[])).
% 87.71/87.91 tff(16787,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 87.71/87.91 inference(quant_inst,[status(thm)],[])).
% 87.71/87.91 tff(16788,plain,
% 87.71/87.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16787, 16786])).
% 87.71/87.92 tff(16789,plain,
% 87.71/87.92 ($false),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16788, 173, 16747, 16785, 16784])).
% 87.71/87.92 tff(16790,plain,((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | m_c_h_element_v_in1(c_e_h_2, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.92 tff(16791,plain,
% 87.71/87.92 ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16790, 16104])).
% 87.71/87.92 tff(16792,plain,
% 87.71/87.92 (m_c_h_element_v_in1(c_e_h_2, c_f, s2)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16791, 16747])).
% 87.71/87.92 tff(16793,plain,
% 87.71/87.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16794,plain,
% 87.71/87.92 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~node17(c_e_h_2, c_f, s2))) <=> ((~node17(c_e_h_2, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16795,plain,
% 87.71/87.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~node17(c_e_h_2, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2)))),
% 87.71/87.92 inference(monotonicity,[status(thm)],[16794])).
% 87.71/87.92 tff(16796,plain,
% 87.71/87.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~node17(c_e_h_2, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 87.71/87.92 inference(transitivity,[status(thm)],[16795, 16793])).
% 87.71/87.92 tff(16797,plain,
% 87.71/87.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~node17(c_e_h_2, c_f, s2)))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16798,plain,
% 87.71/87.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16797, 16796])).
% 87.71/87.92 tff(16799,plain,
% 87.71/87.92 ((~node17(c_e_h_2, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2))),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16798, 209, 16755])).
% 87.71/87.92 tff(16800,plain,
% 87.71/87.92 (~node17(c_e_h_2, c_f, s2)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16799, 16792])).
% 87.71/87.92 tff(16801,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16802,plain,
% 87.71/87.92 ((node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3))) <=> (node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16803,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.92 inference(monotonicity,[status(thm)],[16802])).
% 87.71/87.92 tff(16804,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3))),
% 87.71/87.92 inference(transitivity,[status(thm)],[16803, 16801])).
% 87.71/87.92 tff(16805,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16806,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16805, 16804])).
% 87.71/87.92 tff(16807,plain,
% 87.71/87.92 (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16806, 156, 16766])).
% 87.71/87.92 tff(16808,plain,
% 87.71/87.92 (node18(c_e_h_2, c_f, s2, s3)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16807, 16800])).
% 87.71/87.92 tff(16809,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16810,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16811,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3))),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16810, 16809])).
% 87.71/87.92 tff(16812,plain,
% 87.71/87.92 ($false),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16811, 124, 16747, 16104, 16808])).
% 87.71/87.92 tff(16813,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.92 tff(16814,plain,
% 87.71/87.92 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16815,plain,
% 87.71/87.92 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16816,plain,
% 87.71/87.92 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s3)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16815, 16814])).
% 87.71/87.92 tff(16817,plain,
% 87.71/87.92 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16816, 1666, 16813])).
% 87.71/87.92 tff(16818,plain,
% 87.71/87.92 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s3))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16819,plain,
% 87.71/87.92 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s3))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16820,plain,
% 87.71/87.92 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s3)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16819, 16818])).
% 87.71/87.92 tff(16821,plain,
% 87.71/87.92 (~node20(c_e_h_2, c_q, s3)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16820, 37, 16817])).
% 87.71/87.92 tff(16822,assumption,(node21(c_e_h_2, c_q, s3, s4)), introduced(assumption)).
% 87.71/87.92 tff(16823,assumption,(~node20(c_e_h_2, c_q, s3)), introduced(assumption)).
% 87.71/87.92 tff(16824,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node21(c_e_h_2, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node21(c_e_h_2, c_q, s3, s4)))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16825,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node21(c_e_h_2, c_q, s3, s4)))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16826,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node21(c_e_h_2, c_q, s3, s4))),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16825, 16824])).
% 87.71/87.92 tff(16827,plain,
% 87.71/87.92 ($false),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16826, 51, 16739, 16823, 16822])).
% 87.71/87.92 tff(16828,plain,((~node21(c_e_h_2, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | node20(c_e_h_2, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.92 tff(16829,plain,
% 87.71/87.92 ((~node21(c_e_h_2, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16828, 16821])).
% 87.71/87.92 tff(16830,plain,
% 87.71/87.92 (~node21(c_e_h_2, c_q, s3, s4)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16829, 16739])).
% 87.71/87.92 tff(16831,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16832,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16833,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16832, 16831])).
% 87.71/87.92 tff(16834,plain,
% 87.71/87.92 (node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16833, 81, 679])).
% 87.71/87.92 tff(16835,plain,
% 87.71/87.92 ($false),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16834, 16830, 16746])).
% 87.71/87.92 tff(16836,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.92 tff(16837,plain,
% 87.71/87.92 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s4))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16838,plain,
% 87.71/87.92 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s4))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16839,plain,
% 87.71/87.92 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s4)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16838, 16837])).
% 87.71/87.92 tff(16840,plain,
% 87.71/87.92 (node3(c_e_h_2, c_e_h_3, s4)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16839, 7448, 814])).
% 87.71/87.92 tff(16841,plain,
% 87.71/87.92 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s4)) | (~node3(c_e_h_2, c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s4)) | (~node3(c_e_h_2, c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16842,plain,
% 87.71/87.92 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s4)) | (~node3(c_e_h_2, c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16843,plain,
% 87.71/87.92 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s4)) | (~node3(c_e_h_2, c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16842, 16841])).
% 87.71/87.92 tff(16844,plain,
% 87.71/87.92 ((~m_cell_v_ack(c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16843, 836, 16840])).
% 87.71/87.92 tff(16845,plain,
% 87.71/87.92 (~m_cell_v_ack(c_e_h_3, s4)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16844, 16836])).
% 87.71/87.92 tff(16846,plain,
% 87.71/87.92 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)) | m_cell_v_ack(c_e_h_3, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)) | m_cell_v_ack(c_e_h_3, s4))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16847,plain,
% 87.71/87.92 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)) | m_cell_v_ack(c_e_h_3, s4))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16848,plain,
% 87.71/87.92 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)) | m_cell_v_ack(c_e_h_3, s4)),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16847, 16846])).
% 87.71/87.92 tff(16849,plain,
% 87.71/87.92 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16848, 848, 16845])).
% 87.71/87.92 tff(16850,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)), introduced(assumption)).
% 87.71/87.92 tff(16851,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)), introduced(assumption)).
% 87.71/87.92 tff(16852,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s5)), introduced(assumption)).
% 87.71/87.92 tff(16853,assumption,(node5(c_e_h_3, c_j, s4, s5)), introduced(assumption)).
% 87.71/87.92 tff(16854,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16855,plain,
% 87.71/87.92 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16856,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5))))),
% 87.71/87.92 inference(monotonicity,[status(thm)],[16855])).
% 87.71/87.92 tff(16857,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)))),
% 87.71/87.92 inference(transitivity,[status(thm)],[16856, 16854])).
% 87.71/87.92 tff(16858,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16859,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5))),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16858, 16857])).
% 87.71/87.92 tff(16860,plain,
% 87.71/87.92 ($false),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16859, 862, 16852, 16851, 16850, 16853])).
% 87.71/87.92 tff(16861,plain,((~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.92 tff(16862,plain,
% 87.71/87.92 (~node5(c_e_h_3, c_j, s4, s5)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16861, 16852, 16851, 16850])).
% 87.71/87.92 tff(16863,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s4)), introduced(assumption)).
% 87.71/87.92 tff(16864,assumption,(node6(c_e_h_3, c_j, s4, s5)), introduced(assumption)).
% 87.71/87.92 tff(16865,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5)))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16866,plain,
% 87.71/87.92 (((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5)))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16867,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5))))),
% 87.71/87.92 inference(monotonicity,[status(thm)],[16866])).
% 87.71/87.92 tff(16868,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5)))),
% 87.71/87.92 inference(transitivity,[status(thm)],[16867, 16865])).
% 87.71/87.92 tff(16869,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 87.71/87.92 inference(quant_inst,[status(thm)],[])).
% 87.71/87.92 tff(16870,plain,
% 87.71/87.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5))),
% 87.71/87.92 inference(modus_ponens,[status(thm)],[16869, 16868])).
% 87.71/87.92 tff(16871,plain,
% 87.71/87.92 ($false),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16870, 899, 16852, 16863, 16864])).
% 87.71/87.92 tff(16872,plain,((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.92 tff(16873,plain,
% 87.71/87.92 (~node6(c_e_h_3, c_j, s4, s5)),
% 87.71/87.92 inference(unit_resolution,[status(thm)],[16872, 16852, 16863])).
% 87.71/87.92 tff(16874,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16875,plain,
% 87.71/87.92 ((node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5))),
% 87.71/87.92 inference(rewrite,[status(thm)],[])).
% 87.71/87.92 tff(16876,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5)))),
% 87.71/87.92 inference(monotonicity,[status(thm)],[16875])).
% 87.71/87.92 tff(16877,plain,
% 87.71/87.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5))),
% 87.71/87.93 inference(transitivity,[status(thm)],[16876, 16874])).
% 87.71/87.93 tff(16878,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5) | (~trans(s4, s5)))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16879,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5)),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16878, 16877])).
% 87.71/87.93 tff(16880,plain,
% 87.71/87.93 (node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16879, 881, 1432])).
% 87.71/87.93 tff(16881,plain,
% 87.71/87.93 ($false),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16880, 16873, 16862])).
% 87.71/87.93 tff(16882,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.93 tff(16883,plain,
% 87.71/87.93 ((~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16882, 16849])).
% 87.71/87.93 tff(16884,plain,
% 87.71/87.93 (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16883, 16738, 16173])).
% 87.71/87.93 tff(16885,plain,
% 87.71/87.93 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16886,plain,
% 87.71/87.93 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16887,plain,
% 87.71/87.93 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5)),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16886, 16885])).
% 87.71/87.93 tff(16888,plain,
% 87.71/87.93 (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16887, 309, 16884])).
% 87.71/87.93 tff(16889,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s5)), introduced(assumption)).
% 87.71/87.93 tff(16890,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s6)), introduced(assumption)).
% 87.71/87.93 tff(16891,assumption,(node18(c_e_h_3, c_h, s5, s6)), introduced(assumption)).
% 87.71/87.93 tff(16892,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16893,plain,
% 87.71/87.93 (((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~node18(c_e_h_3, c_h, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16894,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~node18(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6))))),
% 87.71/87.93 inference(monotonicity,[status(thm)],[16893])).
% 87.71/87.93 tff(16895,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~node18(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(transitivity,[status(thm)],[16894, 16892])).
% 87.71/87.93 tff(16896,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~node18(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16897,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16896, 16895])).
% 87.71/87.93 tff(16898,plain,
% 87.71/87.93 ($false),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16897, 124, 16889, 16890, 16891])).
% 87.71/87.93 tff(16899,plain,((~node18(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.93 tff(16900,plain,
% 87.71/87.93 (~node18(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16899, 16890, 16889])).
% 87.71/87.93 tff(16901,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s5)), introduced(assumption)).
% 87.71/87.93 tff(16902,assumption,(~node16(c_e_h_3, c_h, s5)), introduced(assumption)).
% 87.71/87.93 tff(16903,assumption,(node15(c_e_h_3, c_h, s5, s6)), introduced(assumption)).
% 87.71/87.93 tff(16904,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16905,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16906,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16905, 16904])).
% 87.71/87.93 tff(16907,plain,
% 87.71/87.93 ($false),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16906, 173, 16889, 16890, 16903])).
% 87.71/87.93 tff(16908,plain,((~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.93 tff(16909,plain,
% 87.71/87.93 (~node15(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16908, 16890, 16889])).
% 87.71/87.93 tff(16910,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16911,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16912,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16911, 16910])).
% 87.71/87.93 tff(16913,plain,
% 87.71/87.93 (node19(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16912, 141, 1499])).
% 87.71/87.93 tff(16914,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s5) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16915,plain,
% 87.71/87.93 ((node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6))) <=> (node16(c_e_h_3, c_h, s5) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16916,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(monotonicity,[status(thm)],[16915])).
% 87.71/87.93 tff(16917,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s5) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(transitivity,[status(thm)],[16916, 16914])).
% 87.71/87.93 tff(16918,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16919,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s5) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16918, 16917])).
% 87.71/87.93 tff(16920,plain,
% 87.71/87.93 (node16(c_e_h_3, c_h, s5) | node15(c_e_h_3, c_h, s5, s6) | node14(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16919, 189, 16913])).
% 87.71/87.93 tff(16921,plain,
% 87.71/87.93 (node14(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16920, 16909, 16902])).
% 87.71/87.93 tff(16922,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16923,plain,
% 87.71/87.93 (((~node14(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16924,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6))))),
% 87.71/87.93 inference(monotonicity,[status(thm)],[16923])).
% 87.71/87.93 tff(16925,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(transitivity,[status(thm)],[16924, 16922])).
% 87.71/87.93 tff(16926,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16927,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16926, 16925])).
% 87.71/87.93 tff(16928,plain,
% 87.71/87.93 ($false),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16927, 283, 16890, 16921, 16901])).
% 87.71/87.93 tff(16929,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | node16(c_e_h_3, c_h, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.93 tff(16930,plain,
% 87.71/87.93 (node16(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16929, 16889, 16890, 16901])).
% 87.71/87.93 tff(16931,plain,
% 87.71/87.93 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16932,plain,
% 87.71/87.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16933,plain,
% 87.71/87.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16932, 16931])).
% 87.71/87.93 tff(16934,plain,
% 87.71/87.93 ((~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16933, 228, 16901])).
% 87.71/87.93 tff(16935,plain,
% 87.71/87.93 (m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16934, 16930])).
% 87.71/87.93 tff(16936,plain,
% 87.71/87.93 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16937,plain,
% 87.71/87.93 ((m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16938,plain,
% 87.71/87.93 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5)))),
% 87.71/87.93 inference(monotonicity,[status(thm)],[16937])).
% 87.71/87.93 tff(16939,plain,
% 87.71/87.93 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5))),
% 87.71/87.93 inference(transitivity,[status(thm)],[16938, 16936])).
% 87.71/87.93 tff(16940,plain,
% 87.71/87.93 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16941,plain,
% 87.71/87.93 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16940, 16939])).
% 87.71/87.93 tff(16942,plain,
% 87.71/87.93 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5))),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16941, 245, 16901])).
% 87.71/87.93 tff(16943,plain,
% 87.71/87.93 (~node17(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16942, 16935])).
% 87.71/87.93 tff(16944,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16945,plain,
% 87.71/87.93 ((node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6))) <=> (node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16946,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(monotonicity,[status(thm)],[16945])).
% 87.71/87.93 tff(16947,plain,
% 87.71/87.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6))),
% 87.71/87.93 inference(transitivity,[status(thm)],[16946, 16944])).
% 87.71/87.93 tff(16948,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16949,plain,
% 87.71/87.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(modus_ponens,[status(thm)],[16948, 16947])).
% 87.71/87.93 tff(16950,plain,
% 87.71/87.93 (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16949, 156, 16913])).
% 87.71/87.93 tff(16951,plain,
% 87.71/87.93 (node18(c_e_h_3, c_h, s5, s6)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16950, 16943])).
% 87.71/87.93 tff(16952,plain,
% 87.71/87.93 ($false),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16897, 124, 16889, 16890, 16951])).
% 87.71/87.93 tff(16953,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.93 tff(16954,plain,
% 87.71/87.93 (m_c_h_element_v_in1(c_e_h_3, c_h, s5)),
% 87.71/87.93 inference(unit_resolution,[status(thm)],[16953, 16890, 16889])).
% 87.71/87.93 tff(16955,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s5)), introduced(assumption)).
% 87.71/87.93 tff(16956,plain,
% 87.71/87.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5)))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16957,plain,
% 87.71/87.93 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5)))),
% 87.71/87.93 inference(rewrite,[status(thm)],[])).
% 87.71/87.93 tff(16958,plain,
% 87.71/87.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5))))),
% 87.71/87.93 inference(monotonicity,[status(thm)],[16957])).
% 87.71/87.93 tff(16959,plain,
% 87.71/87.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5)))),
% 87.71/87.93 inference(transitivity,[status(thm)],[16958, 16956])).
% 87.71/87.93 tff(16960,plain,
% 87.71/87.93 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)))),
% 87.71/87.93 inference(quant_inst,[status(thm)],[])).
% 87.71/87.93 tff(16961,plain,
% 87.71/87.93 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5))),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[16960, 16959])).
% 87.71/87.94 tff(16962,plain,
% 87.71/87.94 ((~node17(c_e_h_3, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5))),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16961, 209, 16955])).
% 87.71/87.94 tff(16963,plain,
% 87.71/87.94 (~node17(c_e_h_3, c_h, s5)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16962, 16954])).
% 87.71/87.94 tff(16964,plain,
% 87.71/87.94 ($false),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16950, 16963, 16900])).
% 87.71/87.94 tff(16965,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.94 tff(16966,plain,
% 87.71/87.94 (~m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16965, 16888, 16250])).
% 87.71/87.94 tff(16967,plain,
% 87.71/87.94 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(16968,plain,
% 87.71/87.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(16969,plain,
% 87.71/87.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[16968, 16967])).
% 87.71/87.94 tff(16970,plain,
% 87.71/87.94 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16969, 23, 16966])).
% 87.71/87.94 tff(16971,plain,
% 87.71/87.94 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(16972,plain,
% 87.71/87.94 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(16973,plain,
% 87.71/87.94 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[16972, 16971])).
% 87.71/87.94 tff(16974,plain,
% 87.71/87.94 (~node20(c_e_h_3, c_i, s6)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16973, 37, 16970])).
% 87.71/87.94 tff(16975,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)), introduced(assumption)).
% 87.71/87.94 tff(16976,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s6)), introduced(assumption)).
% 87.71/87.94 tff(16977,plain,
% 87.71/87.94 (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16286, 2218, 16976])).
% 87.71/87.94 tff(16978,assumption,(~node20(c_e_h_3, c_i, s6)), introduced(assumption)).
% 87.71/87.94 tff(16979,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s7)), introduced(assumption)).
% 87.71/87.94 tff(16980,assumption,(node22(c_e_h_3, c_i, s6, s7)), introduced(assumption)).
% 87.71/87.94 tff(16981,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(16982,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(16983,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[16982, 16981])).
% 87.71/87.94 tff(16984,plain,
% 87.71/87.94 ($false),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16983, 107, 16976, 16979, 16980])).
% 87.71/87.94 tff(16985,plain,((~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.94 tff(16986,plain,
% 87.71/87.94 (~node22(c_e_h_3, c_i, s6, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16985, 16979, 16976])).
% 87.71/87.94 tff(16987,assumption,(node21(c_e_h_3, c_i, s6, s7)), introduced(assumption)).
% 87.71/87.94 tff(16988,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6) | (~node21(c_e_h_3, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6) | (~node21(c_e_h_3, c_i, s6, s7)))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(16989,plain,
% 87.71/87.94 ((node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node21(c_e_h_3, c_i, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6) | (~node21(c_e_h_3, c_i, s6, s7)))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(16990,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node21(c_e_h_3, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6) | (~node21(c_e_h_3, c_i, s6, s7))))),
% 87.71/87.94 inference(monotonicity,[status(thm)],[16989])).
% 87.71/87.94 tff(16991,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node21(c_e_h_3, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6) | (~node21(c_e_h_3, c_i, s6, s7)))),
% 87.71/87.94 inference(transitivity,[status(thm)],[16990, 16988])).
% 87.71/87.94 tff(16992,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node21(c_e_h_3, c_i, s6, s7)))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(16993,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6) | (~node21(c_e_h_3, c_i, s6, s7))),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[16992, 16991])).
% 87.71/87.94 tff(16994,plain,
% 87.71/87.94 ($false),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16993, 51, 16979, 16987, 16978])).
% 87.71/87.94 tff(16995,plain,((~node21(c_e_h_3, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.94 tff(16996,plain,
% 87.71/87.94 (~node21(c_e_h_3, c_i, s6, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16995, 16979, 16978])).
% 87.71/87.94 tff(16997,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(16998,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(16999,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[16998, 16997])).
% 87.71/87.94 tff(17000,plain,
% 87.71/87.94 (node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16999, 81, 1552])).
% 87.71/87.94 tff(17001,plain,
% 87.71/87.94 ($false),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17000, 16996, 16986])).
% 87.71/87.94 tff(17002,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.94 tff(17003,plain,
% 87.71/87.94 (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17002, 16976, 16978])).
% 87.71/87.94 tff(17004,plain,
% 87.71/87.94 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17005,plain,
% 87.71/87.94 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(17006,plain,
% 87.71/87.94 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[17005, 17004])).
% 87.71/87.94 tff(17007,plain,
% 87.71/87.94 (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17006, 2218, 17003])).
% 87.71/87.94 tff(17008,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s7)), introduced(assumption)).
% 87.71/87.94 tff(17009,plain,
% 87.71/87.94 (~m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[16366, 13405, 16311])).
% 87.71/87.94 tff(17010,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s8)), introduced(assumption)).
% 87.71/87.94 tff(17011,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s7)), introduced(assumption)).
% 87.71/87.94 tff(17012,assumption,(node18(c_e_h_3, c_f, s7, s8)), introduced(assumption)).
% 87.71/87.94 tff(17013,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17014,plain,
% 87.71/87.94 (((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~node18(c_e_h_3, c_f, s7, s8))) <=> ((~node18(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17015,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~node18(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8))))),
% 87.71/87.94 inference(monotonicity,[status(thm)],[17014])).
% 87.71/87.94 tff(17016,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~node18(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))),
% 87.71/87.94 inference(transitivity,[status(thm)],[17015, 17013])).
% 87.71/87.94 tff(17017,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~node18(c_e_h_3, c_f, s7, s8)))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(17018,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[17017, 17016])).
% 87.71/87.94 tff(17019,plain,
% 87.71/87.94 ($false),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17018, 124, 17012, 16370, 17010])).
% 87.71/87.94 tff(17020,plain,((~node18(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.94 tff(17021,plain,
% 87.71/87.94 (~node18(c_e_h_3, c_f, s7, s8)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17020, 17010, 16370])).
% 87.71/87.94 tff(17022,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_f, s7, s8))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17023,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_f, s7, s8))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(17024,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_f, s7, s8)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[17023, 17022])).
% 87.71/87.94 tff(17025,plain,
% 87.71/87.94 (node19(c_e_h_3, c_f, s7, s8)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17024, 141, 2152])).
% 87.71/87.94 tff(17026,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s7) | (~node19(c_e_h_3, c_f, s7, s8)) | node18(c_e_h_3, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s7) | (~node19(c_e_h_3, c_f, s7, s8)) | node18(c_e_h_3, c_f, s7, s8))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17027,plain,
% 87.71/87.94 ((node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8))) <=> (node17(c_e_h_3, c_f, s7) | (~node19(c_e_h_3, c_f, s7, s8)) | node18(c_e_h_3, c_f, s7, s8))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17028,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s7) | (~node19(c_e_h_3, c_f, s7, s8)) | node18(c_e_h_3, c_f, s7, s8)))),
% 87.71/87.94 inference(monotonicity,[status(thm)],[17027])).
% 87.71/87.94 tff(17029,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s7) | (~node19(c_e_h_3, c_f, s7, s8)) | node18(c_e_h_3, c_f, s7, s8))),
% 87.71/87.94 inference(transitivity,[status(thm)],[17028, 17026])).
% 87.71/87.94 tff(17030,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(17031,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s7) | (~node19(c_e_h_3, c_f, s7, s8)) | node18(c_e_h_3, c_f, s7, s8)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[17030, 17029])).
% 87.71/87.94 tff(17032,plain,
% 87.71/87.94 (node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17031, 156, 17025])).
% 87.71/87.94 tff(17033,plain,
% 87.71/87.94 (node17(c_e_h_3, c_f, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17032, 17021])).
% 87.71/87.94 tff(17034,plain,
% 87.71/87.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17035,plain,
% 87.71/87.94 ((m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7))) <=> ((~node17(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17036,plain,
% 87.71/87.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7)))),
% 87.71/87.94 inference(monotonicity,[status(thm)],[17035])).
% 87.71/87.94 tff(17037,plain,
% 87.71/87.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 87.71/87.94 inference(transitivity,[status(thm)],[17036, 17034])).
% 87.71/87.94 tff(17038,plain,
% 87.71/87.94 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(17039,plain,
% 87.71/87.94 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[17038, 17037])).
% 87.71/87.94 tff(17040,plain,
% 87.71/87.94 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17039, 245, 17033])).
% 87.71/87.94 tff(17041,plain,
% 87.71/87.94 (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17040, 17011])).
% 87.71/87.94 tff(17042,assumption,(~node16(c_e_h_3, c_f, s7)), introduced(assumption)).
% 87.71/87.94 tff(17043,assumption,(node14(c_e_h_3, c_f, s7, s8)), introduced(assumption)).
% 87.71/87.94 tff(17044,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17045,plain,
% 87.71/87.94 (((~node14(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8))) <=> ((~node14(c_e_h_3, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17046,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7)))),
% 87.71/87.94 inference(monotonicity,[status(thm)],[17045])).
% 87.71/87.94 tff(17047,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 87.71/87.94 inference(transitivity,[status(thm)],[17046, 17044])).
% 87.71/87.94 tff(17048,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))),
% 87.71/87.94 inference(quant_inst,[status(thm)],[])).
% 87.71/87.94 tff(17049,plain,
% 87.71/87.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7)),
% 87.71/87.94 inference(modus_ponens,[status(thm)],[17048, 17047])).
% 87.71/87.94 tff(17050,plain,
% 87.71/87.94 ($false),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17049, 283, 17043, 17010, 17011])).
% 87.71/87.94 tff(17051,plain,((~node14(c_e_h_3, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.94 tff(17052,plain,
% 87.71/87.94 (~node14(c_e_h_3, c_f, s7, s8)),
% 87.71/87.94 inference(unit_resolution,[status(thm)],[17051, 17010, 17011])).
% 87.71/87.94 tff(17053,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s7, s8)) | node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s7, s8)) | node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17054,plain,
% 87.71/87.94 ((node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8))) <=> ((~node19(c_e_h_3, c_f, s7, s8)) | node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8))),
% 87.71/87.94 inference(rewrite,[status(thm)],[])).
% 87.71/87.94 tff(17055,plain,
% 87.71/87.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s7, s8)) | node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8)))),
% 87.71/87.95 inference(monotonicity,[status(thm)],[17054])).
% 87.71/87.95 tff(17056,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s7, s8)) | node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8))),
% 87.71/87.95 inference(transitivity,[status(thm)],[17055, 17053])).
% 87.71/87.95 tff(17057,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17058,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s7, s8)) | node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17057, 17056])).
% 87.71/87.95 tff(17059,plain,
% 87.71/87.95 (node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17058, 189, 17025])).
% 87.71/87.95 tff(17060,plain,
% 87.71/87.95 (node15(c_e_h_3, c_f, s7, s8)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17059, 17052, 17042])).
% 87.71/87.95 tff(17061,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17062,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17063,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17062, 17061])).
% 87.71/87.95 tff(17064,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17063, 173, 17060, 16370, 17010])).
% 87.71/87.95 tff(17065,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | node16(c_e_h_3, c_f, s7) | m_c_h_element_v_in1(c_e_h_3, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17066,plain,
% 87.71/87.95 (node16(c_e_h_3, c_f, s7)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17065, 17011, 17010, 16370])).
% 87.71/87.95 tff(17067,plain,
% 87.71/87.95 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17068,plain,
% 87.71/87.95 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17069,plain,
% 87.71/87.95 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17068, 17067])).
% 87.71/87.95 tff(17070,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17069, 228, 17066, 17011, 17041])).
% 87.71/87.95 tff(17071,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17072,plain,
% 87.71/87.95 (m_c_h_element_v_in1(c_e_h_3, c_f, s7)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17071, 17010, 16370])).
% 87.71/87.95 tff(17073,plain,
% 87.71/87.95 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node17(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node17(c_e_h_3, c_f, s7)))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17074,plain,
% 87.71/87.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node17(c_e_h_3, c_f, s7)))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17075,plain,
% 87.71/87.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node17(c_e_h_3, c_f, s7))),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17074, 17073])).
% 87.71/87.95 tff(17076,plain,
% 87.71/87.95 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7))),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17075, 209, 17008])).
% 87.71/87.95 tff(17077,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17076, 17033, 17072])).
% 87.71/87.95 tff(17078,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17079,plain,
% 87.71/87.95 (~m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17078, 17009, 17008])).
% 87.71/87.95 tff(17080,plain,
% 87.71/87.95 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[13410, 13405])).
% 87.71/87.95 tff(17081,plain,
% 87.71/87.95 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[16375, 17009])).
% 87.71/87.95 tff(17082,plain,
% 87.71/87.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[11991, 11986])).
% 87.71/87.95 tff(17083,plain,
% 87.71/87.95 (~node9(c_e_h_3, c_n, s6)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[11999, 17082])).
% 87.71/87.95 tff(17084,plain,
% 87.71/87.95 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[12023, 17083, 12002])).
% 87.71/87.95 tff(17085,plain,
% 87.71/87.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[13444, 11986, 16379, 13420])).
% 87.71/87.95 tff(17086,plain,
% 87.71/87.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[13450, 6442, 17085])).
% 87.71/87.95 tff(17087,plain,
% 87.71/87.95 (~node9(c_e_h_3, c_n, s7)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[13454, 1062, 17086])).
% 87.71/87.95 tff(17088,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)), introduced(assumption)).
% 87.71/87.95 tff(17089,plain,
% 87.71/87.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[16415, 17083, 16378, 12002, 13420, 11986])).
% 87.71/87.95 tff(17090,assumption,(node11(c_e_h_3, c_m, s8, s9)), introduced(assumption)).
% 87.71/87.95 tff(17091,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9)))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17092,plain,
% 87.71/87.95 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node11(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9)))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17093,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node11(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9))))),
% 87.71/87.95 inference(monotonicity,[status(thm)],[17092])).
% 87.71/87.95 tff(17094,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node11(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9)))),
% 87.71/87.95 inference(transitivity,[status(thm)],[17093, 17091])).
% 87.71/87.95 tff(17095,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node11(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17096,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9))),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17095, 17094])).
% 87.71/87.95 tff(17097,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17096, 1161, 16975, 17090, 16421])).
% 87.71/87.95 tff(17098,plain,((~node11(c_e_h_3, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17099,plain,
% 87.71/87.95 (~node11(c_e_h_3, c_m, s8, s9)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17098, 16975, 16421])).
% 87.71/87.95 tff(17100,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)), introduced(assumption)).
% 87.71/87.95 tff(17101,assumption,(node10(c_e_h_3, c_m, s8, s9)), introduced(assumption)).
% 87.71/87.95 tff(17102,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17103,plain,
% 87.71/87.95 (((~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17104,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8))))),
% 87.71/87.95 inference(monotonicity,[status(thm)],[17103])).
% 87.71/87.95 tff(17105,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)))),
% 87.71/87.95 inference(transitivity,[status(thm)],[17104, 17102])).
% 87.71/87.95 tff(17106,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17107,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8))),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17106, 17105])).
% 87.71/87.95 tff(17108,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17107, 1191, 16975, 17101, 17088, 17100])).
% 87.71/87.95 tff(17109,plain,((~node10(c_e_h_3, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17110,plain,
% 87.71/87.95 (~node10(c_e_h_3, c_m, s8, s9)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17109, 16975, 17100, 17088])).
% 87.71/87.95 tff(17111,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17112,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17113,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17112, 17111])).
% 87.71/87.95 tff(17114,plain,
% 87.71/87.95 (node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17113, 1092, 2636])).
% 87.71/87.95 tff(17115,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17114, 17110, 17099])).
% 87.71/87.95 tff(17116,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17117,plain,
% 87.71/87.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17116, 17089, 17088, 16975])).
% 87.71/87.95 tff(17118,plain,
% 87.71/87.95 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17119,plain,
% 87.71/87.95 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17120,plain,
% 87.71/87.95 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17119, 17118])).
% 87.71/87.95 tff(17121,plain,
% 87.71/87.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17120, 6378, 17117])).
% 87.71/87.95 tff(17122,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[13478, 17121, 17087, 17084])).
% 87.71/87.95 tff(17123,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17124,plain,
% 87.71/87.95 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17123, 11479])).
% 87.71/87.95 tff(17125,plain,
% 87.71/87.95 ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17124, 11984])).
% 87.71/87.95 tff(17126,plain,
% 87.71/87.95 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17125, 17081, 16975, 17080])).
% 87.71/87.95 tff(17127,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)), introduced(assumption)).
% 87.71/87.95 tff(17128,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s8)), introduced(assumption)).
% 87.71/87.95 tff(17129,plain,
% 87.71/87.95 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17130,plain,
% 87.71/87.95 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17131,plain,
% 87.71/87.95 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17130, 17129])).
% 87.71/87.95 tff(17132,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17131, 6389, 17128, 17127])).
% 87.71/87.95 tff(17133,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17134,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17133, 17126, 17079])).
% 87.71/87.95 tff(17135,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17136,plain,
% 87.71/87.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17135, 13403])).
% 87.71/87.95 tff(17137,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17136, 17007, 16977, 16975])).
% 87.71/87.95 tff(17138,plain,(m_and_h_gate_v_out(c_e_h_3, c_i, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | node20(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17139,plain,
% 87.71/87.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17138, 16974, 16283])).
% 87.71/87.95 tff(17140,plain,
% 87.71/87.95 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17141,plain,
% 87.71/87.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17142,plain,
% 87.71/87.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17141, 17140])).
% 87.71/87.95 tff(17143,plain,
% 87.71/87.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17142, 6442, 17139])).
% 87.71/87.95 tff(17144,plain,
% 87.71/87.95 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17145,plain,
% 87.71/87.95 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17146,plain,
% 87.71/87.95 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17145, 17144])).
% 87.71/87.95 tff(17147,plain,
% 87.71/87.95 (~node9(c_e_h_3, c_n, s9)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17146, 1062, 17143])).
% 87.71/87.95 tff(17148,assumption,(~node9(c_e_h_3, c_n, s9)), introduced(assumption)).
% 87.71/87.95 tff(17149,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)), introduced(assumption)).
% 87.71/87.95 tff(17150,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)), introduced(assumption)).
% 87.71/87.95 tff(17151,assumption,(node11(c_e_h_3, c_n, s9, s10)), introduced(assumption)).
% 87.71/87.95 tff(17152,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17153,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17154,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17153, 17152])).
% 87.71/87.95 tff(17155,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17154, 1130, 17151, 17150, 17149])).
% 87.71/87.95 tff(17156,plain,((~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17157,plain,
% 87.71/87.95 (~node11(c_e_h_3, c_n, s9, s10)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17156, 17149, 17150])).
% 87.71/87.95 tff(17158,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17159,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17160,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17159, 17158])).
% 87.71/87.95 tff(17161,plain,
% 87.71/87.95 (node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17160, 1092, 3175])).
% 87.71/87.95 tff(17162,plain,
% 87.71/87.95 (node10(c_e_h_3, c_n, s9, s10)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17161, 17157])).
% 87.71/87.95 tff(17163,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | node9(c_e_h_3, c_n, s9) | (~node10(c_e_h_3, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | node9(c_e_h_3, c_n, s9) | (~node10(c_e_h_3, c_n, s9, s10)))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17164,plain,
% 87.71/87.95 ((node9(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node10(c_e_h_3, c_n, s9, s10))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | node9(c_e_h_3, c_n, s9) | (~node10(c_e_h_3, c_n, s9, s10)))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17165,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node10(c_e_h_3, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | node9(c_e_h_3, c_n, s9) | (~node10(c_e_h_3, c_n, s9, s10))))),
% 87.71/87.95 inference(monotonicity,[status(thm)],[17164])).
% 87.71/87.95 tff(17166,plain,
% 87.71/87.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node10(c_e_h_3, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | node9(c_e_h_3, c_n, s9) | (~node10(c_e_h_3, c_n, s9, s10)))),
% 87.71/87.95 inference(transitivity,[status(thm)],[17165, 17163])).
% 87.71/87.95 tff(17167,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node10(c_e_h_3, c_n, s9, s10)))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17168,plain,
% 87.71/87.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | node9(c_e_h_3, c_n, s9) | (~node10(c_e_h_3, c_n, s9, s10))),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17167, 17166])).
% 87.71/87.95 tff(17169,plain,
% 87.71/87.95 ($false),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17168, 1076, 17162, 17149, 17148])).
% 87.71/87.95 tff(17170,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | node9(c_e_h_3, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.95 tff(17171,plain,
% 87.71/87.95 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17170, 17147, 16463])).
% 87.71/87.95 tff(17172,plain,
% 87.71/87.95 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17173,plain,
% 87.71/87.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17174,plain,
% 87.71/87.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 87.71/87.95 inference(modus_ponens,[status(thm)],[17173, 17172])).
% 87.71/87.95 tff(17175,plain,
% 87.71/87.95 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)),
% 87.71/87.95 inference(unit_resolution,[status(thm)],[17174, 6513, 17171])).
% 87.71/87.95 tff(17176,plain,
% 87.71/87.95 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s10))),
% 87.71/87.95 inference(rewrite,[status(thm)],[])).
% 87.71/87.95 tff(17177,plain,
% 87.71/87.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s10))),
% 87.71/87.95 inference(quant_inst,[status(thm)],[])).
% 87.71/87.95 tff(17178,plain,
% 87.71/87.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s10)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17177, 17176])).
% 87.71/87.96 tff(17179,plain,
% 87.71/87.96 (~node20(c_e_h_3, c_q, s10)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17178, 1535, 17175])).
% 87.71/87.96 tff(17180,assumption,(~node20(c_e_h_3, c_q, s10)), introduced(assumption)).
% 87.71/87.96 tff(17181,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s10)), introduced(assumption)).
% 87.71/87.96 tff(17182,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s11)), introduced(assumption)).
% 87.71/87.96 tff(17183,assumption,(node22(c_e_h_3, c_q, s10, s11)), introduced(assumption)).
% 87.71/87.96 tff(17184,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17185,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17186,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17185, 17184])).
% 87.71/87.96 tff(17187,plain,
% 87.71/87.96 ($false),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17186, 107, 17181, 17182, 17183])).
% 87.71/87.96 tff(17188,plain,((~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.96 tff(17189,plain,
% 87.71/87.96 (~node22(c_e_h_3, c_q, s10, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17188, 17182, 17181])).
% 87.71/87.96 tff(17190,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17191,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17192,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17191, 17190])).
% 87.71/87.96 tff(17193,plain,
% 87.71/87.96 (node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17192, 81, 3778])).
% 87.71/87.96 tff(17194,plain,
% 87.71/87.96 (node21(c_e_h_3, c_q, s10, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17193, 17189])).
% 87.71/87.96 tff(17195,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node21(c_e_h_3, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node21(c_e_h_3, c_q, s10, s11)))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17196,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node21(c_e_h_3, c_q, s10, s11)))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17197,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node21(c_e_h_3, c_q, s10, s11))),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17196, 17195])).
% 87.71/87.96 tff(17198,plain,
% 87.71/87.96 ($false),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17197, 51, 17182, 17194, 17180])).
% 87.71/87.96 tff(17199,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | node20(c_e_h_3, c_q, s10) | m_and_h_gate_v_out(c_e_h_3, c_q, s10)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.96 tff(17200,plain,
% 87.71/87.96 (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17199, 17179, 16494])).
% 87.71/87.96 tff(17201,plain,
% 87.71/87.96 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s11))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s11))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17202,plain,
% 87.71/87.96 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s11))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17203,plain,
% 87.71/87.96 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s11)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17202, 17201])).
% 87.71/87.96 tff(17204,plain,
% 87.71/87.96 (node3(c_e_h_3, c_e_h_1, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17203, 3860, 814])).
% 87.71/87.96 tff(17205,plain,
% 87.71/87.96 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s11)) | (~node3(c_e_h_3, c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s11)) | (~node3(c_e_h_3, c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17206,plain,
% 87.71/87.96 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s11)) | (~node3(c_e_h_3, c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17207,plain,
% 87.71/87.96 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s11)) | (~node3(c_e_h_3, c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17206, 17205])).
% 87.71/87.96 tff(17208,plain,
% 87.71/87.96 ((~m_cell_v_ack(c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17207, 836, 17204])).
% 87.71/87.96 tff(17209,plain,
% 87.71/87.96 (~m_cell_v_ack(c_e_h_1, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17208, 17200])).
% 87.71/87.96 tff(17210,plain,
% 87.71/87.96 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)) | m_cell_v_ack(c_e_h_1, s11))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)) | m_cell_v_ack(c_e_h_1, s11))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17211,plain,
% 87.71/87.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)) | m_cell_v_ack(c_e_h_1, s11))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17212,plain,
% 87.71/87.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)) | m_cell_v_ack(c_e_h_1, s11)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17211, 17210])).
% 87.71/87.96 tff(17213,plain,
% 87.71/87.96 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17212, 848, 17209])).
% 87.71/87.96 tff(17214,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)), introduced(assumption)).
% 87.71/87.96 tff(17215,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s12)), introduced(assumption)).
% 87.71/87.96 tff(17216,plain,
% 87.71/87.96 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[16541, 16536])).
% 87.71/87.96 tff(17217,plain,
% 87.71/87.96 (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[16571, 17216, 16543])).
% 87.71/87.96 tff(17218,assumption,(node6(c_e_h_1, c_j, s11, s12)), introduced(assumption)).
% 87.71/87.96 tff(17219,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12)))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17220,plain,
% 87.71/87.96 (((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12)))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17221,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12))))),
% 87.71/87.96 inference(monotonicity,[status(thm)],[17220])).
% 87.71/87.96 tff(17222,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12)))),
% 87.71/87.96 inference(transitivity,[status(thm)],[17221, 17219])).
% 87.71/87.96 tff(17223,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17224,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12))),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17223, 17222])).
% 87.71/87.96 tff(17225,plain,
% 87.71/87.96 ($false),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17224, 899, 16574, 17215, 17218])).
% 87.71/87.96 tff(17226,plain,((~node6(c_e_h_1, c_j, s11, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.96 tff(17227,plain,
% 87.71/87.96 (~node6(c_e_h_1, c_j, s11, s12)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17226, 17217, 17215])).
% 87.71/87.96 tff(17228,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17229,plain,
% 87.71/87.96 ((node6(c_e_h_1, c_j, s11, s12) | node5(c_e_h_1, c_j, s11, s12) | (~trans(s11, s12))) <=> ((~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17230,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s11, s12) | node5(c_e_h_1, c_j, s11, s12) | (~trans(s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12)))),
% 87.71/87.96 inference(monotonicity,[status(thm)],[17229])).
% 87.71/87.96 tff(17231,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s11, s12) | node5(c_e_h_1, c_j, s11, s12) | (~trans(s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12))),
% 87.71/87.96 inference(transitivity,[status(thm)],[17230, 17228])).
% 87.71/87.96 tff(17232,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s11, s12) | node5(c_e_h_1, c_j, s11, s12) | (~trans(s11, s12)))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17233,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17232, 17231])).
% 87.71/87.96 tff(17234,plain,
% 87.71/87.96 (node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17233, 881, 4461])).
% 87.71/87.96 tff(17235,plain,
% 87.71/87.96 (node5(c_e_h_1, c_j, s11, s12)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17234, 17227])).
% 87.71/87.96 tff(17236,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)), introduced(assumption)).
% 87.71/87.96 tff(17237,assumption,(node5(c_e_h_1, c_j, s11, s12)), introduced(assumption)).
% 87.71/87.96 tff(17238,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17239,plain,
% 87.71/87.96 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17240,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12))))),
% 87.71/87.96 inference(monotonicity,[status(thm)],[17239])).
% 87.71/87.96 tff(17241,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)))),
% 87.71/87.96 inference(transitivity,[status(thm)],[17240, 17238])).
% 87.71/87.96 tff(17242,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17243,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12))),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17242, 17241])).
% 87.71/87.96 tff(17244,plain,
% 87.71/87.96 ($false),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17243, 862, 17215, 17237, 17214, 17236])).
% 87.71/87.96 tff(17245,plain,((~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.96 tff(17246,plain,
% 87.71/87.96 (m_or_h_gate_v_in1(c_e_h_1, c_j, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17245, 17235, 17215, 17214])).
% 87.71/87.96 tff(17247,plain,
% 87.71/87.96 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17248,plain,
% 87.71/87.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17249,plain,
% 87.71/87.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17248, 17247])).
% 87.71/87.96 tff(17250,plain,
% 87.71/87.96 ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17249, 1638])).
% 87.71/87.96 tff(17251,plain,
% 87.71/87.96 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17250, 7386])).
% 87.71/87.96 tff(17252,plain,
% 87.71/87.96 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s10))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17253,plain,
% 87.71/87.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s10))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17254,plain,
% 87.71/87.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s10)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17253, 17252])).
% 87.71/87.96 tff(17255,plain,
% 87.71/87.96 (~node20(c_e_h_1, c_l, s10)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17254, 1535, 17251])).
% 87.71/87.96 tff(17256,assumption,(~node20(c_e_h_1, c_l, s10)), introduced(assumption)).
% 87.71/87.96 tff(17257,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s11)), introduced(assumption)).
% 87.71/87.96 tff(17258,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11)))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17259,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11)))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17260,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11))),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17259, 17258])).
% 87.71/87.96 tff(17261,plain,
% 87.71/87.96 (node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11))),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17260, 51])).
% 87.71/87.96 tff(17262,plain,
% 87.71/87.96 (~node21(c_e_h_1, c_l, s10, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17261, 17257, 17256])).
% 87.71/87.96 tff(17263,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17264,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17265,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17264, 17263])).
% 87.71/87.96 tff(17266,plain,
% 87.71/87.96 (node22(c_e_h_1, c_l, s10, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17265, 81, 3778, 17262])).
% 87.71/87.96 tff(17267,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node22(c_e_h_1, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node22(c_e_h_1, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17268,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node22(c_e_h_1, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17269,plain,
% 87.71/87.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node22(c_e_h_1, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17268, 17267])).
% 87.71/87.96 tff(17270,plain,
% 87.71/87.96 ($false),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17269, 107, 17257, 16536, 17266])).
% 87.71/87.96 tff(17271,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10) | node20(c_e_h_1, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.96 tff(17272,plain,
% 87.71/87.96 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17271, 17255])).
% 87.71/87.96 tff(17273,plain,
% 87.71/87.96 (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17272, 16536])).
% 87.71/87.96 tff(17274,plain,
% 87.71/87.96 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17275,plain,
% 87.71/87.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17276,plain,
% 87.71/87.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17275, 17274])).
% 87.71/87.96 tff(17277,plain,
% 87.71/87.96 ($false),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17276, 801, 17273, 17246])).
% 87.71/87.96 tff(17278,plain,(m_and_h_gate_v_out(c_e_h_1, c_l, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 87.71/87.96 tff(17279,plain,
% 87.71/87.96 (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17278, 16534, 17213, 16507])).
% 87.71/87.96 tff(17280,plain,
% 87.71/87.96 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17281,plain,
% 87.71/87.96 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))),
% 87.71/87.96 inference(quant_inst,[status(thm)],[])).
% 87.71/87.96 tff(17282,plain,
% 87.71/87.96 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12)),
% 87.71/87.96 inference(modus_ponens,[status(thm)],[17281, 17280])).
% 87.71/87.96 tff(17283,plain,
% 87.71/87.96 (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)),
% 87.71/87.96 inference(unit_resolution,[status(thm)],[17282, 309, 17279])).
% 87.71/87.96 tff(17284,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s13)), introduced(assumption)).
% 87.71/87.96 tff(17285,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s12)), introduced(assumption)).
% 87.71/87.96 tff(17286,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s12)), introduced(assumption)).
% 87.71/87.96 tff(17287,assumption,(node18(c_e_h_1, c_h, s12, s13)), introduced(assumption)).
% 87.71/87.96 tff(17288,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node18(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node18(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17289,plain,
% 87.71/87.96 (((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~node18(c_e_h_1, c_h, s12, s13))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node18(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.96 inference(rewrite,[status(thm)],[])).
% 87.71/87.96 tff(17290,plain,
% 87.71/87.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~node18(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node18(c_e_h_1, c_h, s12, s13))))),
% 87.71/87.97 inference(monotonicity,[status(thm)],[17289])).
% 87.71/87.97 tff(17291,plain,
% 87.71/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~node18(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node18(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(transitivity,[status(thm)],[17290, 17288])).
% 87.71/87.97 tff(17292,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~node18(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(quant_inst,[status(thm)],[])).
% 87.71/87.97 tff(17293,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node18(c_e_h_1, c_h, s12, s13))),
% 87.71/87.97 inference(modus_ponens,[status(thm)],[17292, 17291])).
% 87.71/87.97 tff(17294,plain,
% 87.71/87.97 ($false),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17293, 124, 17285, 17284, 17287])).
% 87.71/87.97 tff(17295,plain,((~node18(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.97 tff(17296,plain,
% 87.71/87.97 (~node18(c_e_h_1, c_h, s12, s13)),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17295, 17285, 17284])).
% 87.71/87.97 tff(17297,plain,
% 87.71/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_h, s12, s13))),
% 87.71/87.97 inference(rewrite,[status(thm)],[])).
% 87.71/87.97 tff(17298,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_h, s12, s13))),
% 87.71/87.97 inference(quant_inst,[status(thm)],[])).
% 87.71/87.97 tff(17299,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_h, s12, s13)),
% 87.71/87.97 inference(modus_ponens,[status(thm)],[17298, 17297])).
% 87.71/87.97 tff(17300,plain,
% 87.71/87.97 (node19(c_e_h_1, c_h, s12, s13)),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17299, 141, 9599])).
% 87.71/87.97 tff(17301,plain,
% 87.71/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(rewrite,[status(thm)],[])).
% 87.71/87.97 tff(17302,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(quant_inst,[status(thm)],[])).
% 87.71/87.97 tff(17303,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13))),
% 87.71/87.97 inference(modus_ponens,[status(thm)],[17302, 17301])).
% 87.71/87.97 tff(17304,plain,
% 87.71/87.97 (node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13)),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17303, 156, 17300])).
% 87.71/87.97 tff(17305,plain,
% 87.71/87.97 (node17(c_e_h_1, c_h, s12)),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17304, 17296])).
% 87.71/87.97 tff(17306,plain,
% 87.71/87.97 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)))),
% 87.71/87.97 inference(rewrite,[status(thm)],[])).
% 87.71/87.97 tff(17307,plain,
% 87.71/87.97 ((m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)))),
% 87.71/87.97 inference(rewrite,[status(thm)],[])).
% 87.71/87.97 tff(17308,plain,
% 87.71/87.97 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12))))),
% 87.71/87.97 inference(monotonicity,[status(thm)],[17307])).
% 87.71/87.97 tff(17309,plain,
% 87.71/87.97 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)))),
% 87.71/87.97 inference(transitivity,[status(thm)],[17308, 17306])).
% 87.71/87.97 tff(17310,plain,
% 87.71/87.97 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))),
% 87.71/87.97 inference(quant_inst,[status(thm)],[])).
% 87.71/87.97 tff(17311,plain,
% 87.71/87.97 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 87.71/87.97 inference(modus_ponens,[status(thm)],[17310, 17309])).
% 87.71/87.97 tff(17312,plain,
% 87.71/87.97 (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17311, 245, 17305])).
% 87.71/87.97 tff(17313,plain,
% 87.71/87.97 (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17312, 17286])).
% 87.71/87.97 tff(17314,assumption,(~node16(c_e_h_1, c_h, s12)), introduced(assumption)).
% 87.71/87.97 tff(17315,assumption,(node14(c_e_h_1, c_h, s12, s13)), introduced(assumption)).
% 87.71/87.97 tff(17316,plain,
% 87.71/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node14(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node14(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(rewrite,[status(thm)],[])).
% 87.71/87.97 tff(17317,plain,
% 87.71/87.97 (((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node14(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(rewrite,[status(thm)],[])).
% 87.71/87.97 tff(17318,plain,
% 87.71/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node14(c_e_h_1, c_h, s12, s13))))),
% 87.71/87.97 inference(monotonicity,[status(thm)],[17317])).
% 87.71/87.97 tff(17319,plain,
% 87.71/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node14(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(transitivity,[status(thm)],[17318, 17316])).
% 87.71/87.97 tff(17320,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)))),
% 87.71/87.97 inference(quant_inst,[status(thm)],[])).
% 87.71/87.97 tff(17321,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node14(c_e_h_1, c_h, s12, s13))),
% 87.71/87.97 inference(modus_ponens,[status(thm)],[17320, 17319])).
% 87.71/87.97 tff(17322,plain,
% 87.71/87.97 ($false),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17321, 283, 17286, 17284, 17315])).
% 87.71/87.97 tff(17323,plain,((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 87.71/87.97 tff(17324,plain,
% 87.71/87.97 (~node14(c_e_h_1, c_h, s12, s13)),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17323, 17284, 17286])).
% 87.71/87.97 tff(17325,plain,
% 87.71/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(rewrite,[status(thm)],[])).
% 87.71/87.97 tff(17326,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))),
% 87.71/87.97 inference(quant_inst,[status(thm)],[])).
% 87.71/87.97 tff(17327,plain,
% 87.71/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13))),
% 87.71/87.97 inference(modus_ponens,[status(thm)],[17326, 17325])).
% 87.71/87.97 tff(17328,plain,
% 87.71/87.97 (node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13)),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17327, 189, 17300])).
% 87.71/87.97 tff(17329,plain,
% 87.71/87.97 (node15(c_e_h_1, c_h, s12, s13)),
% 87.71/87.97 inference(unit_resolution,[status(thm)],[17328, 17324, 17314])).
% 87.71/87.97 tff(17330,plain,
% 87.71/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node15(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node15(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17331,plain,
% 87.79/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node15(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17332,plain,
% 87.79/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node15(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12)),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17331, 17330])).
% 87.79/87.97 tff(17333,plain,
% 87.79/87.97 ($false),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17332, 173, 17285, 17284, 17329])).
% 87.79/87.97 tff(17334,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | node16(c_e_h_1, c_h, s12) | m_c_h_element_v_in1(c_e_h_1, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.97 tff(17335,plain,
% 87.79/87.97 (node16(c_e_h_1, c_h, s12)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17334, 17286, 17284, 17285])).
% 87.79/87.97 tff(17336,plain,
% 87.79/87.97 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17337,plain,
% 87.79/87.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17338,plain,
% 87.79/87.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12)),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17337, 17336])).
% 87.79/87.97 tff(17339,plain,
% 87.79/87.97 ($false),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17338, 228, 17286, 17335, 17313])).
% 87.79/87.97 tff(17340,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.97 tff(17341,plain,
% 87.79/87.97 (m_c_h_element_v_in1(c_e_h_1, c_h, s12)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17340, 17285, 17284])).
% 87.79/87.97 tff(17342,plain,
% 87.79/87.97 (m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node18(c_e_h_1, c_h, s12, s13))),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17293, 124])).
% 87.79/87.97 tff(17343,plain,
% 87.79/87.97 (~node18(c_e_h_1, c_h, s12, s13)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17342, 17285, 17284])).
% 87.79/87.97 tff(17344,plain,
% 87.79/87.97 (node17(c_e_h_1, c_h, s12)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17304, 17343])).
% 87.79/87.97 tff(17345,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s12)), introduced(assumption)).
% 87.79/87.97 tff(17346,plain,
% 87.79/87.97 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17347,plain,
% 87.79/87.97 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17348,plain,
% 87.79/87.97 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12)))),
% 87.79/87.97 inference(monotonicity,[status(thm)],[17347])).
% 87.79/87.97 tff(17349,plain,
% 87.79/87.97 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(transitivity,[status(thm)],[17348, 17346])).
% 87.79/87.97 tff(17350,plain,
% 87.79/87.97 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17351,plain,
% 87.79/87.97 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12)),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17350, 17349])).
% 87.79/87.97 tff(17352,plain,
% 87.79/87.97 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17351, 209, 17345])).
% 87.79/87.97 tff(17353,plain,
% 87.79/87.97 ($false),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17352, 17344, 17341])).
% 87.79/87.97 tff(17354,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 87.79/87.97 tff(17355,plain,
% 87.79/87.97 (m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17354, 17283])).
% 87.79/87.97 tff(17356,plain,
% 87.79/87.97 (~m_c_h_element_v_out(c_e_h_1, c_h, s13)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17355, 16590])).
% 87.79/87.97 tff(17357,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s16)), introduced(assumption)).
% 87.79/87.97 tff(17358,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s13)), introduced(assumption)).
% 87.79/87.97 tff(17359,plain,
% 87.79/87.97 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17360,plain,
% 87.79/87.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17361,plain,
% 87.79/87.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s13)),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17360, 17359])).
% 87.79/87.97 tff(17362,plain,
% 87.79/87.97 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17361, 23, 17358])).
% 87.79/87.97 tff(17363,plain,
% 87.79/87.97 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s13))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17364,plain,
% 87.79/87.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s13))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17365,plain,
% 87.79/87.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s13)),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17364, 17363])).
% 87.79/87.97 tff(17366,plain,
% 87.79/87.97 (~node20(c_e_h_1, c_i, s13)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17365, 37, 17362])).
% 87.79/87.97 tff(17367,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s13)), introduced(assumption)).
% 87.79/87.97 tff(17368,assumption,(node22(c_e_h_1, c_i, s12, s13)), introduced(assumption)).
% 87.79/87.97 tff(17369,plain,
% 87.79/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node22(c_e_h_1, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node22(c_e_h_1, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17370,plain,
% 87.79/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node22(c_e_h_1, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17371,plain,
% 87.79/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node22(c_e_h_1, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17370, 17369])).
% 87.79/87.97 tff(17372,plain,
% 87.79/87.97 ($false),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17371, 107, 17367, 13682, 17368])).
% 87.79/87.97 tff(17373,plain,((~node22(c_e_h_1, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.97 tff(17374,plain,
% 87.79/87.97 (~node22(c_e_h_1, c_i, s12, s13)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17373, 17367, 13682])).
% 87.79/87.97 tff(17375,assumption,(~node20(c_e_h_1, c_i, s12)), introduced(assumption)).
% 87.79/87.97 tff(17376,assumption,(node21(c_e_h_1, c_i, s12, s13)), introduced(assumption)).
% 87.79/87.97 tff(17377,plain,
% 87.79/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node21(c_e_h_1, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node21(c_e_h_1, c_i, s12, s13)))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17378,plain,
% 87.79/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node21(c_e_h_1, c_i, s12, s13)))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17379,plain,
% 87.79/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node21(c_e_h_1, c_i, s12, s13))),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17378, 17377])).
% 87.79/87.97 tff(17380,plain,
% 87.79/87.97 ($false),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17379, 51, 17367, 17376, 17375])).
% 87.79/87.97 tff(17381,plain,((~node21(c_e_h_1, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.97 tff(17382,plain,
% 87.79/87.97 (~node21(c_e_h_1, c_i, s12, s13)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17381, 17367, 17375])).
% 87.79/87.97 tff(17383,plain,
% 87.79/87.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17384,plain,
% 87.79/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17385,plain,
% 87.79/87.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13)),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17384, 17383])).
% 87.79/87.97 tff(17386,plain,
% 87.79/87.97 (node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17385, 81, 9599])).
% 87.79/87.97 tff(17387,plain,
% 87.79/87.97 ($false),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17386, 17382, 17374])).
% 87.79/87.97 tff(17388,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.97 tff(17389,plain,
% 87.79/87.97 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17388, 13680])).
% 87.79/87.97 tff(17390,plain,
% 87.79/87.97 (node20(c_e_h_1, c_i, s12)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17389, 17367])).
% 87.79/87.97 tff(17391,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)), introduced(assumption)).
% 87.79/87.97 tff(17392,assumption,(node20(c_e_h_1, c_i, s12)), introduced(assumption)).
% 87.79/87.97 tff(17393,plain,
% 87.79/87.97 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17394,plain,
% 87.79/87.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12))),
% 87.79/87.97 inference(quant_inst,[status(thm)],[])).
% 87.79/87.97 tff(17395,plain,
% 87.79/87.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12)),
% 87.79/87.97 inference(modus_ponens,[status(thm)],[17394, 17393])).
% 87.79/87.97 tff(17396,plain,
% 87.79/87.97 ($false),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17395, 37, 17392, 17391])).
% 87.79/87.97 tff(17397,plain,((~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.97 tff(17398,plain,
% 87.79/87.97 (m_and_h_gate_v_in1(c_e_h_1, c_i, s12)),
% 87.79/87.97 inference(unit_resolution,[status(thm)],[17397, 17390])).
% 87.79/87.97 tff(17399,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_i, s12)), introduced(assumption)).
% 87.79/87.97 tff(17400,plain,
% 87.79/87.97 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 87.79/87.97 inference(rewrite,[status(thm)],[])).
% 87.79/87.97 tff(17401,plain,
% 87.79/87.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17402,plain,
% 87.79/87.98 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12)),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17401, 17400])).
% 87.79/87.98 tff(17403,plain,
% 87.79/87.98 ($false),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17402, 23, 17285, 17399])).
% 87.79/87.98 tff(17404,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.98 tff(17405,plain,
% 87.79/87.98 (m_c_h_element_v_out(c_e_h_1, c_h, s12)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17404, 17398])).
% 87.79/87.98 tff(17406,plain,
% 87.79/87.98 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[13643, 13638])).
% 87.79/87.98 tff(17407,plain,
% 87.79/87.98 (~m_c_h_element_v_out(c_e_h_1, c_h, s12)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[15912, 13638, 15859])).
% 87.79/87.98 tff(17408,plain,
% 87.79/87.98 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17404, 17407])).
% 87.79/87.98 tff(17409,plain,
% 87.79/87.98 (~node20(c_e_h_1, c_i, s12)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17397, 17408])).
% 87.79/87.98 tff(17410,plain,
% 87.79/87.98 (m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17388, 17409, 17367])).
% 87.79/87.98 tff(17411,plain,
% 87.79/87.98 (~node22(c_e_h_1, c_i, s11, s12)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[13663, 17410, 12103])).
% 87.79/87.98 tff(17412,plain,
% 87.79/87.98 (node21(c_e_h_1, c_i, s11, s12)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[13676, 17411])).
% 87.79/87.98 tff(17413,plain,
% 87.79/87.98 (node20(c_e_h_1, c_i, s11)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[13671, 17412, 17410])).
% 87.79/87.98 tff(17414,plain,
% 87.79/87.98 ($false),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[13649, 37, 17413, 17406])).
% 87.79/87.98 tff(17415,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s11) | m_and_h_gate_v_out(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.98 tff(17416,plain,
% 87.79/87.98 (m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17415, 13656])).
% 87.79/87.98 tff(17417,plain,
% 87.79/87.98 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17416, 13636])).
% 87.79/87.98 tff(17418,plain,
% 87.79/87.98 (m_c_h_element_v_in1(c_e_h_1, c_h, s11)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17417, 17367])).
% 87.79/87.98 tff(17419,plain,
% 87.79/87.98 (~node17(c_e_h_1, c_h, s11)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[16587, 17418])).
% 87.79/87.98 tff(17420,plain,
% 87.79/87.98 (node18(c_e_h_1, c_h, s11, s12)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[15871, 17419])).
% 87.79/87.98 tff(17421,plain,
% 87.79/87.98 ($false),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[15857, 17420, 17405])).
% 87.79/87.98 tff(17422,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.98 tff(17423,assumption,(~node20(c_e_h_1, c_i, s13)), introduced(assumption)).
% 87.79/87.98 tff(17424,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s14)), introduced(assumption)).
% 87.79/87.98 tff(17425,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14)))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17426,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14)))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17427,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14))),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17426, 17425])).
% 87.79/87.98 tff(17428,plain,
% 87.79/87.98 (node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14))),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17427, 51])).
% 87.79/87.98 tff(17429,plain,
% 87.79/87.98 (~node21(c_e_h_1, c_i, s13, s14)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17428, 17424, 17423])).
% 87.79/87.98 tff(17430,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s13)), introduced(assumption)).
% 87.79/87.98 tff(17431,assumption,(node22(c_e_h_1, c_i, s13, s14)), introduced(assumption)).
% 87.79/87.98 tff(17432,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17433,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17434,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17433, 17432])).
% 87.79/87.98 tff(17435,plain,
% 87.79/87.98 ($false),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17434, 107, 17430, 17424, 17431])).
% 87.79/87.98 tff(17436,plain,((~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14))), inference(lemma,lemma(discharge,[]))).
% 87.79/87.98 tff(17437,plain,
% 87.79/87.98 (~node22(c_e_h_1, c_i, s13, s14)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17436, 17424, 17430])).
% 87.79/87.98 tff(17438,assumption,(~node22(c_e_h_1, c_i, s13, s14)), introduced(assumption)).
% 87.79/87.98 tff(17439,assumption,(~node21(c_e_h_1, c_i, s13, s14)), introduced(assumption)).
% 87.79/87.98 tff(17440,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17441,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17442,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14)),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17441, 17440])).
% 87.79/87.98 tff(17443,plain,
% 87.79/87.98 ($false),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17442, 81, 10040, 17439, 17438])).
% 87.79/87.98 tff(17444,plain,(node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.98 tff(17445,plain,
% 87.79/87.98 ($false),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17444, 17437, 17429])).
% 87.79/87.98 tff(17446,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13) | node20(c_e_h_1, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.98 tff(17447,plain,
% 87.79/87.98 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | node20(c_e_h_1, c_i, s13)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17446, 17422])).
% 87.79/87.98 tff(17448,plain,
% 87.79/87.98 (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17447, 17366])).
% 87.79/87.98 tff(17449,plain,
% 87.79/87.98 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17450,plain,
% 87.79/87.98 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17451,plain,
% 87.79/87.98 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17450, 17449])).
% 87.79/87.98 tff(17452,plain,
% 87.79/87.98 (~m_c_h_element_v_in2(c_e_h_1, c_e, s14)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17451, 365, 17448])).
% 87.79/87.98 tff(17453,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s13)), introduced(assumption)).
% 87.79/87.98 tff(17454,plain,
% 87.79/87.98 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17455,plain,
% 87.79/87.98 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17456,plain,
% 87.79/87.98 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17455, 17454])).
% 87.79/87.98 tff(17457,plain,
% 87.79/87.98 ($false),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17456, 365, 17430, 17453])).
% 87.79/87.98 tff(17458,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.98 tff(17459,plain,
% 87.79/87.98 (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17458, 17422])).
% 87.79/87.98 tff(17460,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s13)), introduced(assumption)).
% 87.79/87.98 tff(17461,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s14)), introduced(assumption)).
% 87.79/87.98 tff(17462,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s13)), introduced(assumption)).
% 87.79/87.98 tff(17463,assumption,(node18(c_e_h_1, c_e, s13, s14)), introduced(assumption)).
% 87.79/87.98 tff(17464,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17465,plain,
% 87.79/87.98 (((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~node18(c_e_h_1, c_e, s13, s14))) <=> ((~node18(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17466,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~node18(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14))))),
% 87.79/87.98 inference(monotonicity,[status(thm)],[17465])).
% 87.79/87.98 tff(17467,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~node18(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))),
% 87.79/87.98 inference(transitivity,[status(thm)],[17466, 17464])).
% 87.79/87.98 tff(17468,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~node18(c_e_h_1, c_e, s13, s14)))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17469,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17468, 17467])).
% 87.79/87.98 tff(17470,plain,
% 87.79/87.98 ($false),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17469, 124, 17461, 17462, 17463])).
% 87.79/87.98 tff(17471,plain,((~node18(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.79/87.98 tff(17472,plain,
% 87.79/87.98 (~node18(c_e_h_1, c_e, s13, s14)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17471, 17462, 17461])).
% 87.79/87.98 tff(17473,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_e, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_e, s13, s14))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17474,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_e, s13, s14))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17475,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_e, s13, s14)),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17474, 17473])).
% 87.79/87.98 tff(17476,plain,
% 87.79/87.98 (node19(c_e_h_1, c_e, s13, s14)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17475, 141, 10040])).
% 87.79/87.98 tff(17477,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s13, s14)) | node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17478,plain,
% 87.79/87.98 ((node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14))) <=> ((~node19(c_e_h_1, c_e, s13, s14)) | node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17479,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s13, s14)) | node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14)))),
% 87.79/87.98 inference(monotonicity,[status(thm)],[17478])).
% 87.79/87.98 tff(17480,plain,
% 87.79/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14))),
% 87.79/87.98 inference(transitivity,[status(thm)],[17479, 17477])).
% 87.79/87.98 tff(17481,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17482,plain,
% 87.79/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14)),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17481, 17480])).
% 87.79/87.98 tff(17483,plain,
% 87.79/87.98 (node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17482, 156, 17476])).
% 87.79/87.98 tff(17484,plain,
% 87.79/87.98 (node17(c_e_h_1, c_e, s13)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17483, 17472])).
% 87.79/87.98 tff(17485,plain,
% 87.79/87.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17486,plain,
% 87.79/87.98 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))),
% 87.79/87.98 inference(rewrite,[status(thm)],[])).
% 87.79/87.98 tff(17487,plain,
% 87.79/87.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13))))),
% 87.79/87.98 inference(monotonicity,[status(thm)],[17486])).
% 87.79/87.98 tff(17488,plain,
% 87.79/87.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))),
% 87.79/87.98 inference(transitivity,[status(thm)],[17487, 17485])).
% 87.79/87.98 tff(17489,plain,
% 87.79/87.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)))),
% 87.79/87.98 inference(quant_inst,[status(thm)],[])).
% 87.79/87.98 tff(17490,plain,
% 87.79/87.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13))),
% 87.79/87.98 inference(modus_ponens,[status(thm)],[17489, 17488])).
% 87.79/87.98 tff(17491,plain,
% 87.79/87.98 (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)),
% 87.79/87.98 inference(unit_resolution,[status(thm)],[17490, 209, 17484, 17460])).
% 87.80/87.98 tff(17492,assumption,(node16(c_e_h_1, c_e, s13)), introduced(assumption)).
% 87.80/87.98 tff(17493,assumption,(node17(c_e_h_1, c_e, s13)), introduced(assumption)).
% 87.80/87.98 tff(17494,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s13)), introduced(assumption)).
% 87.80/87.98 tff(17495,plain,
% 87.80/87.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(rewrite,[status(thm)],[])).
% 87.80/87.98 tff(17496,plain,
% 87.80/87.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(quant_inst,[status(thm)],[])).
% 87.80/87.98 tff(17497,plain,
% 87.80/87.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 87.80/87.98 inference(modus_ponens,[status(thm)],[17496, 17495])).
% 87.80/87.98 tff(17498,plain,
% 87.80/87.98 (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17497, 228, 17492])).
% 87.80/87.98 tff(17499,plain,
% 87.80/87.98 (m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17498, 17494])).
% 87.80/87.98 tff(17500,plain,
% 87.80/87.98 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))),
% 87.80/87.98 inference(rewrite,[status(thm)],[])).
% 87.80/87.98 tff(17501,plain,
% 87.80/87.98 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))),
% 87.80/87.98 inference(quant_inst,[status(thm)],[])).
% 87.80/87.98 tff(17502,plain,
% 87.80/87.98 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(modus_ponens,[status(thm)],[17501, 17500])).
% 87.80/87.98 tff(17503,plain,
% 87.80/87.98 (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17502, 245, 17493])).
% 87.80/87.98 tff(17504,plain,
% 87.80/87.98 ($false),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17503, 17499, 17494])).
% 87.80/87.98 tff(17505,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 87.80/87.98 tff(17506,plain,
% 87.80/87.98 (m_c_h_element_v_in1(c_e_h_1, c_e, s13)),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17505, 17493, 17492])).
% 87.80/87.98 tff(17507,plain,
% 87.80/87.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)))),
% 87.80/87.98 inference(rewrite,[status(thm)],[])).
% 87.80/87.98 tff(17508,plain,
% 87.80/87.98 (((~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)))),
% 87.80/87.98 inference(rewrite,[status(thm)],[])).
% 87.80/87.98 tff(17509,plain,
% 87.80/87.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13))))),
% 87.80/87.98 inference(monotonicity,[status(thm)],[17508])).
% 87.80/87.98 tff(17510,plain,
% 87.80/87.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)))),
% 87.80/87.98 inference(transitivity,[status(thm)],[17509, 17507])).
% 87.80/87.98 tff(17511,plain,
% 87.80/87.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 87.80/87.98 inference(quant_inst,[status(thm)],[])).
% 87.80/87.98 tff(17512,plain,
% 87.80/87.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(modus_ponens,[status(thm)],[17511, 17510])).
% 87.80/87.98 tff(17513,plain,
% 87.80/87.98 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17512, 263, 17492])).
% 87.80/87.98 tff(17514,plain,
% 87.80/87.98 (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17513, 17506])).
% 87.80/87.98 tff(17515,plain,
% 87.80/87.98 (m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17490, 209, 17493])).
% 87.80/87.98 tff(17516,plain,
% 87.80/87.98 ($false),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17515, 17514, 17506])).
% 87.80/87.98 tff(17517,plain,((~node17(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 87.80/87.98 tff(17518,plain,
% 87.80/87.98 (~node16(c_e_h_1, c_e, s13)),
% 87.80/87.98 inference(unit_resolution,[status(thm)],[17517, 17484])).
% 87.80/87.98 tff(17519,assumption,(node15(c_e_h_1, c_e, s13, s14)), introduced(assumption)).
% 87.80/87.98 tff(17520,plain,
% 87.80/87.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | (~node15(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | (~node15(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(rewrite,[status(thm)],[])).
% 87.80/87.98 tff(17521,plain,
% 87.80/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | (~node15(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 87.80/87.98 inference(quant_inst,[status(thm)],[])).
% 87.80/87.98 tff(17522,plain,
% 87.80/87.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | (~node15(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13)),
% 87.80/87.98 inference(modus_ponens,[status(thm)],[17521, 17520])).
% 87.80/87.99 tff(17523,plain,
% 87.80/87.99 ($false),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17522, 173, 17461, 17462, 17519])).
% 87.80/87.99 tff(17524,plain,((~node15(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.80/87.99 tff(17525,plain,
% 87.80/87.99 (~node15(c_e_h_1, c_e, s13, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17524, 17462, 17461])).
% 87.80/87.99 tff(17526,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s13, s14)) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13) | node15(c_e_h_1, c_e, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13) | node15(c_e_h_1, c_e, s13, s14))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17527,plain,
% 87.80/87.99 ((node16(c_e_h_1, c_e, s13) | node14(c_e_h_1, c_e, s13, s14) | node15(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14))) <=> ((~node19(c_e_h_1, c_e, s13, s14)) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13) | node15(c_e_h_1, c_e, s13, s14))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17528,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s13) | node14(c_e_h_1, c_e, s13, s14) | node15(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s13, s14)) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13) | node15(c_e_h_1, c_e, s13, s14)))),
% 87.80/87.99 inference(monotonicity,[status(thm)],[17527])).
% 87.80/87.99 tff(17529,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s13) | node14(c_e_h_1, c_e, s13, s14) | node15(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13) | node15(c_e_h_1, c_e, s13, s14))),
% 87.80/87.99 inference(transitivity,[status(thm)],[17528, 17526])).
% 87.80/87.99 tff(17530,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s13) | node14(c_e_h_1, c_e, s13, s14) | node15(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17531,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13) | node15(c_e_h_1, c_e, s13, s14)),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17530, 17529])).
% 87.80/87.99 tff(17532,plain,
% 87.80/87.99 (node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13) | node15(c_e_h_1, c_e, s13, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17531, 189, 17476])).
% 87.80/87.99 tff(17533,plain,
% 87.80/87.99 (node14(c_e_h_1, c_e, s13, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17532, 17525, 17518])).
% 87.80/87.99 tff(17534,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17535,plain,
% 87.80/87.99 (((~node14(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14))) <=> ((~node14(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17536,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13)))),
% 87.80/87.99 inference(monotonicity,[status(thm)],[17535])).
% 87.80/87.99 tff(17537,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13))),
% 87.80/87.99 inference(transitivity,[status(thm)],[17536, 17534])).
% 87.80/87.99 tff(17538,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17539,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13)),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17538, 17537])).
% 87.80/87.99 tff(17540,plain,
% 87.80/87.99 ($false),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17539, 283, 17461, 17533, 17491])).
% 87.80/87.99 tff(17541,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 87.80/87.99 tff(17542,plain,
% 87.80/87.99 ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17541, 13763])).
% 87.80/87.99 tff(17543,plain,
% 87.80/87.99 (~m_c_h_element_v_out(c_e_h_1, c_e, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17542, 17459])).
% 87.80/87.99 tff(17544,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s14)), introduced(assumption)).
% 87.80/87.99 tff(17545,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s14)), introduced(assumption)).
% 87.80/87.99 tff(17546,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s15)), introduced(assumption)).
% 87.80/87.99 tff(17547,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s14)), introduced(assumption)).
% 87.80/87.99 tff(17548,plain,
% 87.80/87.99 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17549,plain,
% 87.80/87.99 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17550,plain,
% 87.80/87.99 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14)),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17549, 17548])).
% 87.80/87.99 tff(17551,plain,
% 87.80/87.99 ((~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17550, 228, 17545])).
% 87.80/87.99 tff(17552,plain,
% 87.80/87.99 (~node16(c_e_h_1, c_e, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17551, 17547])).
% 87.80/87.99 tff(17553,assumption,(~node16(c_e_h_1, c_e, s14)), introduced(assumption)).
% 87.80/87.99 tff(17554,assumption,(node14(c_e_h_1, c_e, s14, s15)), introduced(assumption)).
% 87.80/87.99 tff(17555,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17556,plain,
% 87.80/87.99 (((~node14(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17557,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15))))),
% 87.80/87.99 inference(monotonicity,[status(thm)],[17556])).
% 87.80/87.99 tff(17558,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(transitivity,[status(thm)],[17557, 17555])).
% 87.80/87.99 tff(17559,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17560,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15))),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17559, 17558])).
% 87.80/87.99 tff(17561,plain,
% 87.80/87.99 ($false),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17560, 283, 17546, 17554, 17547])).
% 87.80/87.99 tff(17562,plain,((~node14(c_e_h_1, c_e, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.80/87.99 tff(17563,plain,
% 87.80/87.99 (~node14(c_e_h_1, c_e, s14, s15)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17562, 17546, 17547])).
% 87.80/87.99 tff(17564,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_1, c_e, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_1, c_e, s14, s15))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17565,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_1, c_e, s14, s15))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17566,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_1, c_e, s14, s15)),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17565, 17564])).
% 87.80/87.99 tff(17567,plain,
% 87.80/87.99 (node19(c_e_h_1, c_e, s14, s15)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17566, 141, 10504])).
% 87.80/87.99 tff(17568,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)) | node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)) | node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17569,plain,
% 87.80/87.99 ((node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15))) <=> (node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)) | node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17570,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)) | node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(monotonicity,[status(thm)],[17569])).
% 87.80/87.99 tff(17571,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)) | node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15))),
% 87.80/87.99 inference(transitivity,[status(thm)],[17570, 17568])).
% 87.80/87.99 tff(17572,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17573,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)) | node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15)),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17572, 17571])).
% 87.80/87.99 tff(17574,plain,
% 87.80/87.99 (node15(c_e_h_1, c_e, s14, s15) | node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17573, 189, 17567])).
% 87.80/87.99 tff(17575,plain,
% 87.80/87.99 (node15(c_e_h_1, c_e, s14, s15)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17574, 17563, 17553])).
% 87.80/87.99 tff(17576,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17577,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17578,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14)),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17577, 17576])).
% 87.80/87.99 tff(17579,plain,
% 87.80/87.99 ($false),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17578, 173, 17546, 17575, 17544])).
% 87.80/87.99 tff(17580,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | node16(c_e_h_1, c_e, s14) | m_c_h_element_v_in1(c_e_h_1, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.80/87.99 tff(17581,plain,
% 87.80/87.99 ($false),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17580, 17552, 17547, 17546, 17544])).
% 87.80/87.99 tff(17582,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.80/87.99 tff(17583,plain,
% 87.80/87.99 (m_c_h_element_v_in1(c_e_h_1, c_e, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17582, 17544, 17546, 17545])).
% 87.80/87.99 tff(17584,plain,
% 87.80/87.99 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17585,plain,
% 87.80/87.99 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~node17(c_e_h_1, c_e, s14))) <=> ((~node17(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17586,plain,
% 87.80/87.99 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~node17(c_e_h_1, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14))))),
% 87.80/87.99 inference(monotonicity,[status(thm)],[17585])).
% 87.80/87.99 tff(17587,plain,
% 87.80/87.99 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~node17(c_e_h_1, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)))),
% 87.80/87.99 inference(transitivity,[status(thm)],[17586, 17584])).
% 87.80/87.99 tff(17588,plain,
% 87.80/87.99 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~node17(c_e_h_1, c_e, s14)))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17589,plain,
% 87.80/87.99 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14))),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17588, 17587])).
% 87.80/87.99 tff(17590,plain,
% 87.80/87.99 ((~node17(c_e_h_1, c_e, s14)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14))),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17589, 209, 17545])).
% 87.80/87.99 tff(17591,plain,
% 87.80/87.99 (~node17(c_e_h_1, c_e, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17590, 17583])).
% 87.80/87.99 tff(17592,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s14, s15) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s14, s15) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17593,plain,
% 87.80/87.99 ((node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15))) <=> (node18(c_e_h_1, c_e, s14, s15) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17594,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s14, s15) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15))))),
% 87.80/87.99 inference(monotonicity,[status(thm)],[17593])).
% 87.80/87.99 tff(17595,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s14, s15) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(transitivity,[status(thm)],[17594, 17592])).
% 87.80/87.99 tff(17596,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17597,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s14, s15) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15))),
% 87.80/87.99 inference(modus_ponens,[status(thm)],[17596, 17595])).
% 87.80/87.99 tff(17598,plain,
% 87.80/87.99 (node18(c_e_h_1, c_e, s14, s15) | node17(c_e_h_1, c_e, s14)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17597, 156, 17567])).
% 87.80/87.99 tff(17599,plain,
% 87.80/87.99 (node18(c_e_h_1, c_e, s14, s15)),
% 87.80/87.99 inference(unit_resolution,[status(thm)],[17598, 17591])).
% 87.80/87.99 tff(17600,plain,
% 87.80/87.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~node18(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~node18(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(rewrite,[status(thm)],[])).
% 87.80/87.99 tff(17601,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~node18(c_e_h_1, c_e, s14, s15)))),
% 87.80/87.99 inference(quant_inst,[status(thm)],[])).
% 87.80/87.99 tff(17602,plain,
% 87.80/87.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~node18(c_e_h_1, c_e, s14, s15))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17601, 17600])).
% 87.80/88.00 tff(17603,plain,
% 87.80/88.00 ($false),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17602, 124, 17546, 17599, 17544])).
% 87.80/88.00 tff(17604,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.80/88.00 tff(17605,plain,
% 87.80/88.00 ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17604, 17543])).
% 87.80/88.00 tff(17606,plain,
% 87.80/88.00 (~m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17605, 17452])).
% 87.80/88.00 tff(17607,plain,
% 87.80/88.00 (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17272, 16534])).
% 87.80/88.00 tff(17608,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s11)), introduced(assumption)).
% 87.80/88.00 tff(17609,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s12)), introduced(assumption)).
% 87.80/88.00 tff(17610,assumption,(node22(c_e_h_1, c_l, s11, s12)), introduced(assumption)).
% 87.80/88.00 tff(17611,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17612,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17613,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17612, 17611])).
% 87.80/88.00 tff(17614,plain,
% 87.80/88.00 ($false),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17613, 107, 17608, 17609, 17610])).
% 87.80/88.00 tff(17615,plain,((~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12))), inference(lemma,lemma(discharge,[]))).
% 87.80/88.00 tff(17616,plain,
% 87.80/88.00 (~node22(c_e_h_1, c_l, s11, s12)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17615, 17609, 17608])).
% 87.80/88.00 tff(17617,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17618,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17619,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17618, 17617])).
% 87.80/88.00 tff(17620,plain,
% 87.80/88.00 (node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17619, 81, 4461])).
% 87.80/88.00 tff(17621,plain,
% 87.80/88.00 (node21(c_e_h_1, c_l, s11, s12)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17620, 17616])).
% 87.80/88.00 tff(17622,plain,
% 87.80/88.00 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17623,plain,
% 87.80/88.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17624,plain,
% 87.80/88.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17623, 17622])).
% 87.80/88.00 tff(17625,plain,
% 87.80/88.00 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17624, 1638, 8378])).
% 87.80/88.00 tff(17626,plain,
% 87.80/88.00 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s11))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17627,plain,
% 87.80/88.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s11))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17628,plain,
% 87.80/88.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s11)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17627, 17626])).
% 87.80/88.00 tff(17629,plain,
% 87.80/88.00 (~node20(c_e_h_1, c_l, s11)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17628, 1535, 17625])).
% 87.80/88.00 tff(17630,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | node20(c_e_h_1, c_l, s11) | (~node21(c_e_h_1, c_l, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | node20(c_e_h_1, c_l, s11) | (~node21(c_e_h_1, c_l, s11, s12)))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17631,plain,
% 87.80/88.00 ((node20(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node21(c_e_h_1, c_l, s11, s12))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | node20(c_e_h_1, c_l, s11) | (~node21(c_e_h_1, c_l, s11, s12)))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17632,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node21(c_e_h_1, c_l, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | node20(c_e_h_1, c_l, s11) | (~node21(c_e_h_1, c_l, s11, s12))))),
% 87.80/88.00 inference(monotonicity,[status(thm)],[17631])).
% 87.80/88.00 tff(17633,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node21(c_e_h_1, c_l, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | node20(c_e_h_1, c_l, s11) | (~node21(c_e_h_1, c_l, s11, s12)))),
% 87.80/88.00 inference(transitivity,[status(thm)],[17632, 17630])).
% 87.80/88.00 tff(17634,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node21(c_e_h_1, c_l, s11, s12)))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17635,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | node20(c_e_h_1, c_l, s11) | (~node21(c_e_h_1, c_l, s11, s12))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17634, 17633])).
% 87.80/88.00 tff(17636,plain,
% 87.80/88.00 ($false),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17635, 51, 17609, 17629, 17621])).
% 87.80/88.00 tff(17637,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11)), inference(lemma,lemma(discharge,[]))).
% 87.80/88.00 tff(17638,plain,
% 87.80/88.00 (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17637, 17607])).
% 87.80/88.00 tff(17639,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s12)), introduced(assumption)).
% 87.80/88.00 tff(17640,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s12)), introduced(assumption)).
% 87.80/88.00 tff(17641,plain,
% 87.80/88.00 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17642,plain,
% 87.80/88.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17643,plain,
% 87.80/88.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17642, 17641])).
% 87.80/88.00 tff(17644,plain,
% 87.80/88.00 ($false),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17643, 801, 17640, 17639])).
% 87.80/88.00 tff(17645,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 87.80/88.00 tff(17646,plain,
% 87.80/88.00 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17645, 17638])).
% 87.80/88.00 tff(17647,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s12)), introduced(assumption)).
% 87.80/88.00 tff(17648,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s13)), introduced(assumption)).
% 87.80/88.00 tff(17649,assumption,(node6(c_e_h_1, c_j, s12, s13)), introduced(assumption)).
% 87.80/88.00 tff(17650,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13)))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17651,plain,
% 87.80/88.00 (((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13)))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17652,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13))))),
% 87.80/88.00 inference(monotonicity,[status(thm)],[17651])).
% 87.80/88.00 tff(17653,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13)))),
% 87.80/88.00 inference(transitivity,[status(thm)],[17652, 17650])).
% 87.80/88.00 tff(17654,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17655,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17654, 17653])).
% 87.80/88.00 tff(17656,plain,
% 87.80/88.00 ($false),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17655, 899, 17647, 17648, 17649])).
% 87.80/88.00 tff(17657,plain,((~node6(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13))), inference(lemma,lemma(discharge,[]))).
% 87.80/88.00 tff(17658,plain,
% 87.80/88.00 (~node6(c_e_h_1, c_j, s12, s13)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17657, 17648, 17647])).
% 87.80/88.00 tff(17659,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)), introduced(assumption)).
% 87.80/88.00 tff(17660,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)), introduced(assumption)).
% 87.80/88.00 tff(17661,plain,
% 87.80/88.00 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17662,plain,
% 87.80/88.00 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17663,plain,
% 87.80/88.00 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17662, 17661])).
% 87.80/88.00 tff(17664,plain,
% 87.80/88.00 ($false),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17663, 6378, 17660, 17150])).
% 87.80/88.00 tff(17665,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 87.80/88.00 tff(17666,plain,
% 87.80/88.00 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17665, 16463])).
% 87.80/88.00 tff(17667,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s3)), introduced(assumption)).
% 87.80/88.00 tff(17668,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s4)), introduced(assumption)).
% 87.80/88.00 tff(17669,plain,
% 87.80/88.00 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[16632, 15941, 16629])).
% 87.80/88.00 tff(17670,plain,
% 87.80/88.00 (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[16671, 17669])).
% 87.80/88.00 tff(17671,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s1)), introduced(assumption)).
% 87.80/88.00 tff(17672,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s2)), introduced(assumption)).
% 87.80/88.00 tff(17673,assumption,(node22(c_e_h_3, c_c, s1, s2)), introduced(assumption)).
% 87.80/88.00 tff(17674,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17675,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17676,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17675, 17674])).
% 87.80/88.00 tff(17677,plain,
% 87.80/88.00 ($false),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17676, 107, 17671, 17672, 17673])).
% 87.80/88.00 tff(17678,plain,((~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2))), inference(lemma,lemma(discharge,[]))).
% 87.80/88.00 tff(17679,plain,
% 87.80/88.00 (~node22(c_e_h_3, c_c, s1, s2)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17678, 17672, 17671])).
% 87.80/88.00 tff(17680,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s1)), introduced(assumption)).
% 87.80/88.00 tff(17681,assumption,(node13(c_e_h_3, c_a, s0, s1)), introduced(assumption)).
% 87.80/88.00 tff(17682,plain,
% 87.80/88.00 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)) <=> ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)))),
% 87.80/88.00 inference(bind,[status(th)],[])).
% 87.80/88.00 tff(17683,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 87.80/88.00 inference(quant_intro,[status(thm)],[17682])).
% 87.80/88.00 tff(17684,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17685,plain,
% 87.80/88.00 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_out(I0, I1, X)) | (~node13(I0, I1, X, Y))) <=> ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)))),
% 87.80/88.00 inference(bind,[status(th)],[])).
% 87.80/88.00 tff(17686,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_out(I0, I1, X)) | (~node13(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 87.80/88.00 inference(quant_intro,[status(thm)],[17685])).
% 87.80/88.00 tff(17687,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_out(I0, I1, X)) | (~node13(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_mutex_h_half_5')).
% 87.80/88.00 tff(17688,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17687, 17686])).
% 87.80/88.00 tff(17689,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17688, 17684])).
% 87.80/88.00 tff(17690,plain,(
% 87.80/88.00 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 87.80/88.00 inference(skolemize,[status(sab)],[17689])).
% 87.80/88.00 tff(17691,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17690, 17683])).
% 87.80/88.00 tff(17692,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17693,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17694,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17693, 17692])).
% 87.80/88.00 tff(17695,plain,
% 87.80/88.00 ($false),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17694, 17691, 17680, 16599, 17681])).
% 87.80/88.00 tff(17696,plain,((~node13(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1))), inference(lemma,lemma(discharge,[]))).
% 87.80/88.00 tff(17697,plain,
% 87.80/88.00 (~node13(c_e_h_3, c_a, s0, s1)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17696, 17680])).
% 87.80/88.00 tff(17698,plain,
% 87.80/88.00 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)))),
% 87.80/88.00 inference(bind,[status(th)],[])).
% 87.80/88.00 tff(17699,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 87.80/88.00 inference(quant_intro,[status(thm)],[17698])).
% 87.80/88.00 tff(17700,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17701,plain,
% 87.80/88.00 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) | (~trans(X, Y))) <=> ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)))),
% 87.80/88.00 inference(bind,[status(th)],[])).
% 87.80/88.00 tff(17702,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 87.80/88.00 inference(quant_intro,[status(thm)],[17701])).
% 87.80/88.00 tff(17703,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_mutex_h_half_6')).
% 87.80/88.00 tff(17704,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17703, 17702])).
% 87.80/88.00 tff(17705,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17704, 17700])).
% 87.80/88.00 tff(17706,plain,(
% 87.80/88.00 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 87.80/88.00 inference(skolemize,[status(sab)],[17705])).
% 87.80/88.00 tff(17707,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17706, 17699])).
% 87.80/88.00 tff(17708,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17709,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17710,plain,
% 87.80/88.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17709, 17708])).
% 87.80/88.00 tff(17711,plain,
% 87.80/88.00 (node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17710, 17707, 71])).
% 87.80/88.00 tff(17712,plain,
% 87.80/88.00 (node12(c_e_h_3, c_a, s0, s1)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17711, 17697])).
% 87.80/88.00 tff(17713,plain,
% 87.80/88.00 (^[I0: $i, I1: $i] : refl((~m_user_v_req(I0, I1, s0)) <=> (~m_user_v_req(I0, I1, s0)))),
% 87.80/88.00 inference(bind,[status(th)],[])).
% 87.80/88.00 tff(17714,plain,
% 87.80/88.00 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 87.80/88.00 inference(quant_intro,[status(thm)],[17713])).
% 87.80/88.00 tff(17715,plain,
% 87.80/88.00 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17716,axiom,(![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_user_1')).
% 87.80/88.00 tff(17717,plain,
% 87.80/88.00 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17716, 17715])).
% 87.80/88.00 tff(17718,plain,(
% 87.80/88.00 ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 87.80/88.00 inference(skolemize,[status(sab)],[17717])).
% 87.80/88.00 tff(17719,plain,
% 87.80/88.00 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17718, 17714])).
% 87.80/88.00 tff(17720,plain,
% 87.80/88.00 ((~![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))) | (~m_user_v_req(c_e_h_3, c_u, s0))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17721,plain,
% 87.80/88.00 (~m_user_v_req(c_e_h_3, c_u, s0)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17720, 17719])).
% 87.80/88.00 tff(17722,plain,
% 87.80/88.00 (^[I0: $i, X: $i] : refl(((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X)) <=> ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X)))),
% 87.80/88.00 inference(bind,[status(th)],[])).
% 87.80/88.00 tff(17723,plain,
% 87.80/88.00 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 87.80/88.00 inference(quant_intro,[status(thm)],[17722])).
% 87.80/88.00 tff(17724,plain,
% 87.80/88.00 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17725,axiom,(![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_2')).
% 87.80/88.00 tff(17726,plain,
% 87.80/88.00 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17725, 17724])).
% 87.80/88.00 tff(17727,plain,(
% 87.80/88.00 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 87.80/88.00 inference(skolemize,[status(sab)],[17726])).
% 87.80/88.00 tff(17728,plain,
% 87.80/88.00 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17727, 17723])).
% 87.80/88.00 tff(17729,plain,
% 87.80/88.00 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17730,plain,
% 87.80/88.00 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))),
% 87.80/88.00 inference(quant_inst,[status(thm)],[])).
% 87.80/88.00 tff(17731,plain,
% 87.80/88.00 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0)),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17730, 17729])).
% 87.80/88.00 tff(17732,plain,
% 87.80/88.00 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)),
% 87.80/88.00 inference(unit_resolution,[status(thm)],[17731, 17728, 17721])).
% 87.80/88.00 tff(17733,plain,
% 87.80/88.00 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))) <=> ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))))),
% 87.80/88.00 inference(bind,[status(th)],[])).
% 87.80/88.00 tff(17734,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 87.80/88.00 inference(quant_intro,[status(thm)],[17733])).
% 87.80/88.00 tff(17735,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17736,plain,
% 87.80/88.00 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_inp(I0, I1, X)) | (~node12(I0, I1, X, Y))) <=> ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))))),
% 87.80/88.00 inference(bind,[status(th)],[])).
% 87.80/88.00 tff(17737,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_inp(I0, I1, X)) | (~node12(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 87.80/88.00 inference(quant_intro,[status(thm)],[17736])).
% 87.80/88.00 tff(17738,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_inp(I0, I1, X)) | (~node12(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_mutex_h_half_3')).
% 87.80/88.00 tff(17739,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17738, 17737])).
% 87.80/88.00 tff(17740,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17739, 17735])).
% 87.80/88.00 tff(17741,plain,(
% 87.80/88.00 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 87.80/88.00 inference(skolemize,[status(sab)],[17740])).
% 87.80/88.00 tff(17742,plain,
% 87.80/88.00 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 87.80/88.00 inference(modus_ponens,[status(thm)],[17741, 17734])).
% 87.80/88.00 tff(17743,plain,
% 87.80/88.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node12(c_e_h_3, c_a, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node12(c_e_h_3, c_a, s0, s1)))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.00 tff(17744,plain,
% 87.80/88.00 (((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node12(c_e_h_3, c_a, s0, s1)))),
% 87.80/88.00 inference(rewrite,[status(thm)],[])).
% 87.80/88.01 tff(17745,plain,
% 87.80/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node12(c_e_h_3, c_a, s0, s1))))),
% 87.80/88.01 inference(monotonicity,[status(thm)],[17744])).
% 87.80/88.01 tff(17746,plain,
% 87.80/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node12(c_e_h_3, c_a, s0, s1)))),
% 87.80/88.01 inference(transitivity,[status(thm)],[17745, 17743])).
% 87.80/88.01 tff(17747,plain,
% 87.80/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))),
% 87.80/88.01 inference(quant_inst,[status(thm)],[])).
% 87.80/88.01 tff(17748,plain,
% 87.80/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node12(c_e_h_3, c_a, s0, s1))),
% 87.80/88.01 inference(modus_ponens,[status(thm)],[17747, 17746])).
% 87.80/88.01 tff(17749,plain,
% 87.80/88.01 ($false),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17748, 17742, 17732, 17680, 17712])).
% 87.80/88.01 tff(17750,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 87.80/88.01 tff(17751,plain,
% 87.80/88.01 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 87.80/88.01 inference(rewrite,[status(thm)],[])).
% 87.80/88.01 tff(17752,plain,
% 87.80/88.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 87.80/88.01 inference(quant_inst,[status(thm)],[])).
% 87.80/88.01 tff(17753,plain,
% 87.80/88.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 87.80/88.01 inference(modus_ponens,[status(thm)],[17752, 17751])).
% 87.80/88.01 tff(17754,plain,
% 87.80/88.01 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17753, 477, 17750])).
% 87.80/88.01 tff(17755,plain,
% 87.80/88.01 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))),
% 87.80/88.01 inference(rewrite,[status(thm)],[])).
% 87.80/88.01 tff(17756,plain,
% 87.80/88.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))),
% 87.80/88.01 inference(quant_inst,[status(thm)],[])).
% 87.80/88.01 tff(17757,plain,
% 87.80/88.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1)),
% 87.80/88.01 inference(modus_ponens,[status(thm)],[17756, 17755])).
% 87.80/88.01 tff(17758,plain,
% 87.80/88.01 (~node20(c_e_h_3, c_c, s1)),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17757, 37, 17754])).
% 87.80/88.01 tff(17759,plain,
% 87.80/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))),
% 87.80/88.01 inference(rewrite,[status(thm)],[])).
% 87.80/88.01 tff(17760,plain,
% 87.80/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))),
% 87.80/88.01 inference(quant_inst,[status(thm)],[])).
% 87.80/88.01 tff(17761,plain,
% 87.80/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2))),
% 87.80/88.01 inference(modus_ponens,[status(thm)],[17760, 17759])).
% 87.80/88.01 tff(17762,plain,
% 87.80/88.01 (node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2))),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17761, 51])).
% 87.80/88.01 tff(17763,plain,
% 87.80/88.01 ((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2))),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17762, 17758])).
% 87.80/88.01 tff(17764,plain,
% 87.80/88.01 (~node21(c_e_h_3, c_c, s1, s2)),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17763, 17672])).
% 87.80/88.01 tff(17765,plain,
% 87.80/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))),
% 87.80/88.01 inference(rewrite,[status(thm)],[])).
% 87.80/88.01 tff(17766,plain,
% 87.80/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))),
% 87.80/88.01 inference(quant_inst,[status(thm)],[])).
% 87.80/88.01 tff(17767,plain,
% 87.80/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2)),
% 87.80/88.01 inference(modus_ponens,[status(thm)],[17766, 17765])).
% 87.80/88.01 tff(17768,plain,
% 87.80/88.01 ($false),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17767, 81, 344, 17764, 17679])).
% 87.80/88.01 tff(17769,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 87.80/88.01 tff(17770,plain,
% 87.80/88.01 (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17769, 16629])).
% 87.80/88.01 tff(17771,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s2)), introduced(assumption)).
% 87.80/88.01 tff(17772,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s2)), introduced(assumption)).
% 87.80/88.01 tff(17773,plain,
% 87.80/88.01 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 87.80/88.01 inference(rewrite,[status(thm)],[])).
% 87.80/88.01 tff(17774,plain,
% 87.80/88.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 87.80/88.01 inference(quant_inst,[status(thm)],[])).
% 87.80/88.01 tff(17775,plain,
% 87.80/88.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2)),
% 87.80/88.01 inference(modus_ponens,[status(thm)],[17774, 17773])).
% 87.80/88.01 tff(17776,plain,
% 87.80/88.01 ($false),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17775, 15941, 17772, 17771])).
% 87.80/88.01 tff(17777,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s2) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s2))), inference(lemma,lemma(discharge,[]))).
% 87.80/88.01 tff(17778,plain,
% 87.80/88.01 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)),
% 87.80/88.01 inference(unit_resolution,[status(thm)],[17777, 17770])).
% 87.80/88.01 tff(17779,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)), introduced(assumption)).
% 87.80/88.01 tff(17780,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s3)), introduced(assumption)).
% 87.80/88.01 tff(17781,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s2)), introduced(assumption)).
% 87.80/88.01 tff(17782,assumption,(node22(c_e_h_3, c_d, s1, s2)), introduced(assumption)).
% 87.80/88.01 tff(17783,plain,
% 87.80/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node22(c_e_h_3, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node22(c_e_h_3, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17784,plain,
% 87.83/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node22(c_e_h_3, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17785,plain,
% 87.83/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node22(c_e_h_3, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1)),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17784, 17783])).
% 87.83/88.01 tff(17786,plain,
% 87.83/88.01 ($false),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17785, 107, 17781, 7769, 17782])).
% 87.83/88.01 tff(17787,plain,((~node22(c_e_h_3, c_d, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2))), inference(lemma,lemma(discharge,[]))).
% 87.83/88.01 tff(17788,plain,
% 87.83/88.01 (~node22(c_e_h_3, c_d, s1, s2)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17787, 17781])).
% 87.83/88.01 tff(17789,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s0)), introduced(assumption)).
% 87.83/88.01 tff(17790,plain,
% 87.83/88.01 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17791,plain,
% 87.83/88.01 ($false),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17790, 94, 17789])).
% 87.83/88.01 tff(17792,plain,(~m_and_h_gate_v_out(c_e_h_1, c_p, s0)), inference(lemma,lemma(discharge,[]))).
% 87.83/88.01 tff(17793,plain,
% 87.83/88.01 (^[I0: $i, X: $i] : refl(((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X)) <=> ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X)))),
% 87.83/88.01 inference(bind,[status(th)],[])).
% 87.83/88.01 tff(17794,plain,
% 87.83/88.01 (![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 87.83/88.01 inference(quant_intro,[status(thm)],[17793])).
% 87.83/88.01 tff(17795,plain,
% 87.83/88.01 (![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17796,axiom,(![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_76')).
% 87.83/88.01 tff(17797,plain,
% 87.83/88.01 (![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17796, 17795])).
% 87.83/88.01 tff(17798,plain,(
% 87.83/88.01 ![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 87.83/88.01 inference(skolemize,[status(sab)],[17797])).
% 87.83/88.01 tff(17799,plain,
% 87.83/88.01 (![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17798, 17794])).
% 87.83/88.01 tff(17800,plain,
% 87.83/88.01 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17801,plain,
% 87.83/88.01 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17802,plain,
% 87.83/88.01 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0)),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17801, 17800])).
% 87.83/88.01 tff(17803,plain,
% 87.83/88.01 (~m_cell_v_req(c_e_h_1, s0)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17802, 17799, 17792])).
% 87.83/88.01 tff(17804,plain,
% 87.83/88.01 (^[I0: $i, X: $i, J0: $i] : refl(((~m_cell_v_left(I0, J0)) | node1(I0, J0, X)) <=> ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X)))),
% 87.83/88.01 inference(bind,[status(th)],[])).
% 87.83/88.01 tff(17805,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 87.83/88.01 inference(quant_intro,[status(thm)],[17804])).
% 87.83/88.01 tff(17806,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17807,axiom,(![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_7')).
% 87.83/88.01 tff(17808,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17807, 17806])).
% 87.83/88.01 tff(17809,plain,(
% 87.83/88.01 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 87.83/88.01 inference(skolemize,[status(sab)],[17808])).
% 87.83/88.01 tff(17810,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17809, 17805])).
% 87.83/88.01 tff(17811,plain,
% 87.83/88.01 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s0))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17812,plain,
% 87.83/88.01 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s0))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17813,plain,
% 87.83/88.01 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s0)),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17812, 17811])).
% 87.83/88.01 tff(17814,plain,
% 87.83/88.01 (node1(c_e_h_3, c_e_h_1, s0)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17813, 3860, 17810])).
% 87.83/88.01 tff(17815,plain,
% 87.83/88.01 (^[I0: $i, X: $i, J0: $i] : refl(((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))) <=> ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))))),
% 87.83/88.01 inference(bind,[status(th)],[])).
% 87.83/88.01 tff(17816,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 87.83/88.01 inference(quant_intro,[status(thm)],[17815])).
% 87.83/88.01 tff(17817,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17818,plain,
% 87.83/88.01 (^[I0: $i, X: $i, J0: $i] : rewrite((((~m_mutex_h_half_v_inp(I0, c_b, X)) | m_cell_v_req(J0, X)) | (~node1(I0, J0, X))) <=> ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))))),
% 87.83/88.01 inference(bind,[status(th)],[])).
% 87.83/88.01 tff(17819,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : (((~m_mutex_h_half_v_inp(I0, c_b, X)) | m_cell_v_req(J0, X)) | (~node1(I0, J0, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 87.83/88.01 inference(quant_intro,[status(thm)],[17818])).
% 87.83/88.01 tff(17820,axiom,(![I0: $i, X: $i, J0: $i] : (((~m_mutex_h_half_v_inp(I0, c_b, X)) | m_cell_v_req(J0, X)) | (~node1(I0, J0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_6')).
% 87.83/88.01 tff(17821,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17820, 17819])).
% 87.83/88.01 tff(17822,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17821, 17817])).
% 87.83/88.01 tff(17823,plain,(
% 87.83/88.01 ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 87.83/88.01 inference(skolemize,[status(sab)],[17822])).
% 87.83/88.01 tff(17824,plain,
% 87.83/88.01 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17823, 17816])).
% 87.83/88.01 tff(17825,plain,
% 87.83/88.01 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | m_cell_v_req(c_e_h_1, s0) | (~node1(c_e_h_3, c_e_h_1, s0)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | m_cell_v_req(c_e_h_1, s0) | (~node1(c_e_h_3, c_e_h_1, s0)))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17826,plain,
% 87.83/88.01 (((~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0))) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | m_cell_v_req(c_e_h_1, s0) | (~node1(c_e_h_3, c_e_h_1, s0)))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17827,plain,
% 87.83/88.01 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | m_cell_v_req(c_e_h_1, s0) | (~node1(c_e_h_3, c_e_h_1, s0))))),
% 87.83/88.01 inference(monotonicity,[status(thm)],[17826])).
% 87.83/88.01 tff(17828,plain,
% 87.83/88.01 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | m_cell_v_req(c_e_h_1, s0) | (~node1(c_e_h_3, c_e_h_1, s0)))),
% 87.83/88.01 inference(transitivity,[status(thm)],[17827, 17825])).
% 87.83/88.01 tff(17829,plain,
% 87.83/88.01 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17830,plain,
% 87.83/88.01 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | m_cell_v_req(c_e_h_1, s0) | (~node1(c_e_h_3, c_e_h_1, s0))),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17829, 17828])).
% 87.83/88.01 tff(17831,plain,
% 87.83/88.01 ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | m_cell_v_req(c_e_h_1, s0)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17830, 17824, 17814])).
% 87.83/88.01 tff(17832,plain,
% 87.83/88.01 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17831, 17803])).
% 87.83/88.01 tff(17833,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s1)), introduced(assumption)).
% 87.83/88.01 tff(17834,assumption,(node13(c_e_h_3, c_b, s0, s1)), introduced(assumption)).
% 87.83/88.01 tff(17835,plain,
% 87.83/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node13(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node13(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17836,plain,
% 87.83/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node13(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17837,plain,
% 87.83/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node13(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0)),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17836, 17835])).
% 87.83/88.01 tff(17838,plain,
% 87.83/88.01 ($false),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17837, 17691, 7737, 17834, 17833])).
% 87.83/88.01 tff(17839,plain,((~node13(c_e_h_3, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1))), inference(lemma,lemma(discharge,[]))).
% 87.83/88.01 tff(17840,plain,
% 87.83/88.01 (~node13(c_e_h_3, c_b, s0, s1)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17839, 17833])).
% 87.83/88.01 tff(17841,plain,
% 87.83/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17842,plain,
% 87.83/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17843,plain,
% 87.83/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1)),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17842, 17841])).
% 87.83/88.01 tff(17844,plain,
% 87.83/88.01 (node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17843, 17707, 71])).
% 87.83/88.01 tff(17845,plain,
% 87.83/88.01 (node12(c_e_h_3, c_b, s0, s1)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17844, 17840])).
% 87.83/88.01 tff(17846,plain,
% 87.83/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17847,plain,
% 87.83/88.01 (((~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17848,plain,
% 87.83/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)))),
% 87.83/88.01 inference(monotonicity,[status(thm)],[17847])).
% 87.83/88.01 tff(17849,plain,
% 87.83/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0))),
% 87.83/88.01 inference(transitivity,[status(thm)],[17848, 17846])).
% 87.83/88.01 tff(17850,plain,
% 87.83/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17851,plain,
% 87.83/88.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17850, 17849])).
% 87.83/88.01 tff(17852,plain,
% 87.83/88.01 ($false),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17851, 17742, 17845, 17833, 17832])).
% 87.83/88.01 tff(17853,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)), inference(lemma,lemma(discharge,[]))).
% 87.83/88.01 tff(17854,plain,
% 87.83/88.01 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17855,plain,
% 87.83/88.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17856,plain,
% 87.83/88.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1)),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17855, 17854])).
% 87.83/88.01 tff(17857,plain,
% 87.83/88.01 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17856, 7744, 17853])).
% 87.83/88.01 tff(17858,plain,
% 87.83/88.01 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s1))),
% 87.83/88.01 inference(rewrite,[status(thm)],[])).
% 87.83/88.01 tff(17859,plain,
% 87.83/88.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s1))),
% 87.83/88.01 inference(quant_inst,[status(thm)],[])).
% 87.83/88.01 tff(17860,plain,
% 87.83/88.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s1)),
% 87.83/88.01 inference(modus_ponens,[status(thm)],[17859, 17858])).
% 87.83/88.01 tff(17861,plain,
% 87.83/88.01 (~node20(c_e_h_3, c_d, s1)),
% 87.83/88.01 inference(unit_resolution,[status(thm)],[17860, 37, 17857])).
% 87.83/88.01 tff(17862,assumption,(node21(c_e_h_3, c_d, s1, s2)), introduced(assumption)).
% 87.83/88.01 tff(17863,assumption,(~node20(c_e_h_3, c_d, s1)), introduced(assumption)).
% 87.83/88.01 tff(17864,plain,
% 87.83/88.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node21(c_e_h_3, c_d, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node21(c_e_h_3, c_d, s1, s2)))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17865,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node21(c_e_h_3, c_d, s1, s2)))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17866,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node21(c_e_h_3, c_d, s1, s2))),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17865, 17864])).
% 87.83/88.02 tff(17867,plain,
% 87.83/88.02 ($false),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17866, 51, 17863, 17781, 17862])).
% 87.83/88.02 tff(17868,plain,((~node21(c_e_h_3, c_d, s1, s2)) | node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2))), inference(lemma,lemma(discharge,[]))).
% 87.83/88.02 tff(17869,plain,
% 87.83/88.02 ((~node21(c_e_h_3, c_d, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17868, 17861])).
% 87.83/88.02 tff(17870,plain,
% 87.83/88.02 (~node21(c_e_h_3, c_d, s1, s2)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17869, 17781])).
% 87.83/88.02 tff(17871,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17872,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17873,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2)),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17872, 17871])).
% 87.83/88.02 tff(17874,plain,
% 87.83/88.02 (node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17873, 81, 344])).
% 87.83/88.02 tff(17875,plain,
% 87.83/88.02 ($false),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17874, 17870, 17788])).
% 87.83/88.02 tff(17876,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 87.83/88.02 tff(17877,plain,
% 87.83/88.02 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17878,plain,
% 87.83/88.02 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17879,plain,
% 87.83/88.02 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2)),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17878, 17877])).
% 87.83/88.02 tff(17880,plain,
% 87.83/88.02 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17879, 15952, 17876])).
% 87.83/88.02 tff(17881,assumption,(node5(c_e_h_3, c_g, s2, s3)), introduced(assumption)).
% 87.83/88.02 tff(17882,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17883,plain,
% 87.83/88.02 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17884,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3))))),
% 87.83/88.02 inference(monotonicity,[status(thm)],[17883])).
% 87.83/88.02 tff(17885,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)))),
% 87.83/88.02 inference(transitivity,[status(thm)],[17884, 17882])).
% 87.83/88.02 tff(17886,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17887,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3))),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17886, 17885])).
% 87.83/88.02 tff(17888,plain,
% 87.83/88.02 ($false),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17887, 862, 17780, 17881, 17880, 17779])).
% 87.83/88.02 tff(17889,plain,((~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 87.83/88.02 tff(17890,plain,
% 87.83/88.02 (~node5(c_e_h_3, c_g, s2, s3)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17889, 17780, 17779])).
% 87.83/88.02 tff(17891,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17892,plain,
% 87.83/88.02 ((node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17893,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3)))),
% 87.83/88.02 inference(monotonicity,[status(thm)],[17892])).
% 87.83/88.02 tff(17894,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3))),
% 87.83/88.02 inference(transitivity,[status(thm)],[17893, 17891])).
% 87.83/88.02 tff(17895,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3) | (~trans(s2, s3)))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17896,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3)),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17895, 17894])).
% 87.83/88.02 tff(17897,plain,
% 87.83/88.02 (node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17896, 881, 582])).
% 87.83/88.02 tff(17898,plain,
% 87.83/88.02 (node6(c_e_h_3, c_g, s2, s3)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17897, 17890])).
% 87.83/88.02 tff(17899,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s2)), introduced(assumption)).
% 87.83/88.02 tff(17900,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node6(c_e_h_3, c_g, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node6(c_e_h_3, c_g, s2, s3)))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17901,plain,
% 87.83/88.02 (((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node6(c_e_h_3, c_g, s2, s3)))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17902,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node6(c_e_h_3, c_g, s2, s3))))),
% 87.83/88.02 inference(monotonicity,[status(thm)],[17901])).
% 87.83/88.02 tff(17903,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node6(c_e_h_3, c_g, s2, s3)))),
% 87.83/88.02 inference(transitivity,[status(thm)],[17902, 17900])).
% 87.83/88.02 tff(17904,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17905,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node6(c_e_h_3, c_g, s2, s3))),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17904, 17903])).
% 87.83/88.02 tff(17906,plain,
% 87.83/88.02 ($false),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17905, 899, 17780, 17899, 17898])).
% 87.83/88.02 tff(17907,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 87.83/88.02 tff(17908,plain,
% 87.83/88.02 ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17907, 17778])).
% 87.83/88.02 tff(17909,plain,
% 87.83/88.02 (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17908, 17670])).
% 87.83/88.02 tff(17910,plain,
% 87.83/88.02 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17911,plain,
% 87.83/88.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17912,plain,
% 87.83/88.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3)),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17911, 17910])).
% 87.83/88.02 tff(17913,plain,
% 87.83/88.02 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17912, 13114, 17909])).
% 87.83/88.02 tff(17914,plain,
% 87.83/88.02 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s3))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17915,plain,
% 87.83/88.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s3))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17916,plain,
% 87.83/88.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s3)),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17915, 17914])).
% 87.83/88.02 tff(17917,plain,
% 87.83/88.02 (~node20(c_e_h_3, c_k, s3)),
% 87.83/88.02 inference(unit_resolution,[status(thm)],[17916, 37, 17913])).
% 87.83/88.02 tff(17918,assumption,(~node20(c_e_h_3, c_k, s3)), introduced(assumption)).
% 87.83/88.02 tff(17919,assumption,(node21(c_e_h_3, c_k, s3, s4)), introduced(assumption)).
% 87.83/88.02 tff(17920,plain,
% 87.83/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node21(c_e_h_3, c_k, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node21(c_e_h_3, c_k, s3, s4)))),
% 87.83/88.02 inference(rewrite,[status(thm)],[])).
% 87.83/88.02 tff(17921,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node21(c_e_h_3, c_k, s3, s4)))),
% 87.83/88.02 inference(quant_inst,[status(thm)],[])).
% 87.83/88.02 tff(17922,plain,
% 87.83/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node21(c_e_h_3, c_k, s3, s4))),
% 87.83/88.02 inference(modus_ponens,[status(thm)],[17921, 17920])).
% 87.83/88.02 tff(17923,plain,
% 87.83/88.02 ($false),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17922, 51, 17919, 17668, 17918])).
% 87.84/88.02 tff(17924,plain,((~node21(c_e_h_3, c_k, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | node20(c_e_h_3, c_k, s3)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.02 tff(17925,plain,
% 87.84/88.02 (~node21(c_e_h_3, c_k, s3, s4)),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17924, 17668, 17917])).
% 87.84/88.02 tff(17926,plain,
% 87.84/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4))),
% 87.84/88.02 inference(rewrite,[status(thm)],[])).
% 87.84/88.02 tff(17927,plain,
% 87.84/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4))),
% 87.84/88.02 inference(quant_inst,[status(thm)],[])).
% 87.84/88.02 tff(17928,plain,
% 87.84/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4)),
% 87.84/88.02 inference(modus_ponens,[status(thm)],[17927, 17926])).
% 87.84/88.02 tff(17929,plain,
% 87.84/88.02 (node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4)),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17928, 81, 679])).
% 87.84/88.02 tff(17930,plain,
% 87.84/88.02 (node22(c_e_h_3, c_k, s3, s4)),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17929, 17925])).
% 87.84/88.02 tff(17931,plain,
% 87.84/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node22(c_e_h_3, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node22(c_e_h_3, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 87.84/88.02 inference(rewrite,[status(thm)],[])).
% 87.84/88.02 tff(17932,plain,
% 87.84/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node22(c_e_h_3, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 87.84/88.02 inference(quant_inst,[status(thm)],[])).
% 87.84/88.02 tff(17933,plain,
% 87.84/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node22(c_e_h_3, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3)),
% 87.84/88.02 inference(modus_ponens,[status(thm)],[17932, 17931])).
% 87.84/88.02 tff(17934,plain,
% 87.84/88.02 ($false),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17933, 107, 17930, 17668, 17667])).
% 87.84/88.02 tff(17935,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.02 tff(17936,plain,
% 87.84/88.02 (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17935, 16707])).
% 87.84/88.02 tff(17937,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s4)), introduced(assumption)).
% 87.84/88.02 tff(17938,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s4)), introduced(assumption)).
% 87.84/88.02 tff(17939,plain,
% 87.84/88.02 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))),
% 87.84/88.02 inference(rewrite,[status(thm)],[])).
% 87.84/88.02 tff(17940,plain,
% 87.84/88.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))),
% 87.84/88.02 inference(quant_inst,[status(thm)],[])).
% 87.84/88.02 tff(17941,plain,
% 87.84/88.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4)),
% 87.84/88.02 inference(modus_ponens,[status(thm)],[17940, 17939])).
% 87.84/88.02 tff(17942,plain,
% 87.84/88.02 ($false),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17941, 10554, 17938, 17937])).
% 87.84/88.02 tff(17943,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.02 tff(17944,plain,
% 87.84/88.02 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17943, 17936])).
% 87.84/88.02 tff(17945,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)), introduced(assumption)).
% 87.84/88.02 tff(17946,assumption,(node20(c_e_h_3, c_l, s4)), introduced(assumption)).
% 87.84/88.02 tff(17947,plain,
% 87.84/88.02 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4))),
% 87.84/88.02 inference(rewrite,[status(thm)],[])).
% 87.84/88.02 tff(17948,plain,
% 87.84/88.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4))),
% 87.84/88.02 inference(quant_inst,[status(thm)],[])).
% 87.84/88.02 tff(17949,plain,
% 87.84/88.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4)),
% 87.84/88.02 inference(modus_ponens,[status(thm)],[17948, 17947])).
% 87.84/88.02 tff(17950,plain,
% 87.84/88.02 ($false),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17949, 37, 17946, 17945])).
% 87.84/88.02 tff(17951,plain,((~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.02 tff(17952,plain,
% 87.84/88.02 (~node20(c_e_h_3, c_l, s4)),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17951, 17944])).
% 87.84/88.02 tff(17953,assumption,(~node20(c_e_h_3, c_l, s4)), introduced(assumption)).
% 87.84/88.02 tff(17954,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s5)), introduced(assumption)).
% 87.84/88.02 tff(17955,assumption,(node21(c_e_h_3, c_l, s4, s5)), introduced(assumption)).
% 87.84/88.02 tff(17956,plain,
% 87.84/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node21(c_e_h_3, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node21(c_e_h_3, c_l, s4, s5)))),
% 87.84/88.02 inference(rewrite,[status(thm)],[])).
% 87.84/88.02 tff(17957,plain,
% 87.84/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node21(c_e_h_3, c_l, s4, s5)))),
% 87.84/88.02 inference(quant_inst,[status(thm)],[])).
% 87.84/88.02 tff(17958,plain,
% 87.84/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node21(c_e_h_3, c_l, s4, s5))),
% 87.84/88.02 inference(modus_ponens,[status(thm)],[17957, 17956])).
% 87.84/88.02 tff(17959,plain,
% 87.84/88.02 ($false),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17958, 51, 17954, 17953, 17955])).
% 87.84/88.02 tff(17960,plain,((~node21(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | node20(c_e_h_3, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.02 tff(17961,plain,
% 87.84/88.02 (~node21(c_e_h_3, c_l, s4, s5)),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17960, 17954, 17953])).
% 87.84/88.02 tff(17962,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s4)), introduced(assumption)).
% 87.84/88.02 tff(17963,plain,
% 87.84/88.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 87.84/88.02 inference(rewrite,[status(thm)],[])).
% 87.84/88.02 tff(17964,plain,
% 87.84/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 87.84/88.02 inference(quant_inst,[status(thm)],[])).
% 87.84/88.02 tff(17965,plain,
% 87.84/88.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 87.84/88.02 inference(modus_ponens,[status(thm)],[17964, 17963])).
% 87.84/88.02 tff(17966,plain,
% 87.84/88.02 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 87.84/88.02 inference(unit_resolution,[status(thm)],[17965, 107])).
% 87.84/88.02 tff(17967,plain,
% 87.84/88.03 (~node22(c_e_h_3, c_l, s4, s5)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17966, 17954, 17962])).
% 87.84/88.03 tff(17968,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(17969,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(17970,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[17969, 17968])).
% 87.84/88.03 tff(17971,plain,
% 87.84/88.03 ($false),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17970, 81, 1432, 17967, 17961])).
% 87.84/88.03 tff(17972,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | node20(c_e_h_3, c_l, s4) | m_and_h_gate_v_out(c_e_h_3, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.03 tff(17973,plain,
% 87.84/88.03 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17972, 17952])).
% 87.84/88.03 tff(17974,plain,
% 87.84/88.03 (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17973, 16734])).
% 87.84/88.03 tff(17975,plain,
% 87.84/88.03 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(17976,plain,
% 87.84/88.03 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(17977,plain,
% 87.84/88.03 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[17976, 17975])).
% 87.84/88.03 tff(17978,plain,
% 87.84/88.03 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17977, 801, 17974])).
% 87.84/88.03 tff(17979,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s5)), introduced(assumption)).
% 87.84/88.03 tff(17980,assumption,(node21(c_e_h_2, c_q, s4, s5)), introduced(assumption)).
% 87.84/88.03 tff(17981,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s4)), introduced(assumption)).
% 87.84/88.03 tff(17982,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s3)), introduced(assumption)).
% 87.84/88.03 tff(17983,assumption,(node18(c_e_h_2, c_f, s3, s4)), introduced(assumption)).
% 87.84/88.03 tff(17984,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(17985,plain,
% 87.84/88.03 (((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~node18(c_e_h_2, c_f, s3, s4))) <=> ((~node18(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(17986,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~node18(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))))),
% 87.84/88.03 inference(monotonicity,[status(thm)],[17985])).
% 87.84/88.03 tff(17987,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~node18(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 87.84/88.03 inference(transitivity,[status(thm)],[17986, 17984])).
% 87.84/88.03 tff(17988,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~node18(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(17989,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[17988, 17987])).
% 87.84/88.03 tff(17990,plain,
% 87.84/88.03 ($false),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17989, 124, 17981, 17983, 17982])).
% 87.84/88.03 tff(17991,plain,((~node18(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.03 tff(17992,plain,
% 87.84/88.03 ((~node18(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17991, 16813])).
% 87.84/88.03 tff(17993,plain,
% 87.84/88.03 (~node18(c_e_h_2, c_f, s3, s4)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17992, 17981])).
% 87.84/88.03 tff(17994,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s3)), introduced(assumption)).
% 87.84/88.03 tff(17995,plain,
% 87.84/88.03 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(17996,plain,
% 87.84/88.03 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(17997,plain,
% 87.84/88.03 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[17996, 17995])).
% 87.84/88.03 tff(17998,plain,
% 87.84/88.03 (~m_c_h_element_v_in2(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[17997, 2218, 960])).
% 87.84/88.03 tff(17999,plain,
% 87.84/88.03 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18000,plain,
% 87.84/88.03 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18001,plain,
% 87.84/88.03 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18000, 17999])).
% 87.84/88.03 tff(18002,plain,
% 87.84/88.03 ((~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18001, 228, 17998])).
% 87.84/88.03 tff(18003,plain,
% 87.84/88.03 (~node16(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18002, 17994])).
% 87.84/88.03 tff(18004,assumption,(node14(c_e_h_2, c_f, s3, s4)), introduced(assumption)).
% 87.84/88.03 tff(18005,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~node14(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~node14(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18006,plain,
% 87.84/88.03 (((~node14(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~node14(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18007,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~node14(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))))),
% 87.84/88.03 inference(monotonicity,[status(thm)],[18006])).
% 87.84/88.03 tff(18008,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~node14(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 87.84/88.03 inference(transitivity,[status(thm)],[18007, 18005])).
% 87.84/88.03 tff(18009,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18010,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~node14(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18009, 18008])).
% 87.84/88.03 tff(18011,plain,
% 87.84/88.03 ($false),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18010, 283, 17981, 18004, 17994])).
% 87.84/88.03 tff(18012,plain,((~node14(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.03 tff(18013,plain,
% 87.84/88.03 (~node14(c_e_h_2, c_f, s3, s4)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18012, 17981, 17994])).
% 87.84/88.03 tff(18014,assumption,(node15(c_e_h_2, c_f, s3, s4)), introduced(assumption)).
% 87.84/88.03 tff(18015,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18016,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18017,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18016, 18015])).
% 87.84/88.03 tff(18018,plain,
% 87.84/88.03 ($false),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18017, 173, 17981, 18014, 17982])).
% 87.84/88.03 tff(18019,plain,((~node15(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.03 tff(18020,plain,
% 87.84/88.03 (~node15(c_e_h_2, c_f, s3, s4)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18019, 17981, 17982])).
% 87.84/88.03 tff(18021,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_f, s3, s4))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18022,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_f, s3, s4))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18023,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_f, s3, s4)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18022, 18021])).
% 87.84/88.03 tff(18024,plain,
% 87.84/88.03 (node19(c_e_h_2, c_f, s3, s4)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18023, 141, 679])).
% 87.84/88.03 tff(18025,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s3) | node15(c_e_h_2, c_f, s3, s4) | node14(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s3) | node15(c_e_h_2, c_f, s3, s4) | node14(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18026,plain,
% 87.84/88.03 ((node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4) | node15(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4))) <=> (node16(c_e_h_2, c_f, s3) | node15(c_e_h_2, c_f, s3, s4) | node14(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18027,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4) | node15(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s3) | node15(c_e_h_2, c_f, s3, s4) | node14(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4))))),
% 87.84/88.03 inference(monotonicity,[status(thm)],[18026])).
% 87.84/88.03 tff(18028,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4) | node15(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s3) | node15(c_e_h_2, c_f, s3, s4) | node14(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(transitivity,[status(thm)],[18027, 18025])).
% 87.84/88.03 tff(18029,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4) | node15(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18030,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s3) | node15(c_e_h_2, c_f, s3, s4) | node14(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4))),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18029, 18028])).
% 87.84/88.03 tff(18031,plain,
% 87.84/88.03 (node16(c_e_h_2, c_f, s3) | node15(c_e_h_2, c_f, s3, s4) | node14(c_e_h_2, c_f, s3, s4)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18030, 189, 18024])).
% 87.84/88.03 tff(18032,plain,
% 87.84/88.03 ($false),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18031, 18020, 18013, 18003])).
% 87.84/88.03 tff(18033,plain,((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | m_c_h_element_v_in1(c_e_h_2, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.03 tff(18034,plain,
% 87.84/88.03 ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18033, 16813])).
% 87.84/88.03 tff(18035,plain,
% 87.84/88.03 (m_c_h_element_v_in1(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18034, 17981])).
% 87.84/88.03 tff(18036,plain,
% 87.84/88.03 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18037,plain,
% 87.84/88.03 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | (~node17(c_e_h_2, c_f, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18038,plain,
% 87.84/88.03 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | (~node17(c_e_h_2, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3)))),
% 87.84/88.03 inference(monotonicity,[status(thm)],[18037])).
% 87.84/88.03 tff(18039,plain,
% 87.84/88.03 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | (~node17(c_e_h_2, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 87.84/88.03 inference(transitivity,[status(thm)],[18038, 18036])).
% 87.84/88.03 tff(18040,plain,
% 87.84/88.03 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | (~node17(c_e_h_2, c_f, s3)))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18041,plain,
% 87.84/88.03 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18040, 18039])).
% 87.84/88.03 tff(18042,plain,
% 87.84/88.03 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3))),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18041, 209, 17998])).
% 87.84/88.03 tff(18043,plain,
% 87.84/88.03 (~node17(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18042, 18035])).
% 87.84/88.03 tff(18044,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_f, s3, s4) | node17(c_e_h_2, c_f, s3) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s3, s4) | node17(c_e_h_2, c_f, s3) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18045,plain,
% 87.84/88.03 ((node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4))) <=> (node18(c_e_h_2, c_f, s3, s4) | node17(c_e_h_2, c_f, s3) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18046,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_f, s3, s4) | node17(c_e_h_2, c_f, s3) | (~node19(c_e_h_2, c_f, s3, s4))))),
% 87.84/88.03 inference(monotonicity,[status(thm)],[18045])).
% 87.84/88.03 tff(18047,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s3, s4) | node17(c_e_h_2, c_f, s3) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(transitivity,[status(thm)],[18046, 18044])).
% 87.84/88.03 tff(18048,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18049,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s3, s4) | node17(c_e_h_2, c_f, s3) | (~node19(c_e_h_2, c_f, s3, s4))),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18048, 18047])).
% 87.84/88.03 tff(18050,plain,
% 87.84/88.03 (node18(c_e_h_2, c_f, s3, s4) | node17(c_e_h_2, c_f, s3)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18049, 156, 18024])).
% 87.84/88.03 tff(18051,plain,
% 87.84/88.03 ($false),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18050, 18043, 17993])).
% 87.84/88.03 tff(18052,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.03 tff(18053,plain,
% 87.84/88.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18054,plain,
% 87.84/88.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18055,plain,
% 87.84/88.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18054, 18053])).
% 87.84/88.03 tff(18056,plain,
% 87.84/88.03 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18055, 1666, 18052])).
% 87.84/88.03 tff(18057,plain,
% 87.84/88.03 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s4))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18058,plain,
% 87.84/88.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s4))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18059,plain,
% 87.84/88.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s4)),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18058, 18057])).
% 87.84/88.03 tff(18060,plain,
% 87.84/88.03 (~node20(c_e_h_2, c_q, s4)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18059, 37, 18056])).
% 87.84/88.03 tff(18061,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node21(c_e_h_2, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node21(c_e_h_2, c_q, s4, s5)))),
% 87.84/88.03 inference(rewrite,[status(thm)],[])).
% 87.84/88.03 tff(18062,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node21(c_e_h_2, c_q, s4, s5)))),
% 87.84/88.03 inference(quant_inst,[status(thm)],[])).
% 87.84/88.03 tff(18063,plain,
% 87.84/88.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node21(c_e_h_2, c_q, s4, s5))),
% 87.84/88.03 inference(modus_ponens,[status(thm)],[18062, 18061])).
% 87.84/88.03 tff(18064,plain,
% 87.84/88.03 ($false),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18063, 51, 17979, 18060, 17980])).
% 87.84/88.03 tff(18065,plain,((~node21(c_e_h_2, c_q, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.03 tff(18066,plain,
% 87.84/88.03 (~node21(c_e_h_2, c_q, s4, s5)),
% 87.84/88.03 inference(unit_resolution,[status(thm)],[18065, 17979])).
% 87.84/88.03 tff(18067,assumption,(node22(c_e_h_2, c_q, s4, s5)), introduced(assumption)).
% 87.84/88.03 tff(18068,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s4)), introduced(assumption)).
% 87.84/88.03 tff(18069,plain,
% 87.84/88.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node22(c_e_h_2, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node22(c_e_h_2, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18070,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node22(c_e_h_2, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18071,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node22(c_e_h_2, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18070, 18069])).
% 87.84/88.04 tff(18072,plain,
% 87.84/88.04 ($false),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18071, 107, 17979, 18068, 18067])).
% 87.84/88.04 tff(18073,plain,((~node22(c_e_h_2, c_q, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.04 tff(18074,plain,
% 87.84/88.04 ((~node22(c_e_h_2, c_q, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18073, 16836])).
% 87.84/88.04 tff(18075,plain,
% 87.84/88.04 (~node22(c_e_h_2, c_q, s4, s5)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18074, 17979])).
% 87.84/88.04 tff(18076,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18077,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18078,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18077, 18076])).
% 87.84/88.04 tff(18079,plain,
% 87.84/88.04 (node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18078, 81, 1432])).
% 87.84/88.04 tff(18080,plain,
% 87.84/88.04 ($false),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18079, 18075, 18066])).
% 87.84/88.04 tff(18081,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.04 tff(18082,assumption,(~node3(c_e_h_2, c_e_h_3, s5)), introduced(assumption)).
% 87.84/88.04 tff(18083,plain,
% 87.84/88.04 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s5))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18084,plain,
% 87.84/88.04 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s5))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18085,plain,
% 87.84/88.04 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s5)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18084, 18083])).
% 87.84/88.04 tff(18086,plain,
% 87.84/88.04 ($false),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18085, 7448, 814, 18082])).
% 87.84/88.04 tff(18087,plain,(node3(c_e_h_2, c_e_h_3, s5)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.04 tff(18088,plain,
% 87.84/88.04 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18089,plain,
% 87.84/88.04 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18090,plain,
% 87.84/88.04 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18089, 18088])).
% 87.84/88.04 tff(18091,plain,
% 87.84/88.04 ((~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18090, 836])).
% 87.84/88.04 tff(18092,plain,
% 87.84/88.04 ((~m_cell_v_ack(c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18091, 18087])).
% 87.84/88.04 tff(18093,plain,
% 87.84/88.04 (~m_cell_v_ack(c_e_h_3, s5)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18092, 18081])).
% 87.84/88.04 tff(18094,plain,
% 87.84/88.04 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)) | m_cell_v_ack(c_e_h_3, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)) | m_cell_v_ack(c_e_h_3, s5))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18095,plain,
% 87.84/88.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)) | m_cell_v_ack(c_e_h_3, s5))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18096,plain,
% 87.84/88.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)) | m_cell_v_ack(c_e_h_3, s5)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18095, 18094])).
% 87.84/88.04 tff(18097,plain,
% 87.84/88.04 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18096, 848, 18093])).
% 87.84/88.04 tff(18098,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)), introduced(assumption)).
% 87.84/88.04 tff(18099,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)), introduced(assumption)).
% 87.84/88.04 tff(18100,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s5)), introduced(assumption)).
% 87.84/88.04 tff(18101,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s6)), introduced(assumption)).
% 87.84/88.04 tff(18102,assumption,(node6(c_e_h_3, c_j, s5, s6)), introduced(assumption)).
% 87.84/88.04 tff(18103,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~node6(c_e_h_3, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~node6(c_e_h_3, c_j, s5, s6)))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18104,plain,
% 87.84/88.04 (((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~node6(c_e_h_3, c_j, s5, s6)))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18105,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~node6(c_e_h_3, c_j, s5, s6))))),
% 87.84/88.04 inference(monotonicity,[status(thm)],[18104])).
% 87.84/88.04 tff(18106,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~node6(c_e_h_3, c_j, s5, s6)))),
% 87.84/88.04 inference(transitivity,[status(thm)],[18105, 18103])).
% 87.84/88.04 tff(18107,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18108,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~node6(c_e_h_3, c_j, s5, s6))),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18107, 18106])).
% 87.84/88.04 tff(18109,plain,
% 87.84/88.04 ($false),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18108, 899, 18101, 18100, 18102])).
% 87.84/88.04 tff(18110,plain,((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.04 tff(18111,plain,
% 87.84/88.04 (~node6(c_e_h_3, c_j, s5, s6)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18110, 18101, 18100])).
% 87.84/88.04 tff(18112,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18113,plain,
% 87.84/88.04 ((node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6) | (~trans(s5, s6))) <=> ((~trans(s5, s6)) | node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18114,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6)))),
% 87.84/88.04 inference(monotonicity,[status(thm)],[18113])).
% 87.84/88.04 tff(18115,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6))),
% 87.84/88.04 inference(transitivity,[status(thm)],[18114, 18112])).
% 87.84/88.04 tff(18116,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6) | (~trans(s5, s6)))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18117,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18116, 18115])).
% 87.84/88.04 tff(18118,plain,
% 87.84/88.04 (node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18117, 881, 1499])).
% 87.84/88.04 tff(18119,plain,
% 87.84/88.04 (node5(c_e_h_3, c_j, s5, s6)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18118, 18111])).
% 87.84/88.04 tff(18120,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18121,plain,
% 87.84/88.04 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18122,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5)))),
% 87.84/88.04 inference(monotonicity,[status(thm)],[18121])).
% 87.84/88.04 tff(18123,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5))),
% 87.84/88.04 inference(transitivity,[status(thm)],[18122, 18120])).
% 87.84/88.04 tff(18124,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18125,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18124, 18123])).
% 87.84/88.04 tff(18126,plain,
% 87.84/88.04 ($false),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18125, 862, 18101, 18119, 18099, 18098])).
% 87.84/88.04 tff(18127,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_out(c_e_h_3, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.04 tff(18128,plain,
% 87.84/88.04 (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18127, 18097, 17978, 16884])).
% 87.84/88.04 tff(18129,plain,
% 87.84/88.04 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18130,plain,
% 87.84/88.04 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18131,plain,
% 87.84/88.04 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18130, 18129])).
% 87.84/88.04 tff(18132,plain,
% 87.84/88.04 (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18131, 309, 18128])).
% 87.84/88.04 tff(18133,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s7)), introduced(assumption)).
% 87.84/88.04 tff(18134,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s6)), introduced(assumption)).
% 87.84/88.04 tff(18135,assumption,(node18(c_e_h_3, c_h, s6, s7)), introduced(assumption)).
% 87.84/88.04 tff(18136,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~node18(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~node18(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18137,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~node18(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18138,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~node18(c_e_h_3, c_h, s6, s7))),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18137, 18136])).
% 87.84/88.04 tff(18139,plain,
% 87.84/88.04 ($false),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18138, 124, 18133, 18134, 18135])).
% 87.84/88.04 tff(18140,plain,((~node18(c_e_h_3, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.04 tff(18141,plain,
% 87.84/88.04 (~node18(c_e_h_3, c_h, s6, s7)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18140, 18134, 18133])).
% 87.84/88.04 tff(18142,plain,
% 87.84/88.04 (~node18(c_e_h_3, c_h, s6, s7)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18140, 18133, 18134])).
% 87.84/88.04 tff(18143,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_h, s6, s7))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18144,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_h, s6, s7))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18145,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_h, s6, s7)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18144, 18143])).
% 87.84/88.04 tff(18146,plain,
% 87.84/88.04 (node19(c_e_h_3, c_h, s6, s7)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18145, 141, 1552])).
% 87.84/88.04 tff(18147,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s6) | (~node19(c_e_h_3, c_h, s6, s7)) | node18(c_e_h_3, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s6) | (~node19(c_e_h_3, c_h, s6, s7)) | node18(c_e_h_3, c_h, s6, s7))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18148,plain,
% 87.84/88.04 ((node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7))) <=> (node17(c_e_h_3, c_h, s6) | (~node19(c_e_h_3, c_h, s6, s7)) | node18(c_e_h_3, c_h, s6, s7))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18149,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s6) | (~node19(c_e_h_3, c_h, s6, s7)) | node18(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.04 inference(monotonicity,[status(thm)],[18148])).
% 87.84/88.04 tff(18150,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s6) | (~node19(c_e_h_3, c_h, s6, s7)) | node18(c_e_h_3, c_h, s6, s7))),
% 87.84/88.04 inference(transitivity,[status(thm)],[18149, 18147])).
% 87.84/88.04 tff(18151,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18152,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s6) | (~node19(c_e_h_3, c_h, s6, s7)) | node18(c_e_h_3, c_h, s6, s7)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18151, 18150])).
% 87.84/88.04 tff(18153,plain,
% 87.84/88.04 (node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18152, 156, 18146])).
% 87.84/88.04 tff(18154,plain,
% 87.84/88.04 (node17(c_e_h_3, c_h, s6)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18153, 18142])).
% 87.84/88.04 tff(18155,assumption,(node15(c_e_h_3, c_h, s6, s7)), introduced(assumption)).
% 87.84/88.04 tff(18156,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | (~node15(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | (~node15(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.04 tff(18157,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | (~node15(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 87.84/88.04 inference(quant_inst,[status(thm)],[])).
% 87.84/88.04 tff(18158,plain,
% 87.84/88.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | (~node15(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 87.84/88.04 inference(modus_ponens,[status(thm)],[18157, 18156])).
% 87.84/88.04 tff(18159,plain,
% 87.84/88.04 ($false),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18158, 173, 18133, 18134, 18155])).
% 87.84/88.04 tff(18160,plain,((~node15(c_e_h_3, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.04 tff(18161,plain,
% 87.84/88.04 (~node15(c_e_h_3, c_h, s6, s7)),
% 87.84/88.04 inference(unit_resolution,[status(thm)],[18160, 18133, 18134])).
% 87.84/88.04 tff(18162,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s6)), introduced(assumption)).
% 87.84/88.04 tff(18163,assumption,(node14(c_e_h_3, c_h, s6, s7)), introduced(assumption)).
% 87.84/88.04 tff(18164,plain,
% 87.84/88.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.04 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18165,plain,
% 87.84/88.05 (((~node14(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18166,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7))))),
% 87.84/88.05 inference(monotonicity,[status(thm)],[18165])).
% 87.84/88.05 tff(18167,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.05 inference(transitivity,[status(thm)],[18166, 18164])).
% 87.84/88.05 tff(18168,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18169,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7))),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18168, 18167])).
% 87.84/88.05 tff(18170,plain,
% 87.84/88.05 ($false),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18169, 283, 18133, 18163, 18162])).
% 87.84/88.05 tff(18171,plain,((~node14(c_e_h_3, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.05 tff(18172,plain,
% 87.84/88.05 (~node14(c_e_h_3, c_h, s6, s7)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18171, 18133, 18162])).
% 87.84/88.05 tff(18173,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18174,plain,
% 87.84/88.05 ((node16(c_e_h_3, c_h, s6) | node14(c_e_h_3, c_h, s6, s7) | node15(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7))) <=> (node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18175,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node14(c_e_h_3, c_h, s6, s7) | node15(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7))))),
% 87.84/88.05 inference(monotonicity,[status(thm)],[18174])).
% 87.84/88.05 tff(18176,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node14(c_e_h_3, c_h, s6, s7) | node15(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.05 inference(transitivity,[status(thm)],[18175, 18173])).
% 87.84/88.05 tff(18177,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node14(c_e_h_3, c_h, s6, s7) | node15(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18178,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7))),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18177, 18176])).
% 87.84/88.05 tff(18179,plain,
% 87.84/88.05 (node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18178, 189, 18146])).
% 87.84/88.05 tff(18180,plain,
% 87.84/88.05 (node16(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18179, 18172, 18161])).
% 87.84/88.05 tff(18181,assumption,(node17(c_e_h_3, c_h, s6)), introduced(assumption)).
% 87.84/88.05 tff(18182,assumption,(node16(c_e_h_3, c_h, s6)), introduced(assumption)).
% 87.84/88.05 tff(18183,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18184,plain,
% 87.84/88.05 ((m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | (~node17(c_e_h_3, c_h, s6))) <=> ((~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18185,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | (~node17(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6)))),
% 87.84/88.05 inference(monotonicity,[status(thm)],[18184])).
% 87.84/88.05 tff(18186,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | (~node17(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(transitivity,[status(thm)],[18185, 18183])).
% 87.84/88.05 tff(18187,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | (~node17(c_e_h_3, c_h, s6)))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18188,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18187, 18186])).
% 87.84/88.05 tff(18189,plain,
% 87.84/88.05 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18188, 245, 18181])).
% 87.84/88.05 tff(18190,plain,
% 87.84/88.05 (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18189, 18162])).
% 87.84/88.05 tff(18191,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18192,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18193,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18192, 18191])).
% 87.84/88.05 tff(18194,plain,
% 87.84/88.05 (m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18193, 228, 18182])).
% 87.84/88.05 tff(18195,plain,
% 87.84/88.05 ($false),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18194, 18190, 18162])).
% 87.84/88.05 tff(18196,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node16(c_e_h_3, c_h, s6)) | (~node17(c_e_h_3, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.05 tff(18197,plain,
% 87.84/88.05 (m_c_h_element_v_in1(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18196, 18182, 18181])).
% 87.84/88.05 tff(18198,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18199,plain,
% 87.84/88.05 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18200,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6))))),
% 87.84/88.05 inference(monotonicity,[status(thm)],[18199])).
% 87.84/88.05 tff(18201,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)))),
% 87.84/88.05 inference(transitivity,[status(thm)],[18200, 18198])).
% 87.84/88.05 tff(18202,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18203,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18202, 18201])).
% 87.84/88.05 tff(18204,plain,
% 87.84/88.05 (m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18203, 209, 18181])).
% 87.84/88.05 tff(18205,plain,
% 87.84/88.05 (m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18204, 18197])).
% 87.84/88.05 tff(18206,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18207,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18208,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18207, 18206])).
% 87.84/88.05 tff(18209,plain,
% 87.84/88.05 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18208, 263, 18182])).
% 87.84/88.05 tff(18210,plain,
% 87.84/88.05 ($false),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18209, 18205, 18197])).
% 87.84/88.05 tff(18211,plain,((~node16(c_e_h_3, c_h, s6)) | (~node17(c_e_h_3, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.05 tff(18212,plain,
% 87.84/88.05 ($false),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18211, 18180, 18154])).
% 87.84/88.05 tff(18213,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_out(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.05 tff(18214,plain,
% 87.84/88.05 (m_c_h_element_v_in1(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18213, 18134, 18133])).
% 87.84/88.05 tff(18215,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s6)), introduced(assumption)).
% 87.84/88.05 tff(18216,plain,
% 87.84/88.05 ((~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6))),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18203, 209, 18215])).
% 87.84/88.05 tff(18217,plain,
% 87.84/88.05 (~node17(c_e_h_3, c_h, s6)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18216, 18214])).
% 87.84/88.05 tff(18218,plain,
% 87.84/88.05 ($false),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18153, 18217, 18141])).
% 87.84/88.05 tff(18219,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.05 tff(18220,plain,
% 87.84/88.05 (~m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18219, 18132, 16966])).
% 87.84/88.05 tff(18221,plain,
% 87.84/88.05 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18222,plain,
% 87.84/88.05 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18223,plain,
% 87.84/88.05 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18222, 18221])).
% 87.84/88.05 tff(18224,plain,
% 87.84/88.05 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18223, 23, 18220])).
% 87.84/88.05 tff(18225,plain,
% 87.84/88.05 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s7))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18226,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s7))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18227,plain,
% 87.84/88.05 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s7)),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18226, 18225])).
% 87.84/88.05 tff(18228,plain,
% 87.84/88.05 (~node20(c_e_h_3, c_i, s7)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18227, 37, 18224])).
% 87.84/88.05 tff(18229,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s9)), introduced(assumption)).
% 87.84/88.05 tff(18230,assumption,(~node20(c_e_h_3, c_i, s7)), introduced(assumption)).
% 87.84/88.05 tff(18231,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s8)), introduced(assumption)).
% 87.84/88.05 tff(18232,assumption,(node21(c_e_h_3, c_i, s7, s8)), introduced(assumption)).
% 87.84/88.05 tff(18233,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node21(c_e_h_3, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node21(c_e_h_3, c_i, s7, s8)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18234,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node21(c_e_h_3, c_i, s7, s8)))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18235,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node21(c_e_h_3, c_i, s7, s8))),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18234, 18233])).
% 87.84/88.05 tff(18236,plain,
% 87.84/88.05 ($false),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18235, 51, 18231, 18232, 18230])).
% 87.84/88.05 tff(18237,plain,((~node21(c_e_h_3, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | node20(c_e_h_3, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.05 tff(18238,plain,
% 87.84/88.05 (~node21(c_e_h_3, c_i, s7, s8)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18237, 18231, 18230])).
% 87.84/88.05 tff(18239,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s7)), introduced(assumption)).
% 87.84/88.05 tff(18240,assumption,(node22(c_e_h_3, c_i, s7, s8)), introduced(assumption)).
% 87.84/88.05 tff(18241,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node22(c_e_h_3, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node22(c_e_h_3, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18242,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node22(c_e_h_3, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18243,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node22(c_e_h_3, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18242, 18241])).
% 87.84/88.05 tff(18244,plain,
% 87.84/88.05 ($false),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18243, 107, 18231, 18239, 18240])).
% 87.84/88.05 tff(18245,plain,((~node22(c_e_h_3, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.05 tff(18246,plain,
% 87.84/88.05 (~node22(c_e_h_3, c_i, s7, s8)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18245, 18231, 18239])).
% 87.84/88.05 tff(18247,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18248,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18249,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8)),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18248, 18247])).
% 87.84/88.05 tff(18250,plain,
% 87.84/88.05 (node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18249, 81, 2152])).
% 87.84/88.05 tff(18251,plain,
% 87.84/88.05 ($false),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18250, 18246, 18238])).
% 87.84/88.05 tff(18252,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7) | node20(c_e_h_3, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.05 tff(18253,plain,
% 87.84/88.05 (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18252, 17003, 18230])).
% 87.84/88.05 tff(18254,plain,
% 87.84/88.05 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18255,plain,
% 87.84/88.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18256,plain,
% 87.84/88.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18255, 18254])).
% 87.84/88.05 tff(18257,plain,
% 87.84/88.05 (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18256, 2218, 18253])).
% 87.84/88.05 tff(18258,plain,
% 87.84/88.05 (~m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[16366, 16977, 13405])).
% 87.84/88.05 tff(18259,plain,
% 87.84/88.05 (~m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[17078, 17007, 18258])).
% 87.84/88.05 tff(18260,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18261,plain,
% 87.84/88.05 (((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~node18(c_e_h_3, c_f, s8, s9))) <=> ((~node18(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18262,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~node18(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9))))),
% 87.84/88.05 inference(monotonicity,[status(thm)],[18261])).
% 87.84/88.05 tff(18263,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~node18(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))),
% 87.84/88.05 inference(transitivity,[status(thm)],[18262, 18260])).
% 87.84/88.05 tff(18264,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~node18(c_e_h_3, c_f, s8, s9)))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18265,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18264, 18263])).
% 87.84/88.05 tff(18266,plain,
% 87.84/88.05 ((~node18(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18265, 124])).
% 87.84/88.05 tff(18267,plain,
% 87.84/88.05 (~node18(c_e_h_3, c_f, s8, s9)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18266, 18229, 17128])).
% 87.84/88.05 tff(18268,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_f, s8, s9))),
% 87.84/88.05 inference(rewrite,[status(thm)],[])).
% 87.84/88.05 tff(18269,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_f, s8, s9))),
% 87.84/88.05 inference(quant_inst,[status(thm)],[])).
% 87.84/88.05 tff(18270,plain,
% 87.84/88.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_f, s8, s9)),
% 87.84/88.05 inference(modus_ponens,[status(thm)],[18269, 18268])).
% 87.84/88.05 tff(18271,plain,
% 87.84/88.05 (node19(c_e_h_3, c_f, s8, s9)),
% 87.84/88.05 inference(unit_resolution,[status(thm)],[18270, 141, 2636])).
% 87.84/88.05 tff(18272,plain,
% 87.84/88.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9) | node17(c_e_h_3, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9) | node17(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18273,plain,
% 87.84/88.06 ((node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9))) <=> ((~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9) | node17(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18274,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9) | node17(c_e_h_3, c_f, s8)))),
% 87.84/88.06 inference(monotonicity,[status(thm)],[18273])).
% 87.84/88.06 tff(18275,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9) | node17(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(transitivity,[status(thm)],[18274, 18272])).
% 87.84/88.06 tff(18276,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18277,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9) | node17(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18276, 18275])).
% 87.84/88.06 tff(18278,plain,
% 87.84/88.06 (node18(c_e_h_3, c_f, s8, s9) | node17(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18277, 156, 18271])).
% 87.84/88.06 tff(18279,plain,
% 87.84/88.06 (node17(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18278, 18267])).
% 87.84/88.06 tff(18280,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s8)), introduced(assumption)).
% 87.84/88.06 tff(18281,plain,
% 87.84/88.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18282,plain,
% 87.84/88.06 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18283,plain,
% 87.84/88.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8)))),
% 87.84/88.06 inference(monotonicity,[status(thm)],[18282])).
% 87.84/88.06 tff(18284,plain,
% 87.84/88.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(transitivity,[status(thm)],[18283, 18281])).
% 87.84/88.06 tff(18285,plain,
% 87.84/88.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18286,plain,
% 87.84/88.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18285, 18284])).
% 87.84/88.06 tff(18287,plain,
% 87.84/88.06 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18286, 209, 18280])).
% 87.84/88.06 tff(18288,plain,
% 87.84/88.06 (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18287, 18279])).
% 87.84/88.06 tff(18289,assumption,(node15(c_e_h_3, c_f, s8, s9)), introduced(assumption)).
% 87.84/88.06 tff(18290,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18291,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18292,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18291, 18290])).
% 87.84/88.06 tff(18293,plain,
% 87.84/88.06 ($false),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18292, 173, 18229, 17128, 18289])).
% 87.84/88.06 tff(18294,plain,((~node15(c_e_h_3, c_f, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.06 tff(18295,plain,
% 87.84/88.06 (~node15(c_e_h_3, c_f, s8, s9)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18294, 18229, 17128])).
% 87.84/88.06 tff(18296,plain,
% 87.84/88.06 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18297,plain,
% 87.84/88.06 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18298,plain,
% 87.84/88.06 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18297, 18296])).
% 87.84/88.06 tff(18299,plain,
% 87.84/88.06 ((~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18298, 228, 18280])).
% 87.84/88.06 tff(18300,plain,
% 87.84/88.06 (~node16(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18299, 18288])).
% 87.84/88.06 tff(18301,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)) | node16(c_e_h_3, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)) | node16(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18302,plain,
% 87.84/88.06 ((node16(c_e_h_3, c_f, s8) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9))) <=> (node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)) | node16(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18303,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s8) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)) | node16(c_e_h_3, c_f, s8)))),
% 87.84/88.06 inference(monotonicity,[status(thm)],[18302])).
% 87.84/88.06 tff(18304,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s8) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)) | node16(c_e_h_3, c_f, s8))),
% 87.84/88.06 inference(transitivity,[status(thm)],[18303, 18301])).
% 87.84/88.06 tff(18305,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s8) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18306,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)) | node16(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18305, 18304])).
% 87.84/88.06 tff(18307,plain,
% 87.84/88.06 (node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | node16(c_e_h_3, c_f, s8)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18306, 189, 18271])).
% 87.84/88.06 tff(18308,plain,
% 87.84/88.06 (node14(c_e_h_3, c_f, s8, s9)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18307, 18300, 18295])).
% 87.84/88.06 tff(18309,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9)))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18310,plain,
% 87.84/88.06 (((~node14(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9)))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18311,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9))))),
% 87.84/88.06 inference(monotonicity,[status(thm)],[18310])).
% 87.84/88.06 tff(18312,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9)))),
% 87.84/88.06 inference(transitivity,[status(thm)],[18311, 18309])).
% 87.84/88.06 tff(18313,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18314,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9))),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18313, 18312])).
% 87.84/88.06 tff(18315,plain,
% 87.84/88.06 ($false),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18314, 283, 18229, 18308, 18288])).
% 87.84/88.06 tff(18316,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.06 tff(18317,plain,
% 87.84/88.06 ($false),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18316, 18259, 18257, 18229])).
% 87.84/88.06 tff(18318,plain,(m_and_h_gate_v_out(c_e_h_3, c_i, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | node20(c_e_h_3, c_i, s7) | node20(c_e_h_3, c_i, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.06 tff(18319,plain,
% 87.84/88.06 (m_and_h_gate_v_out(c_e_h_3, c_i, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | node20(c_e_h_3, c_i, s7) | node20(c_e_h_3, c_i, s6)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18318, 13403])).
% 87.84/88.06 tff(18320,plain,
% 87.84/88.06 (~m_c_h_element_v_out(c_e_h_3, c_f, s9)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18319, 18228, 16974, 16283])).
% 87.84/88.06 tff(18321,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s9)), introduced(assumption)).
% 87.84/88.06 tff(18322,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)), introduced(assumption)).
% 87.84/88.06 tff(18323,plain,
% 87.84/88.06 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18324,plain,
% 87.84/88.06 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18325,plain,
% 87.84/88.06 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9)),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18324, 18323])).
% 87.84/88.06 tff(18326,plain,
% 87.84/88.06 ($false),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18325, 6389, 18322, 18321])).
% 87.84/88.06 tff(18327,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s9) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.06 tff(18328,plain,
% 87.84/88.06 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18327, 18320])).
% 87.84/88.06 tff(18329,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)), introduced(assumption)).
% 87.84/88.06 tff(18330,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)), introduced(assumption)).
% 87.84/88.06 tff(18331,assumption,(node11(c_e_h_3, c_m, s9, s10)), introduced(assumption)).
% 87.84/88.06 tff(18332,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18333,plain,
% 87.84/88.06 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18334,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10))))),
% 87.84/88.06 inference(monotonicity,[status(thm)],[18333])).
% 87.84/88.06 tff(18335,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)))),
% 87.84/88.06 inference(transitivity,[status(thm)],[18334, 18332])).
% 87.84/88.06 tff(18336,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18337,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10))),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18336, 18335])).
% 87.84/88.06 tff(18338,plain,
% 87.84/88.06 ($false),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18337, 1161, 18329, 18330, 18331])).
% 87.84/88.06 tff(18339,plain,((~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.06 tff(18340,plain,
% 87.84/88.06 (~node11(c_e_h_3, c_m, s9, s10)),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18339, 18330, 18329])).
% 87.84/88.06 tff(18341,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)), introduced(assumption)).
% 87.84/88.06 tff(18342,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)), introduced(assumption)).
% 87.84/88.06 tff(18343,assumption,(node10(c_e_h_3, c_m, s9, s10)), introduced(assumption)).
% 87.84/88.06 tff(18344,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node10(c_e_h_3, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node10(c_e_h_3, c_m, s9, s10)))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18345,plain,
% 87.84/88.06 (((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node10(c_e_h_3, c_m, s9, s10)))),
% 87.84/88.06 inference(rewrite,[status(thm)],[])).
% 87.84/88.06 tff(18346,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node10(c_e_h_3, c_m, s9, s10))))),
% 87.84/88.06 inference(monotonicity,[status(thm)],[18345])).
% 87.84/88.06 tff(18347,plain,
% 87.84/88.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node10(c_e_h_3, c_m, s9, s10)))),
% 87.84/88.06 inference(transitivity,[status(thm)],[18346, 18344])).
% 87.84/88.06 tff(18348,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))),
% 87.84/88.06 inference(quant_inst,[status(thm)],[])).
% 87.84/88.06 tff(18349,plain,
% 87.84/88.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node10(c_e_h_3, c_m, s9, s10))),
% 87.84/88.06 inference(modus_ponens,[status(thm)],[18348, 18347])).
% 87.84/88.06 tff(18350,plain,
% 87.84/88.06 ($false),
% 87.84/88.06 inference(unit_resolution,[status(thm)],[18349, 1191, 18342, 18341, 18330, 18343])).
% 87.84/88.06 tff(18351,plain,((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.06 tff(18352,plain,
% 87.84/88.06 (~node10(c_e_h_3, c_m, s9, s10)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18351, 18330, 18342, 18341])).
% 87.84/88.07 tff(18353,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18354,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18355,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18354, 18353])).
% 87.84/88.07 tff(18356,plain,
% 87.84/88.07 (node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18355, 1092, 3175])).
% 87.84/88.07 tff(18357,plain,
% 87.84/88.07 ($false),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18356, 18352, 18340])).
% 87.84/88.07 tff(18358,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.07 tff(18359,plain,
% 87.84/88.07 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18358, 18328, 17666, 17139])).
% 87.84/88.07 tff(18360,plain,
% 87.84/88.07 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18361,plain,
% 87.84/88.07 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18362,plain,
% 87.84/88.07 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18361, 18360])).
% 87.84/88.07 tff(18363,plain,
% 87.84/88.07 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18362, 6442, 18359])).
% 87.84/88.07 tff(18364,plain,
% 87.84/88.07 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18365,plain,
% 87.84/88.07 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18366,plain,
% 87.84/88.07 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18365, 18364])).
% 87.84/88.07 tff(18367,plain,
% 87.84/88.07 (~node9(c_e_h_3, c_n, s10)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18366, 1062, 18363])).
% 87.84/88.07 tff(18368,assumption,(~node9(c_e_h_3, c_n, s10)), introduced(assumption)).
% 87.84/88.07 tff(18369,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)), introduced(assumption)).
% 87.84/88.07 tff(18370,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)), introduced(assumption)).
% 87.84/88.07 tff(18371,assumption,(node11(c_e_h_3, c_n, s10, s11)), introduced(assumption)).
% 87.84/88.07 tff(18372,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18373,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18374,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18373, 18372])).
% 87.84/88.07 tff(18375,plain,
% 87.84/88.07 ($false),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18374, 1130, 18370, 18371, 18369])).
% 87.84/88.07 tff(18376,plain,((~node11(c_e_h_3, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.07 tff(18377,plain,
% 87.84/88.07 (~node11(c_e_h_3, c_n, s10, s11)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18376, 18370, 18369])).
% 87.84/88.07 tff(18378,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18379,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18380,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18379, 18378])).
% 87.84/88.07 tff(18381,plain,
% 87.84/88.07 (node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18380, 1092, 3778])).
% 87.84/88.07 tff(18382,plain,
% 87.84/88.07 (node10(c_e_h_3, c_n, s10, s11)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18381, 18377])).
% 87.84/88.07 tff(18383,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10) | (~node10(c_e_h_3, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10) | (~node10(c_e_h_3, c_n, s10, s11)))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18384,plain,
% 87.84/88.07 ((node9(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node10(c_e_h_3, c_n, s10, s11))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10) | (~node10(c_e_h_3, c_n, s10, s11)))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18385,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node10(c_e_h_3, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10) | (~node10(c_e_h_3, c_n, s10, s11))))),
% 87.84/88.07 inference(monotonicity,[status(thm)],[18384])).
% 87.84/88.07 tff(18386,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node10(c_e_h_3, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10) | (~node10(c_e_h_3, c_n, s10, s11)))),
% 87.84/88.07 inference(transitivity,[status(thm)],[18385, 18383])).
% 87.84/88.07 tff(18387,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node10(c_e_h_3, c_n, s10, s11)))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18388,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10) | (~node10(c_e_h_3, c_n, s10, s11))),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18387, 18386])).
% 87.84/88.07 tff(18389,plain,
% 87.84/88.07 ($false),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18388, 1076, 18370, 18382, 18368])).
% 87.84/88.07 tff(18390,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.07 tff(18391,plain,
% 87.84/88.07 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18390, 18367, 17171])).
% 87.84/88.07 tff(18392,plain,
% 87.84/88.07 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18393,plain,
% 87.84/88.07 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18394,plain,
% 87.84/88.07 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18393, 18392])).
% 87.84/88.07 tff(18395,plain,
% 87.84/88.07 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18394, 6513, 18391])).
% 87.84/88.07 tff(18396,plain,
% 87.84/88.07 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s11))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18397,plain,
% 87.84/88.07 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s11))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18398,plain,
% 87.84/88.07 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s11)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18397, 18396])).
% 87.84/88.07 tff(18399,plain,
% 87.84/88.07 (~node20(c_e_h_3, c_q, s11)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18398, 1535, 18395])).
% 87.84/88.07 tff(18400,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s11)), introduced(assumption)).
% 87.84/88.07 tff(18401,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s12)), introduced(assumption)).
% 87.84/88.07 tff(18402,assumption,(node22(c_e_h_3, c_q, s11, s12)), introduced(assumption)).
% 87.84/88.07 tff(18403,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18404,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18405,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18404, 18403])).
% 87.84/88.07 tff(18406,plain,
% 87.84/88.07 ($false),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18405, 107, 18401, 18400, 18402])).
% 87.84/88.07 tff(18407,plain,((~node22(c_e_h_3, c_q, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.07 tff(18408,plain,
% 87.84/88.07 (~node22(c_e_h_3, c_q, s11, s12)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18407, 18401, 18400])).
% 87.84/88.07 tff(18409,assumption,(~node20(c_e_h_3, c_q, s11)), introduced(assumption)).
% 87.84/88.07 tff(18410,assumption,(node21(c_e_h_3, c_q, s11, s12)), introduced(assumption)).
% 87.84/88.07 tff(18411,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12)))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18412,plain,
% 87.84/88.07 ((node20(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node21(c_e_h_3, c_q, s11, s12))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12)))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18413,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node21(c_e_h_3, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12))))),
% 87.84/88.07 inference(monotonicity,[status(thm)],[18412])).
% 87.84/88.07 tff(18414,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node21(c_e_h_3, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12)))),
% 87.84/88.07 inference(transitivity,[status(thm)],[18413, 18411])).
% 87.84/88.07 tff(18415,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node21(c_e_h_3, c_q, s11, s12)))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18416,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12))),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18415, 18414])).
% 87.84/88.07 tff(18417,plain,
% 87.84/88.07 ($false),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18416, 51, 18401, 18410, 18409])).
% 87.84/88.07 tff(18418,plain,((~node21(c_e_h_3, c_q, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.07 tff(18419,plain,
% 87.84/88.07 (~node21(c_e_h_3, c_q, s11, s12)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18418, 18401, 18409])).
% 87.84/88.07 tff(18420,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18421,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18422,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18421, 18420])).
% 87.84/88.07 tff(18423,plain,
% 87.84/88.07 (node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18422, 81, 4461])).
% 87.84/88.07 tff(18424,plain,
% 87.84/88.07 ($false),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18423, 18419, 18408])).
% 87.84/88.07 tff(18425,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | m_and_h_gate_v_out(c_e_h_3, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.07 tff(18426,plain,
% 87.84/88.07 (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18425, 18399, 17200])).
% 87.84/88.07 tff(18427,plain,
% 87.84/88.07 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s12))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18428,plain,
% 87.84/88.07 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s12))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18429,plain,
% 87.84/88.07 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s12)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18428, 18427])).
% 87.84/88.07 tff(18430,plain,
% 87.84/88.07 (node3(c_e_h_3, c_e_h_1, s12)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18429, 3860, 814])).
% 87.84/88.07 tff(18431,plain,
% 87.84/88.07 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s12)) | (~node3(c_e_h_3, c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s12)) | (~node3(c_e_h_3, c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18432,plain,
% 87.84/88.07 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s12)) | (~node3(c_e_h_3, c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18433,plain,
% 87.84/88.07 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s12)) | (~node3(c_e_h_3, c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18432, 18431])).
% 87.84/88.07 tff(18434,plain,
% 87.84/88.07 ((~m_cell_v_ack(c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18433, 836, 18430])).
% 87.84/88.07 tff(18435,plain,
% 87.84/88.07 (~m_cell_v_ack(c_e_h_1, s12)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18434, 18426])).
% 87.84/88.07 tff(18436,plain,
% 87.84/88.07 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)) | m_cell_v_ack(c_e_h_1, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)) | m_cell_v_ack(c_e_h_1, s12))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18437,plain,
% 87.84/88.07 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)) | m_cell_v_ack(c_e_h_1, s12))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18438,plain,
% 87.84/88.07 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)) | m_cell_v_ack(c_e_h_1, s12)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18437, 18436])).
% 87.84/88.07 tff(18439,plain,
% 87.84/88.07 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18438, 848, 18435])).
% 87.84/88.07 tff(18440,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)), introduced(assumption)).
% 87.84/88.07 tff(18441,assumption,(node5(c_e_h_1, c_j, s12, s13)), introduced(assumption)).
% 87.84/88.07 tff(18442,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18443,plain,
% 87.84/88.07 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18444,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12)))),
% 87.84/88.07 inference(monotonicity,[status(thm)],[18443])).
% 87.84/88.07 tff(18445,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12))),
% 87.84/88.07 inference(transitivity,[status(thm)],[18444, 18442])).
% 87.84/88.07 tff(18446,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18447,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18446, 18445])).
% 87.84/88.07 tff(18448,plain,
% 87.84/88.07 ($false),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18447, 862, 17648, 18441, 18440, 17659])).
% 87.84/88.07 tff(18449,plain,((~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.07 tff(18450,plain,
% 87.84/88.07 (~node5(c_e_h_1, c_j, s12, s13)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18449, 17648, 18439, 17659])).
% 87.84/88.07 tff(18451,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s12, s13)) | node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18452,plain,
% 87.84/88.07 ((node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13) | (~trans(s12, s13))) <=> ((~trans(s12, s13)) | node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13))),
% 87.84/88.07 inference(rewrite,[status(thm)],[])).
% 87.84/88.07 tff(18453,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13) | (~trans(s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s12, s13)) | node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13)))),
% 87.84/88.07 inference(monotonicity,[status(thm)],[18452])).
% 87.84/88.07 tff(18454,plain,
% 87.84/88.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13) | (~trans(s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13))),
% 87.84/88.07 inference(transitivity,[status(thm)],[18453, 18451])).
% 87.84/88.07 tff(18455,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13) | (~trans(s12, s13)))),
% 87.84/88.07 inference(quant_inst,[status(thm)],[])).
% 87.84/88.07 tff(18456,plain,
% 87.84/88.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13)),
% 87.84/88.07 inference(modus_ponens,[status(thm)],[18455, 18454])).
% 87.84/88.07 tff(18457,plain,
% 87.84/88.07 (node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18456, 881, 9599])).
% 87.84/88.07 tff(18458,plain,
% 87.84/88.07 ($false),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18457, 18450, 17658])).
% 87.84/88.07 tff(18459,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_out(c_e_h_1, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.07 tff(18460,plain,
% 87.84/88.07 (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)),
% 87.84/88.07 inference(unit_resolution,[status(thm)],[18459, 17646, 17279])).
% 87.84/88.08 tff(18461,plain,
% 87.84/88.08 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18462,plain,
% 87.84/88.08 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18463,plain,
% 87.84/88.08 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13)),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18462, 18461])).
% 87.84/88.08 tff(18464,plain,
% 87.84/88.08 (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18463, 309, 18460])).
% 87.84/88.08 tff(18465,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s14)), introduced(assumption)).
% 87.84/88.08 tff(18466,assumption,(node18(c_e_h_1, c_h, s13, s14)), introduced(assumption)).
% 87.84/88.08 tff(18467,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18468,plain,
% 87.84/88.08 (((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~node18(c_e_h_1, c_h, s13, s14))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18469,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~node18(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14))))),
% 87.84/88.08 inference(monotonicity,[status(thm)],[18468])).
% 87.84/88.08 tff(18470,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~node18(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(transitivity,[status(thm)],[18469, 18467])).
% 87.84/88.08 tff(18471,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~node18(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18472,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14))),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18471, 18470])).
% 87.84/88.08 tff(18473,plain,
% 87.84/88.08 ($false),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18472, 124, 17358, 18465, 18466])).
% 87.84/88.08 tff(18474,plain,((~node18(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.08 tff(18475,plain,
% 87.84/88.08 (~node18(c_e_h_1, c_h, s13, s14)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18474, 17358, 18465])).
% 87.84/88.08 tff(18476,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s13)), introduced(assumption)).
% 87.84/88.08 tff(18477,assumption,(node14(c_e_h_1, c_h, s13, s14)), introduced(assumption)).
% 87.84/88.08 tff(18478,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18479,plain,
% 87.84/88.08 (((~node14(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18480,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14))))),
% 87.84/88.08 inference(monotonicity,[status(thm)],[18479])).
% 87.84/88.08 tff(18481,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(transitivity,[status(thm)],[18480, 18478])).
% 87.84/88.08 tff(18482,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18483,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14))),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18482, 18481])).
% 87.84/88.08 tff(18484,plain,
% 87.84/88.08 ($false),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18483, 283, 18465, 18477, 18476])).
% 87.84/88.08 tff(18485,plain,((~node14(c_e_h_1, c_h, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.08 tff(18486,plain,
% 87.84/88.08 (~node14(c_e_h_1, c_h, s13, s14)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18485, 18465, 18476])).
% 87.84/88.08 tff(18487,assumption,(node15(c_e_h_1, c_h, s13, s14)), introduced(assumption)).
% 87.84/88.08 tff(18488,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18489,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18490,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18489, 18488])).
% 87.84/88.08 tff(18491,plain,
% 87.84/88.08 ($false),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18490, 173, 17358, 18465, 18487])).
% 87.84/88.08 tff(18492,plain,((~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.08 tff(18493,plain,
% 87.84/88.08 (~node15(c_e_h_1, c_h, s13, s14)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18492, 18465, 17358])).
% 87.84/88.08 tff(18494,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_h, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_h, s13, s14))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18495,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_h, s13, s14))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18496,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_h, s13, s14)),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18495, 18494])).
% 87.84/88.08 tff(18497,plain,
% 87.84/88.08 (node19(c_e_h_1, c_h, s13, s14)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18496, 141, 10040])).
% 87.84/88.08 tff(18498,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | (~node19(c_e_h_1, c_h, s13, s14)) | node15(c_e_h_1, c_h, s13, s14) | node14(c_e_h_1, c_h, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s13) | (~node19(c_e_h_1, c_h, s13, s14)) | node15(c_e_h_1, c_h, s13, s14) | node14(c_e_h_1, c_h, s13, s14))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18499,plain,
% 87.84/88.08 ((node16(c_e_h_1, c_h, s13) | node14(c_e_h_1, c_h, s13, s14) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14))) <=> (node16(c_e_h_1, c_h, s13) | (~node19(c_e_h_1, c_h, s13, s14)) | node15(c_e_h_1, c_h, s13, s14) | node14(c_e_h_1, c_h, s13, s14))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18500,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | node14(c_e_h_1, c_h, s13, s14) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | (~node19(c_e_h_1, c_h, s13, s14)) | node15(c_e_h_1, c_h, s13, s14) | node14(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(monotonicity,[status(thm)],[18499])).
% 87.84/88.08 tff(18501,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | node14(c_e_h_1, c_h, s13, s14) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s13) | (~node19(c_e_h_1, c_h, s13, s14)) | node15(c_e_h_1, c_h, s13, s14) | node14(c_e_h_1, c_h, s13, s14))),
% 87.84/88.08 inference(transitivity,[status(thm)],[18500, 18498])).
% 87.84/88.08 tff(18502,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | node14(c_e_h_1, c_h, s13, s14) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18503,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s13) | (~node19(c_e_h_1, c_h, s13, s14)) | node15(c_e_h_1, c_h, s13, s14) | node14(c_e_h_1, c_h, s13, s14)),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18502, 18501])).
% 87.84/88.08 tff(18504,plain,
% 87.84/88.08 (node16(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | node14(c_e_h_1, c_h, s13, s14)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18503, 189, 18497])).
% 87.84/88.08 tff(18505,plain,
% 87.84/88.08 (node16(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18504, 18493, 18486])).
% 87.84/88.08 tff(18506,assumption,(node17(c_e_h_1, c_h, s13)), introduced(assumption)).
% 87.84/88.08 tff(18507,assumption,(node16(c_e_h_1, c_h, s13)), introduced(assumption)).
% 87.84/88.08 tff(18508,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s13)), introduced(assumption)).
% 87.84/88.08 tff(18509,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18510,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18511,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18510, 18509])).
% 87.84/88.08 tff(18512,plain,
% 87.84/88.08 (m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18511, 245, 18506])).
% 87.84/88.08 tff(18513,plain,
% 87.84/88.08 (m_c_h_element_v_in1(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18512, 18508])).
% 87.84/88.08 tff(18514,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18515,plain,
% 87.84/88.08 (((~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13))) <=> ((~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18516,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13))))),
% 87.84/88.08 inference(monotonicity,[status(thm)],[18515])).
% 87.84/88.08 tff(18517,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(transitivity,[status(thm)],[18516, 18514])).
% 87.84/88.08 tff(18518,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18519,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18518, 18517])).
% 87.84/88.08 tff(18520,plain,
% 87.84/88.08 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18519, 263, 18507])).
% 87.84/88.08 tff(18521,plain,
% 87.84/88.08 ($false),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18520, 18513, 18508])).
% 87.84/88.08 tff(18522,plain,((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node16(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.08 tff(18523,plain,
% 87.84/88.08 (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18522, 18507, 18506])).
% 87.84/88.08 tff(18524,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18525,plain,
% 87.84/88.08 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18526,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13))))),
% 87.84/88.08 inference(monotonicity,[status(thm)],[18525])).
% 87.84/88.08 tff(18527,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(transitivity,[status(thm)],[18526, 18524])).
% 87.84/88.08 tff(18528,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18529,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18528, 18527])).
% 87.84/88.08 tff(18530,plain,
% 87.84/88.08 (m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18529, 209, 18506])).
% 87.84/88.08 tff(18531,plain,
% 87.84/88.08 (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18530, 18523])).
% 87.84/88.08 tff(18532,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18533,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18534,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18533, 18532])).
% 87.84/88.08 tff(18535,plain,
% 87.84/88.08 (m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18534, 228, 18507])).
% 87.84/88.08 tff(18536,plain,
% 87.84/88.08 ($false),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18535, 18531, 18523])).
% 87.84/88.08 tff(18537,plain,((~node16(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.08 tff(18538,plain,
% 87.84/88.08 (~node17(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18537, 18505])).
% 87.84/88.08 tff(18539,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18540,plain,
% 87.84/88.08 ((node17(c_e_h_1, c_h, s13) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14))) <=> (node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18541,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s13) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13)))),
% 87.84/88.08 inference(monotonicity,[status(thm)],[18540])).
% 87.84/88.08 tff(18542,plain,
% 87.84/88.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s13) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(transitivity,[status(thm)],[18541, 18539])).
% 87.84/88.08 tff(18543,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s13) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18544,plain,
% 87.84/88.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18543, 18542])).
% 87.84/88.08 tff(18545,plain,
% 87.84/88.08 (node18(c_e_h_1, c_h, s13, s14) | node17(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18544, 156, 18497])).
% 87.84/88.08 tff(18546,plain,
% 87.84/88.08 (node18(c_e_h_1, c_h, s13, s14)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18545, 18538])).
% 87.84/88.08 tff(18547,plain,
% 87.84/88.08 ($false),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18472, 124, 17358, 18465, 18546])).
% 87.84/88.08 tff(18548,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | m_c_h_element_v_in1(c_e_h_1, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.08 tff(18549,plain,
% 87.84/88.08 (m_c_h_element_v_in1(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18548, 17358, 18465])).
% 87.84/88.08 tff(18550,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s13)), introduced(assumption)).
% 87.84/88.08 tff(18551,plain,
% 87.84/88.08 ((~node17(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13))),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18529, 209, 18550])).
% 87.84/88.08 tff(18552,plain,
% 87.84/88.08 (~node17(c_e_h_1, c_h, s13)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18551, 18549])).
% 87.84/88.08 tff(18553,plain,
% 87.84/88.08 ($false),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18545, 18552, 18475])).
% 87.84/88.08 tff(18554,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.08 tff(18555,plain,
% 87.84/88.08 (m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18554, 18464])).
% 87.84/88.08 tff(18556,plain,
% 87.84/88.08 (~m_c_h_element_v_out(c_e_h_1, c_h, s14)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18555, 17358])).
% 87.84/88.08 tff(18557,plain,
% 87.84/88.08 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18558,plain,
% 87.84/88.08 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18559,plain,
% 87.84/88.08 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s14)),
% 87.84/88.08 inference(modus_ponens,[status(thm)],[18558, 18557])).
% 87.84/88.08 tff(18560,plain,
% 87.84/88.08 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)),
% 87.84/88.08 inference(unit_resolution,[status(thm)],[18559, 23, 18556])).
% 87.84/88.08 tff(18561,plain,
% 87.84/88.08 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s14))),
% 87.84/88.08 inference(rewrite,[status(thm)],[])).
% 87.84/88.08 tff(18562,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s14))),
% 87.84/88.08 inference(quant_inst,[status(thm)],[])).
% 87.84/88.08 tff(18563,plain,
% 87.84/88.08 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s14)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18562, 18561])).
% 87.84/88.09 tff(18564,plain,
% 87.84/88.09 (~node20(c_e_h_1, c_i, s14)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18563, 37, 18560])).
% 87.84/88.09 tff(18565,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s15)), introduced(assumption)).
% 87.84/88.09 tff(18566,assumption,(~node20(c_e_h_1, c_i, s14)), introduced(assumption)).
% 87.84/88.09 tff(18567,assumption,(node21(c_e_h_1, c_i, s14, s15)), introduced(assumption)).
% 87.84/88.09 tff(18568,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node21(c_e_h_1, c_i, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node21(c_e_h_1, c_i, s14, s15)))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18569,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node21(c_e_h_1, c_i, s14, s15)))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18570,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node21(c_e_h_1, c_i, s14, s15))),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18569, 18568])).
% 87.84/88.09 tff(18571,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18570, 51, 18566, 18567, 18565])).
% 87.84/88.09 tff(18572,plain,((~node21(c_e_h_1, c_i, s14, s15)) | node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18573,plain,
% 87.84/88.09 (~node21(c_e_h_1, c_i, s14, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18572, 18565, 18566])).
% 87.84/88.09 tff(18574,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18575,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18576,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18575, 18574])).
% 87.84/88.09 tff(18577,plain,
% 87.84/88.09 (node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18576, 81, 10504])).
% 87.84/88.09 tff(18578,plain,
% 87.84/88.09 (node22(c_e_h_1, c_i, s14, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18577, 18573])).
% 87.84/88.09 tff(18579,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s14)), introduced(assumption)).
% 87.84/88.09 tff(18580,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18581,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18582,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18581, 18580])).
% 87.84/88.09 tff(18583,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18582, 107, 18579, 18578, 18565])).
% 87.84/88.09 tff(18584,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14) | node20(c_e_h_1, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18585,plain,
% 87.84/88.09 (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18584, 18564, 17448])).
% 87.84/88.09 tff(18586,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s15)), introduced(assumption)).
% 87.84/88.09 tff(18587,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s15)), introduced(assumption)).
% 87.84/88.09 tff(18588,plain,
% 87.84/88.09 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18589,plain,
% 87.84/88.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18590,plain,
% 87.84/88.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18589, 18588])).
% 87.84/88.09 tff(18591,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18590, 365, 18587, 18586])).
% 87.84/88.09 tff(18592,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18593,plain,
% 87.84/88.09 (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18592, 18585])).
% 87.84/88.09 tff(18594,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s15)), introduced(assumption)).
% 87.84/88.09 tff(18595,assumption,(node18(c_e_h_1, c_e, s15, s16)), introduced(assumption)).
% 87.84/88.09 tff(18596,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node18(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node18(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18597,plain,
% 87.84/88.09 (((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~node18(c_e_h_1, c_e, s15, s16))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node18(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18598,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~node18(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node18(c_e_h_1, c_e, s15, s16))))),
% 87.84/88.09 inference(monotonicity,[status(thm)],[18597])).
% 87.84/88.09 tff(18599,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~node18(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node18(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(transitivity,[status(thm)],[18598, 18596])).
% 87.84/88.09 tff(18600,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~node18(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18601,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node18(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18600, 18599])).
% 87.84/88.09 tff(18602,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18601, 124, 18594, 17357, 18595])).
% 87.84/88.09 tff(18603,plain,((~node18(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18604,plain,
% 87.84/88.09 (~node18(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18603, 17357, 18594])).
% 87.84/88.09 tff(18605,assumption,(node15(c_e_h_1, c_e, s15, s16)), introduced(assumption)).
% 87.84/88.09 tff(18606,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18607,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18608,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18607, 18606])).
% 87.84/88.09 tff(18609,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18608, 173, 18594, 17357, 18605])).
% 87.84/88.09 tff(18610,plain,((~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18611,plain,
% 87.84/88.09 (~node15(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18610, 17357, 18594])).
% 87.84/88.09 tff(18612,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s15)), introduced(assumption)).
% 87.84/88.09 tff(18613,assumption,(~node15(c_e_h_1, c_e, s15, s16)), introduced(assumption)).
% 87.84/88.09 tff(18614,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s15)), introduced(assumption)).
% 87.84/88.09 tff(18615,plain,
% 87.84/88.09 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18616,plain,
% 87.84/88.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18617,plain,
% 87.84/88.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_in2(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18616, 18615])).
% 87.84/88.09 tff(18618,plain,
% 87.84/88.09 ((~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18617, 228, 18612])).
% 87.84/88.09 tff(18619,plain,
% 87.84/88.09 (~node16(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18618, 18614])).
% 87.84/88.09 tff(18620,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_1, c_e, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18621,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18622,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18621, 18620])).
% 87.84/88.09 tff(18623,plain,
% 87.84/88.09 (node19(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18622, 141, 12879])).
% 87.84/88.09 tff(18624,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18625,plain,
% 87.84/88.09 ((node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16))) <=> (node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18626,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(monotonicity,[status(thm)],[18625])).
% 87.84/88.09 tff(18627,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(transitivity,[status(thm)],[18626, 18624])).
% 87.84/88.09 tff(18628,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18629,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18628, 18627])).
% 87.84/88.09 tff(18630,plain,
% 87.84/88.09 (node15(c_e_h_1, c_e, s15, s16) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18629, 189, 18623])).
% 87.84/88.09 tff(18631,plain,
% 87.84/88.09 (node14(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18630, 18619, 18613])).
% 87.84/88.09 tff(18632,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~node14(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~node14(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18633,plain,
% 87.84/88.09 (((~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~node14(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18634,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~node14(c_e_h_1, c_e, s15, s16))))),
% 87.84/88.09 inference(monotonicity,[status(thm)],[18633])).
% 87.84/88.09 tff(18635,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~node14(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(transitivity,[status(thm)],[18634, 18632])).
% 87.84/88.09 tff(18636,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18637,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~node14(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18636, 18635])).
% 87.84/88.09 tff(18638,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18637, 283, 17357, 18631, 18614])).
% 87.84/88.09 tff(18639,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | node15(c_e_h_1, c_e, s15, s16) | m_c_h_element_v_in2(c_e_h_1, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18640,plain,
% 87.84/88.09 (m_c_h_element_v_in1(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18639, 18612, 17357, 18613])).
% 87.84/88.09 tff(18641,assumption,(node17(c_e_h_1, c_e, s15)), introduced(assumption)).
% 87.84/88.09 tff(18642,plain,
% 87.84/88.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18643,plain,
% 87.84/88.09 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18644,plain,
% 87.84/88.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15)))),
% 87.84/88.09 inference(monotonicity,[status(thm)],[18643])).
% 87.84/88.09 tff(18645,plain,
% 87.84/88.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 87.84/88.09 inference(transitivity,[status(thm)],[18644, 18642])).
% 87.84/88.09 tff(18646,plain,
% 87.84/88.09 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15)))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18647,plain,
% 87.84/88.09 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18646, 18645])).
% 87.84/88.09 tff(18648,plain,
% 87.84/88.09 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18647, 209, 18641])).
% 87.84/88.09 tff(18649,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18648, 18640, 18612])).
% 87.84/88.09 tff(18650,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | node15(c_e_h_1, c_e, s15, s16)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18651,plain,
% 87.84/88.09 (~node17(c_e_h_1, c_e, s15)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18650, 17357, 18612, 18611])).
% 87.84/88.09 tff(18652,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18653,plain,
% 87.84/88.09 ((node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16))) <=> (node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18654,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(monotonicity,[status(thm)],[18653])).
% 87.84/88.09 tff(18655,plain,
% 87.84/88.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16))),
% 87.84/88.09 inference(transitivity,[status(thm)],[18654, 18652])).
% 87.84/88.09 tff(18656,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18657,plain,
% 87.84/88.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18656, 18655])).
% 87.84/88.09 tff(18658,plain,
% 87.84/88.09 (node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18657, 156, 18623])).
% 87.84/88.09 tff(18659,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18658, 18651, 18604])).
% 87.84/88.09 tff(18660,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18661,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18660, 18593, 17606, 17357])).
% 87.84/88.09 tff(18662,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18663,plain,
% 87.84/88.09 (~m_c_h_element_v_out(c_e_h_1, c_e, s16)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18662, 17356])).
% 87.84/88.09 tff(18664,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)), introduced(assumption)).
% 87.84/88.09 tff(18665,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s16)), introduced(assumption)).
% 87.84/88.09 tff(18666,plain,
% 87.84/88.09 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16))),
% 87.84/88.09 inference(rewrite,[status(thm)],[])).
% 87.84/88.09 tff(18667,plain,
% 87.84/88.09 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16))),
% 87.84/88.09 inference(quant_inst,[status(thm)],[])).
% 87.84/88.09 tff(18668,plain,
% 87.84/88.09 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16)),
% 87.84/88.09 inference(modus_ponens,[status(thm)],[18667, 18666])).
% 87.84/88.09 tff(18669,plain,
% 87.84/88.09 ($false),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18668, 976, 18665, 18664])).
% 87.84/88.09 tff(18670,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s16) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.09 tff(18671,plain,
% 87.84/88.09 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[18670, 18663])).
% 87.84/88.09 tff(18672,plain,
% 87.84/88.09 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[17361, 23, 17356])).
% 87.84/88.09 tff(18673,plain,
% 87.84/88.09 (~node20(c_e_h_1, c_i, s13)),
% 87.84/88.09 inference(unit_resolution,[status(thm)],[17365, 37, 18672])).
% 87.84/88.10 tff(18674,plain,
% 87.84/88.10 (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[17447, 18673])).
% 87.84/88.10 tff(18675,plain,
% 87.84/88.10 (~m_c_h_element_v_in2(c_e_h_1, c_e, s14)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[17451, 365, 18674])).
% 87.84/88.10 tff(18676,plain,
% 87.84/88.10 (~m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[17605, 18675])).
% 87.84/88.10 tff(18677,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)), introduced(assumption)).
% 87.84/88.10 tff(18678,plain,
% 87.84/88.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18679,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18680,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18679, 18678])).
% 87.84/88.10 tff(18681,plain,
% 87.84/88.10 ($false),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18680, 976, 18594, 18677])).
% 87.84/88.10 tff(18682,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.10 tff(18683,plain,
% 87.84/88.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18682, 18676])).
% 87.84/88.10 tff(18684,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)), introduced(assumption)).
% 87.84/88.10 tff(18685,plain,
% 87.84/88.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18686,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18687,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18686, 18685])).
% 87.84/88.10 tff(18688,plain,
% 87.84/88.10 ($false),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18687, 976, 17544, 18684])).
% 87.84/88.10 tff(18689,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.10 tff(18690,plain,
% 87.84/88.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18689, 17543])).
% 87.84/88.10 tff(18691,plain,
% 87.84/88.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18692,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18693,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18692, 18691])).
% 87.84/88.10 tff(18694,plain,
% 87.84/88.10 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18693, 1142, 12408])).
% 87.84/88.10 tff(18695,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)), introduced(assumption)).
% 87.84/88.10 tff(18696,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)), introduced(assumption)).
% 87.84/88.10 tff(18697,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)), introduced(assumption)).
% 87.84/88.10 tff(18698,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)), introduced(assumption)).
% 87.84/88.10 tff(18699,assumption,(node11(c_e_h_1, c_n, s14, s15)), introduced(assumption)).
% 87.84/88.10 tff(18700,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15)))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18701,plain,
% 87.84/88.10 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15)))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18702,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15))))),
% 87.84/88.10 inference(monotonicity,[status(thm)],[18701])).
% 87.84/88.10 tff(18703,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15)))),
% 87.84/88.10 inference(transitivity,[status(thm)],[18702, 18700])).
% 87.84/88.10 tff(18704,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18705,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15))),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18704, 18703])).
% 87.84/88.10 tff(18706,plain,
% 87.84/88.10 ($false),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18705, 1161, 18698, 18697, 18699])).
% 87.84/88.10 tff(18707,plain,((~node11(c_e_h_1, c_n, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.10 tff(18708,plain,
% 87.84/88.10 (~node11(c_e_h_1, c_n, s14, s15)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18707, 18698, 18697])).
% 87.84/88.10 tff(18709,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18710,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18711,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18710, 18709])).
% 87.84/88.10 tff(18712,plain,
% 87.84/88.10 (node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18711, 1092, 10504])).
% 87.84/88.10 tff(18713,plain,
% 87.84/88.10 (node10(c_e_h_1, c_n, s14, s15)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18712, 18708])).
% 87.84/88.10 tff(18714,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~node10(c_e_h_1, c_n, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~node10(c_e_h_1, c_n, s14, s15)))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18715,plain,
% 87.84/88.10 (((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~node10(c_e_h_1, c_n, s14, s15)))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18716,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~node10(c_e_h_1, c_n, s14, s15))))),
% 87.84/88.10 inference(monotonicity,[status(thm)],[18715])).
% 87.84/88.10 tff(18717,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~node10(c_e_h_1, c_n, s14, s15)))),
% 87.84/88.10 inference(transitivity,[status(thm)],[18716, 18714])).
% 87.84/88.10 tff(18718,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18719,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~node10(c_e_h_1, c_n, s14, s15))),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18718, 18717])).
% 87.84/88.10 tff(18720,plain,
% 87.84/88.10 ($false),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18719, 1191, 18698, 18713, 18696, 18695])).
% 87.84/88.10 tff(18721,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.10 tff(18722,plain,
% 87.84/88.10 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18721, 18694])).
% 87.84/88.10 tff(18723,plain,
% 87.84/88.10 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14))),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18722, 13842])).
% 87.84/88.10 tff(18724,plain,
% 87.84/88.10 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18723, 18690])).
% 87.84/88.10 tff(18725,plain,
% 87.84/88.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18726,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18727,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18726, 18725])).
% 87.84/88.10 tff(18728,plain,
% 87.84/88.10 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18727, 1048, 18724])).
% 87.84/88.10 tff(18729,plain,
% 87.84/88.10 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18730,plain,
% 87.84/88.10 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18731,plain,
% 87.84/88.10 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18730, 18729])).
% 87.84/88.10 tff(18732,plain,
% 87.84/88.10 (~node9(c_e_h_1, c_m, s15)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18731, 1062, 18728])).
% 87.84/88.10 tff(18733,assumption,(~node9(c_e_h_1, c_m, s15)), introduced(assumption)).
% 87.84/88.10 tff(18734,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)), introduced(assumption)).
% 87.84/88.10 tff(18735,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)), introduced(assumption)).
% 87.84/88.10 tff(18736,assumption,(node11(c_e_h_1, c_m, s15, s16)), introduced(assumption)).
% 87.84/88.10 tff(18737,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18738,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18739,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18738, 18737])).
% 87.84/88.10 tff(18740,plain,
% 87.84/88.10 ($false),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18739, 1130, 18734, 18736, 18735])).
% 87.84/88.10 tff(18741,plain,((~node11(c_e_h_1, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.10 tff(18742,plain,
% 87.84/88.10 ((~node11(c_e_h_1, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18741, 13875])).
% 87.84/88.10 tff(18743,plain,
% 87.84/88.10 (~node11(c_e_h_1, c_m, s15, s16)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18742, 18734])).
% 87.84/88.10 tff(18744,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18745,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18746,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18745, 18744])).
% 87.84/88.10 tff(18747,plain,
% 87.84/88.10 (node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18746, 1092, 12879])).
% 87.84/88.10 tff(18748,plain,
% 87.84/88.10 (node10(c_e_h_1, c_m, s15, s16)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18747, 18743])).
% 87.84/88.10 tff(18749,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)) | node9(c_e_h_1, c_m, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)) | node9(c_e_h_1, c_m, s15))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18750,plain,
% 87.84/88.10 ((node9(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)) | node9(c_e_h_1, c_m, s15))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18751,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)) | node9(c_e_h_1, c_m, s15)))),
% 87.84/88.10 inference(monotonicity,[status(thm)],[18750])).
% 87.84/88.10 tff(18752,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)) | node9(c_e_h_1, c_m, s15))),
% 87.84/88.10 inference(transitivity,[status(thm)],[18751, 18749])).
% 87.84/88.10 tff(18753,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18754,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)) | node9(c_e_h_1, c_m, s15)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18753, 18752])).
% 87.84/88.10 tff(18755,plain,
% 87.84/88.10 ($false),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18754, 1076, 18734, 18748, 18733])).
% 87.84/88.10 tff(18756,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | node9(c_e_h_1, c_m, s15)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.10 tff(18757,plain,
% 87.84/88.10 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18756, 18732])).
% 87.84/88.10 tff(18758,plain,
% 87.84/88.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18759,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18760,plain,
% 87.84/88.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18759, 18758])).
% 87.84/88.10 tff(18761,plain,
% 87.84/88.10 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18760, 1521])).
% 87.84/88.10 tff(18762,plain,
% 87.84/88.10 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18761, 18757])).
% 87.84/88.10 tff(18763,assumption,(node20(c_e_h_1, c_r, s16)), introduced(assumption)).
% 87.84/88.10 tff(18764,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)), introduced(assumption)).
% 87.84/88.10 tff(18765,plain,
% 87.84/88.10 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s16))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18766,plain,
% 87.84/88.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s16))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18767,plain,
% 87.84/88.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s16)),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18766, 18765])).
% 87.84/88.10 tff(18768,plain,
% 87.84/88.10 ($false),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18767, 1535, 18764, 18763])).
% 87.84/88.10 tff(18769,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s16) | (~node20(c_e_h_1, c_r, s16))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.10 tff(18770,plain,
% 87.84/88.10 (~node20(c_e_h_1, c_r, s16)),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18769, 18762])).
% 87.84/88.10 tff(18771,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s17)), introduced(assumption)).
% 87.84/88.10 tff(18772,assumption,(~node20(c_e_h_1, c_r, s16)), introduced(assumption)).
% 87.84/88.10 tff(18773,assumption,(node21(c_e_h_1, c_r, s16, s17)), introduced(assumption)).
% 87.84/88.10 tff(18774,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16) | (~node21(c_e_h_1, c_r, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16) | (~node21(c_e_h_1, c_r, s16, s17)))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18775,plain,
% 87.84/88.10 ((node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node21(c_e_h_1, c_r, s16, s17))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16) | (~node21(c_e_h_1, c_r, s16, s17)))),
% 87.84/88.10 inference(rewrite,[status(thm)],[])).
% 87.84/88.10 tff(18776,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node21(c_e_h_1, c_r, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16) | (~node21(c_e_h_1, c_r, s16, s17))))),
% 87.84/88.10 inference(monotonicity,[status(thm)],[18775])).
% 87.84/88.10 tff(18777,plain,
% 87.84/88.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node21(c_e_h_1, c_r, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16) | (~node21(c_e_h_1, c_r, s16, s17)))),
% 87.84/88.10 inference(transitivity,[status(thm)],[18776, 18774])).
% 87.84/88.10 tff(18778,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node21(c_e_h_1, c_r, s16, s17)))),
% 87.84/88.10 inference(quant_inst,[status(thm)],[])).
% 87.84/88.10 tff(18779,plain,
% 87.84/88.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16) | (~node21(c_e_h_1, c_r, s16, s17))),
% 87.84/88.10 inference(modus_ponens,[status(thm)],[18778, 18777])).
% 87.84/88.10 tff(18780,plain,
% 87.84/88.10 ($false),
% 87.84/88.10 inference(unit_resolution,[status(thm)],[18779, 51, 18773, 18772, 18771])).
% 87.84/88.10 tff(18781,plain,((~node21(c_e_h_1, c_r, s16, s17)) | node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.10 tff(18782,plain,
% 87.84/88.10 (~node21(c_e_h_1, c_r, s16, s17)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18781, 18771, 18772])).
% 87.84/88.11 tff(18783,plain,
% 87.84/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17))),
% 87.84/88.11 inference(rewrite,[status(thm)],[])).
% 87.84/88.11 tff(18784,plain,
% 87.84/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17))),
% 87.84/88.11 inference(quant_inst,[status(thm)],[])).
% 87.84/88.11 tff(18785,plain,
% 87.84/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17)),
% 87.84/88.11 inference(modus_ponens,[status(thm)],[18784, 18783])).
% 87.84/88.11 tff(18786,plain,
% 87.84/88.11 (node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18785, 81, 14096])).
% 87.84/88.11 tff(18787,plain,
% 87.84/88.11 (node22(c_e_h_1, c_r, s16, s17)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18786, 18782])).
% 87.84/88.11 tff(18788,plain,
% 87.84/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node22(c_e_h_1, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node22(c_e_h_1, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))),
% 87.84/88.11 inference(rewrite,[status(thm)],[])).
% 87.84/88.11 tff(18789,plain,
% 87.84/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node22(c_e_h_1, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))),
% 87.84/88.11 inference(quant_inst,[status(thm)],[])).
% 87.84/88.11 tff(18790,plain,
% 87.84/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node22(c_e_h_1, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16)),
% 87.84/88.11 inference(modus_ponens,[status(thm)],[18789, 18788])).
% 87.84/88.11 tff(18791,plain,
% 87.84/88.11 ($false),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18790, 107, 18787, 13914, 18771])).
% 87.84/88.11 tff(18792,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16) | node20(c_e_h_1, c_r, s16)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.11 tff(18793,plain,
% 87.84/88.11 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18792, 13913])).
% 87.84/88.11 tff(18794,plain,
% 87.84/88.11 (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18793, 18770])).
% 87.84/88.11 tff(18795,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s17)), introduced(assumption)).
% 87.84/88.11 tff(18796,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s19)), introduced(assumption)).
% 87.84/88.11 tff(18797,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)), introduced(assumption)).
% 87.84/88.11 tff(18798,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)), introduced(assumption)).
% 87.84/88.11 tff(18799,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)), introduced(assumption)).
% 87.84/88.11 tff(18800,plain,
% 87.84/88.11 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[12407, 11793, 12337, 11895])).
% 87.84/88.11 tff(18801,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)), introduced(assumption)).
% 87.84/88.11 tff(18802,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)), introduced(assumption)).
% 87.84/88.11 tff(18803,plain,
% 87.84/88.11 ($false),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[11791, 1142, 11187, 18802])).
% 87.84/88.11 tff(18804,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)), inference(lemma,lemma(discharge,[]))).
% 87.84/88.11 tff(18805,plain,
% 87.84/88.11 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18804, 11187])).
% 87.84/88.11 tff(18806,plain,
% 87.84/88.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[11821, 11785, 11793, 18805])).
% 87.84/88.11 tff(18807,plain,
% 87.84/88.11 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[12393, 18806, 12369, 12337])).
% 87.84/88.11 tff(18808,plain,
% 87.84/88.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[12400, 18807])).
% 87.84/88.11 tff(18809,plain,
% 87.84/88.11 (node9(c_e_h_1, c_m, s11)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[11208, 18808, 11187])).
% 87.84/88.11 tff(18810,plain,
% 87.84/88.11 ($false),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[11184, 1062, 11786, 18809])).
% 87.84/88.11 tff(18811,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.11 tff(18812,plain,
% 87.84/88.11 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18811, 8378])).
% 87.84/88.11 tff(18813,plain,
% 87.84/88.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18812, 11793, 12337, 11177])).
% 87.84/88.11 tff(18814,plain,
% 87.84/88.11 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[11859, 11793, 11177])).
% 87.84/88.11 tff(18815,plain,
% 87.84/88.11 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[13773, 18814])).
% 87.84/88.11 tff(18816,plain,
% 87.84/88.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[13840, 18815, 13823, 18813])).
% 87.84/88.11 tff(18817,plain,
% 87.84/88.11 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18693, 1142, 18800])).
% 87.84/88.11 tff(18818,plain,
% 87.84/88.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18721, 18817, 18695, 18816])).
% 87.84/88.11 tff(18819,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)), introduced(assumption)).
% 87.84/88.11 tff(18820,assumption,(node11(c_e_h_1, c_n, s15, s16)), introduced(assumption)).
% 87.84/88.11 tff(18821,plain,
% 87.84/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16)))),
% 87.84/88.11 inference(rewrite,[status(thm)],[])).
% 87.84/88.11 tff(18822,plain,
% 87.84/88.11 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node11(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16)))),
% 87.84/88.11 inference(rewrite,[status(thm)],[])).
% 87.84/88.11 tff(18823,plain,
% 87.84/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node11(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16))))),
% 87.84/88.11 inference(monotonicity,[status(thm)],[18822])).
% 87.84/88.11 tff(18824,plain,
% 87.84/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node11(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16)))),
% 87.84/88.11 inference(transitivity,[status(thm)],[18823, 18821])).
% 87.84/88.11 tff(18825,plain,
% 87.84/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node11(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))),
% 87.84/88.11 inference(quant_inst,[status(thm)],[])).
% 87.84/88.11 tff(18826,plain,
% 87.84/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16))),
% 87.84/88.11 inference(modus_ponens,[status(thm)],[18825, 18824])).
% 87.84/88.11 tff(18827,plain,
% 87.84/88.11 ($false),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18826, 1161, 18801, 18820, 18819])).
% 87.84/88.11 tff(18828,plain,((~node11(c_e_h_1, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 87.84/88.11 tff(18829,plain,
% 87.84/88.11 (~node11(c_e_h_1, c_n, s15, s16)),
% 87.84/88.11 inference(unit_resolution,[status(thm)],[18828, 18801, 18819])).
% 87.84/88.11 tff(18830,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)), introduced(assumption)).
% 87.84/88.11 tff(18831,assumption,(node10(c_e_h_1, c_n, s15, s16)), introduced(assumption)).
% 87.84/88.11 tff(18832,plain,
% 87.84/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)))),
% 87.84/88.11 inference(rewrite,[status(thm)],[])).
% 87.84/88.11 tff(18833,plain,
% 87.84/88.11 (((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)))),
% 87.84/88.11 inference(rewrite,[status(thm)],[])).
% 87.84/88.11 tff(18834,plain,
% 87.84/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15))))),
% 87.84/88.11 inference(monotonicity,[status(thm)],[18833])).
% 87.84/88.11 tff(18835,plain,
% 87.84/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)))),
% 87.93/88.11 inference(transitivity,[status(thm)],[18834, 18832])).
% 87.93/88.11 tff(18836,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))),
% 87.93/88.11 inference(quant_inst,[status(thm)],[])).
% 87.93/88.11 tff(18837,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15))),
% 87.93/88.11 inference(modus_ponens,[status(thm)],[18836, 18835])).
% 87.93/88.11 tff(18838,plain,
% 87.93/88.11 ($false),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18837, 1191, 18801, 18831, 18797, 18830])).
% 87.93/88.11 tff(18839,plain,((~node10(c_e_h_1, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.11 tff(18840,plain,
% 87.93/88.11 (~node10(c_e_h_1, c_n, s15, s16)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18839, 18801, 18830, 18797])).
% 87.93/88.11 tff(18841,plain,
% 87.93/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18842,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16))),
% 87.93/88.11 inference(quant_inst,[status(thm)],[])).
% 87.93/88.11 tff(18843,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16)),
% 87.93/88.11 inference(modus_ponens,[status(thm)],[18842, 18841])).
% 87.93/88.11 tff(18844,plain,
% 87.93/88.11 (node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18843, 1092, 12879])).
% 87.93/88.11 tff(18845,plain,
% 87.93/88.11 ($false),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18844, 18840, 18829])).
% 87.93/88.11 tff(18846,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.11 tff(18847,plain,
% 87.93/88.11 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18846, 18818, 18797, 18801])).
% 87.93/88.11 tff(18848,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)), introduced(assumption)).
% 87.93/88.11 tff(18849,plain,
% 87.93/88.11 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18850,plain,
% 87.93/88.11 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 87.93/88.11 inference(quant_inst,[status(thm)],[])).
% 87.93/88.11 tff(18851,plain,
% 87.93/88.11 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 87.93/88.11 inference(modus_ponens,[status(thm)],[18850, 18849])).
% 87.93/88.11 tff(18852,plain,
% 87.93/88.11 ($false),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18851, 1142, 18735, 18848])).
% 87.93/88.11 tff(18853,plain,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.11 tff(18854,plain,
% 87.93/88.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18853, 18847])).
% 87.93/88.11 tff(18855,plain,
% 87.93/88.11 (node9(c_e_h_1, c_m, s14)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[13873, 18854, 18800])).
% 87.93/88.11 tff(18856,plain,
% 87.93/88.11 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[13845, 1048, 18816])).
% 87.93/88.11 tff(18857,plain,
% 87.93/88.11 ($false),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[13849, 1062, 18856, 18855])).
% 87.93/88.11 tff(18858,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.11 tff(18859,plain,
% 87.93/88.11 ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13))),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18858, 11784, 12327])).
% 87.93/88.11 tff(18860,plain,
% 87.93/88.11 ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14))),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18859, 13767])).
% 87.93/88.11 tff(18861,plain,
% 87.93/88.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18860, 18695, 18797])).
% 87.93/88.11 tff(18862,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)), introduced(assumption)).
% 87.93/88.11 tff(18863,plain,
% 87.93/88.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18864,plain,
% 87.93/88.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 87.93/88.11 inference(quant_inst,[status(thm)],[])).
% 87.93/88.11 tff(18865,plain,
% 87.93/88.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))),
% 87.93/88.11 inference(modus_ponens,[status(thm)],[18864, 18863])).
% 87.93/88.11 tff(18866,plain,
% 87.93/88.11 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18865, 1048, 18862])).
% 87.93/88.11 tff(18867,plain,
% 87.93/88.11 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18868,plain,
% 87.93/88.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16))),
% 87.93/88.11 inference(quant_inst,[status(thm)],[])).
% 87.93/88.11 tff(18869,plain,
% 87.93/88.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)),
% 87.93/88.11 inference(modus_ponens,[status(thm)],[18868, 18867])).
% 87.93/88.11 tff(18870,plain,
% 87.93/88.11 (~node9(c_e_h_1, c_m, s16)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18869, 1062, 18866])).
% 87.93/88.11 tff(18871,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)), introduced(assumption)).
% 87.93/88.11 tff(18872,plain,
% 87.93/88.11 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18873,plain,
% 87.93/88.11 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 87.93/88.11 inference(quant_inst,[status(thm)],[])).
% 87.93/88.11 tff(18874,plain,
% 87.93/88.11 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 87.93/88.11 inference(modus_ponens,[status(thm)],[18873, 18872])).
% 87.93/88.11 tff(18875,plain,
% 87.93/88.11 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18874, 1142, 18871])).
% 87.93/88.11 tff(18876,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)), introduced(assumption)).
% 87.93/88.11 tff(18877,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)), introduced(assumption)).
% 87.93/88.11 tff(18878,assumption,(node10(c_e_h_1, c_n, s16, s17)), introduced(assumption)).
% 87.93/88.11 tff(18879,plain,
% 87.93/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18880,plain,
% 87.93/88.11 (((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18881,plain,
% 87.93/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16))))),
% 87.93/88.11 inference(monotonicity,[status(thm)],[18880])).
% 87.93/88.11 tff(18882,plain,
% 87.93/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)))),
% 87.93/88.11 inference(transitivity,[status(thm)],[18881, 18879])).
% 87.93/88.11 tff(18883,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))),
% 87.93/88.11 inference(quant_inst,[status(thm)],[])).
% 87.93/88.11 tff(18884,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16))),
% 87.93/88.11 inference(modus_ponens,[status(thm)],[18883, 18882])).
% 87.93/88.11 tff(18885,plain,
% 87.93/88.11 ($false),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18884, 1191, 18878, 18876, 18877, 18798])).
% 87.93/88.11 tff(18886,plain,((~node10(c_e_h_1, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.11 tff(18887,plain,
% 87.93/88.11 (~node10(c_e_h_1, c_n, s16, s17)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18886, 18876, 18877, 18798])).
% 87.93/88.11 tff(18888,plain,
% 87.93/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18889,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17))),
% 87.93/88.11 inference(quant_inst,[status(thm)],[])).
% 87.93/88.11 tff(18890,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17)),
% 87.93/88.11 inference(modus_ponens,[status(thm)],[18889, 18888])).
% 87.93/88.11 tff(18891,plain,
% 87.93/88.11 (node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18890, 1092, 14096])).
% 87.93/88.11 tff(18892,plain,
% 87.93/88.11 (node11(c_e_h_1, c_n, s16, s17)),
% 87.93/88.11 inference(unit_resolution,[status(thm)],[18891, 18887])).
% 87.93/88.11 tff(18893,plain,
% 87.93/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~node11(c_e_h_1, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_1, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18894,plain,
% 87.93/88.11 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))) <=> ((~node11(c_e_h_1, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 87.93/88.11 inference(rewrite,[status(thm)],[])).
% 87.93/88.11 tff(18895,plain,
% 87.93/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~node11(c_e_h_1, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))))),
% 87.93/88.11 inference(monotonicity,[status(thm)],[18894])).
% 87.93/88.11 tff(18896,plain,
% 87.93/88.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_1, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 87.93/88.11 inference(transitivity,[status(thm)],[18895, 18893])).
% 87.93/88.11 tff(18897,plain,
% 87.93/88.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18898,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~node11(c_e_h_1, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18897, 18896])).
% 87.93/88.12 tff(18899,plain,
% 87.93/88.12 ($false),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18898, 1161, 18862, 18892, 18876])).
% 87.93/88.12 tff(18900,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.12 tff(18901,plain,
% 87.93/88.12 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18900, 18875, 18798, 18862])).
% 87.93/88.12 tff(18902,plain,
% 87.93/88.12 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18903,plain,
% 87.93/88.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18904,plain,
% 87.93/88.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18903, 18902])).
% 87.93/88.12 tff(18905,plain,
% 87.93/88.12 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18904, 1048, 18901])).
% 87.93/88.12 tff(18906,plain,
% 87.93/88.12 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18907,plain,
% 87.93/88.12 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18908,plain,
% 87.93/88.12 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18907, 18906])).
% 87.93/88.12 tff(18909,plain,
% 87.93/88.12 (~node9(c_e_h_1, c_m, s17)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18908, 1062, 18905])).
% 87.93/88.12 tff(18910,assumption,(~node9(c_e_h_1, c_m, s17)), introduced(assumption)).
% 87.93/88.12 tff(18911,assumption,(node10(c_e_h_1, c_m, s17, s18)), introduced(assumption)).
% 87.93/88.12 tff(18912,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s17, s18)) | node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s17, s18)) | node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18913,plain,
% 87.93/88.12 ((node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node10(c_e_h_1, c_m, s17, s18))) <=> ((~node10(c_e_h_1, c_m, s17, s18)) | node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18914,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node10(c_e_h_1, c_m, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s17, s18)) | node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))))),
% 87.93/88.12 inference(monotonicity,[status(thm)],[18913])).
% 87.93/88.12 tff(18915,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node10(c_e_h_1, c_m, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s17, s18)) | node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)))),
% 87.93/88.12 inference(transitivity,[status(thm)],[18914, 18912])).
% 87.93/88.12 tff(18916,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node10(c_e_h_1, c_m, s17, s18)))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18917,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s17, s18)) | node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18916, 18915])).
% 87.93/88.12 tff(18918,plain,
% 87.93/88.12 ($false),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18917, 1076, 18799, 18911, 18910])).
% 87.93/88.12 tff(18919,plain,((~node10(c_e_h_1, c_m, s17, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.12 tff(18920,plain,
% 87.93/88.12 (~node10(c_e_h_1, c_m, s17, s18)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18919, 18909, 18799])).
% 87.93/88.12 tff(18921,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s17, s18)) | node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s17, s18)) | node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18922,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s17, s18)) | node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18923,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s17, s18)) | node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18922, 18921])).
% 87.93/88.12 tff(18924,plain,
% 87.93/88.12 (node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18923, 1092, 15701])).
% 87.93/88.12 tff(18925,plain,
% 87.93/88.12 (node11(c_e_h_1, c_m, s17, s18)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18924, 18920])).
% 87.93/88.12 tff(18926,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node11(c_e_h_1, c_m, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node11(c_e_h_1, c_m, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18927,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node11(c_e_h_1, c_m, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18928,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node11(c_e_h_1, c_m, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18927, 18926])).
% 87.93/88.12 tff(18929,plain,
% 87.93/88.12 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18928, 1130, 18799, 18925])).
% 87.93/88.12 tff(18930,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)), introduced(assumption)).
% 87.93/88.12 tff(18931,assumption,(node11(c_e_h_1, c_m, s16, s17)), introduced(assumption)).
% 87.93/88.12 tff(18932,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18933,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18934,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18933, 18932])).
% 87.93/88.12 tff(18935,plain,
% 87.93/88.12 ($false),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18934, 1130, 18931, 18871, 18930])).
% 87.93/88.12 tff(18936,plain,((~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.12 tff(18937,plain,
% 87.93/88.12 (~node11(c_e_h_1, c_m, s16, s17)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18936, 18929, 18871])).
% 87.93/88.12 tff(18938,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18939,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18940,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18939, 18938])).
% 87.93/88.12 tff(18941,plain,
% 87.93/88.12 (node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18940, 1092, 14096])).
% 87.93/88.12 tff(18942,plain,
% 87.93/88.12 (node10(c_e_h_1, c_m, s16, s17)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18941, 18937])).
% 87.93/88.12 tff(18943,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s16, s17)) | node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s16, s17)) | node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18944,plain,
% 87.93/88.12 ((node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node10(c_e_h_1, c_m, s16, s17))) <=> ((~node10(c_e_h_1, c_m, s16, s17)) | node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18945,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node10(c_e_h_1, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s16, s17)) | node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))))),
% 87.93/88.12 inference(monotonicity,[status(thm)],[18944])).
% 87.93/88.12 tff(18946,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node10(c_e_h_1, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s16, s17)) | node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)))),
% 87.93/88.12 inference(transitivity,[status(thm)],[18945, 18943])).
% 87.93/88.12 tff(18947,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node10(c_e_h_1, c_m, s16, s17)))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18948,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s16, s17)) | node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18947, 18946])).
% 87.93/88.12 tff(18949,plain,
% 87.93/88.12 ($false),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18948, 1076, 18942, 18929, 18870])).
% 87.93/88.12 tff(18950,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.12 tff(18951,plain,
% 87.93/88.12 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18950, 18861, 18799, 18798])).
% 87.93/88.12 tff(18952,plain,
% 87.93/88.12 (node9(c_e_h_1, c_m, s15)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18756, 18951])).
% 87.93/88.12 tff(18953,plain,
% 87.93/88.12 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18723, 18695])).
% 87.93/88.12 tff(18954,plain,
% 87.93/88.12 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18727, 1048, 18953])).
% 87.93/88.12 tff(18955,plain,
% 87.93/88.12 ($false),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18731, 1062, 18954, 18952])).
% 87.93/88.12 tff(18956,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.12 tff(18957,plain,
% 87.93/88.12 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18956, 18695, 18798, 18797])).
% 87.93/88.12 tff(18958,plain,
% 87.93/88.12 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18959,plain,
% 87.93/88.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18960,plain,
% 87.93/88.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18959, 18958])).
% 87.93/88.12 tff(18961,plain,
% 87.93/88.12 ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18960, 1521])).
% 87.93/88.12 tff(18962,plain,
% 87.93/88.12 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18961, 18957])).
% 87.93/88.12 tff(18963,plain,
% 87.93/88.12 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s18))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18964,plain,
% 87.93/88.12 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s18))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18965,plain,
% 87.93/88.12 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s18)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18964, 18963])).
% 87.93/88.12 tff(18966,plain,
% 87.93/88.12 (~node20(c_e_h_1, c_r, s18)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18965, 1535, 18962])).
% 87.93/88.12 tff(18967,assumption,(~node20(c_e_h_1, c_r, s18)), introduced(assumption)).
% 87.93/88.12 tff(18968,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s18)), introduced(assumption)).
% 87.93/88.12 tff(18969,assumption,(node22(c_e_h_1, c_r, s18, s19)), introduced(assumption)).
% 87.93/88.12 tff(18970,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18971,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18972,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18971, 18970])).
% 87.93/88.12 tff(18973,plain,
% 87.93/88.12 ($false),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18972, 107, 18796, 18969, 18968])).
% 87.93/88.12 tff(18974,plain,((~node22(c_e_h_1, c_r, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.12 tff(18975,plain,
% 87.93/88.12 (~node22(c_e_h_1, c_r, s18, s19)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18974, 18796, 18968])).
% 87.93/88.12 tff(18976,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18977,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18978,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18977, 18976])).
% 87.93/88.12 tff(18979,plain,
% 87.93/88.12 (node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18978, 81, 15727])).
% 87.93/88.12 tff(18980,plain,
% 87.93/88.12 (node21(c_e_h_1, c_r, s18, s19)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18979, 18975])).
% 87.93/88.12 tff(18981,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_r, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18982,plain,
% 87.93/88.12 ((node20(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node21(c_e_h_1, c_r, s18, s19))) <=> ((~node21(c_e_h_1, c_r, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18983,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node21(c_e_h_1, c_r, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_r, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18)))),
% 87.93/88.12 inference(monotonicity,[status(thm)],[18982])).
% 87.93/88.12 tff(18984,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node21(c_e_h_1, c_r, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18))),
% 87.93/88.12 inference(transitivity,[status(thm)],[18983, 18981])).
% 87.93/88.12 tff(18985,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node21(c_e_h_1, c_r, s18, s19)))),
% 87.93/88.12 inference(quant_inst,[status(thm)],[])).
% 87.93/88.12 tff(18986,plain,
% 87.93/88.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_r, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18)),
% 87.93/88.12 inference(modus_ponens,[status(thm)],[18985, 18984])).
% 87.93/88.12 tff(18987,plain,
% 87.93/88.12 ($false),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18986, 51, 18796, 18980, 18967])).
% 87.93/88.12 tff(18988,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18) | m_and_h_gate_v_out(c_e_h_1, c_r, s18)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.12 tff(18989,plain,
% 87.93/88.12 (m_and_h_gate_v_out(c_e_h_1, c_r, s18)),
% 87.93/88.12 inference(unit_resolution,[status(thm)],[18988, 18966, 18796])).
% 87.93/88.12 tff(18990,assumption,(~node20(c_e_h_1, c_r, s17)), introduced(assumption)).
% 87.93/88.12 tff(18991,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s18)), introduced(assumption)).
% 87.93/88.12 tff(18992,assumption,(node21(c_e_h_1, c_r, s17, s18)), introduced(assumption)).
% 87.93/88.12 tff(18993,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18)))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18994,plain,
% 87.93/88.12 ((node20(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node21(c_e_h_1, c_r, s17, s18))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18)))),
% 87.93/88.12 inference(rewrite,[status(thm)],[])).
% 87.93/88.12 tff(18995,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node21(c_e_h_1, c_r, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18))))),
% 87.93/88.12 inference(monotonicity,[status(thm)],[18994])).
% 87.93/88.12 tff(18996,plain,
% 87.93/88.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node21(c_e_h_1, c_r, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18)))),
% 87.93/88.13 inference(transitivity,[status(thm)],[18995, 18993])).
% 87.93/88.13 tff(18997,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node21(c_e_h_1, c_r, s17, s18)))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(18998,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18))),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[18997, 18996])).
% 87.93/88.13 tff(18999,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[18998, 51, 18991, 18992, 18990])).
% 87.93/88.13 tff(19000,plain,((~node21(c_e_h_1, c_r, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19001,plain,
% 87.93/88.13 (~node21(c_e_h_1, c_r, s17, s18)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19000, 18991, 18990])).
% 87.93/88.13 tff(19002,plain,
% 87.93/88.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19003,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19004,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19003, 19002])).
% 87.93/88.13 tff(19005,plain,
% 87.93/88.13 (node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19004, 81, 15701])).
% 87.93/88.13 tff(19006,plain,
% 87.93/88.13 (node22(c_e_h_1, c_r, s17, s18)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19005, 19001])).
% 87.93/88.13 tff(19007,plain,
% 87.93/88.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19008,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19009,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19008, 19007])).
% 87.93/88.13 tff(19010,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19009, 107, 18991, 19006, 18795])).
% 87.93/88.13 tff(19011,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17) | node20(c_e_h_1, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19012,plain,
% 87.93/88.13 (node20(c_e_h_1, c_r, s17)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19011, 18989, 18795])).
% 87.93/88.13 tff(19013,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)), introduced(assumption)).
% 87.93/88.13 tff(19014,assumption,(node20(c_e_h_1, c_r, s17)), introduced(assumption)).
% 87.93/88.13 tff(19015,plain,
% 87.93/88.13 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s17))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19016,plain,
% 87.93/88.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s17))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19017,plain,
% 87.93/88.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s17)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19016, 19015])).
% 87.93/88.13 tff(19018,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19017, 1535, 19014, 19013])).
% 87.93/88.13 tff(19019,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s17) | (~node20(c_e_h_1, c_r, s17))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19020,plain,
% 87.93/88.13 (m_and_h_gate_v_in2(c_e_h_1, c_r, s17)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19019, 19012])).
% 87.93/88.13 tff(19021,plain,
% 87.93/88.13 (~node9(c_e_h_1, c_m, s15)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[18731, 1062, 18954])).
% 87.93/88.13 tff(19022,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[18756, 19021])).
% 87.93/88.13 tff(19023,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[18865, 1048, 18861])).
% 87.93/88.13 tff(19024,plain,
% 87.93/88.13 (~node9(c_e_h_1, c_m, s16)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[18869, 1062, 19023])).
% 87.93/88.13 tff(19025,assumption,(~node9(c_e_h_1, c_m, s16)), introduced(assumption)).
% 87.93/88.13 tff(19026,plain,
% 87.93/88.13 (~node11(c_e_h_1, c_m, s16, s17)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[18936, 18930, 18871])).
% 87.93/88.13 tff(19027,plain,
% 87.93/88.13 (node10(c_e_h_1, c_m, s16, s17)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[18941, 19026])).
% 87.93/88.13 tff(19028,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[18948, 1076, 19027, 18930, 19025])).
% 87.93/88.13 tff(19029,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | node9(c_e_h_1, c_m, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19030,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19029, 19024, 19022])).
% 87.93/88.13 tff(19031,plain,
% 87.93/88.13 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19032,plain,
% 87.93/88.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19033,plain,
% 87.93/88.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19032, 19031])).
% 87.93/88.13 tff(19034,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19033, 1521, 19030, 19020])).
% 87.93/88.13 tff(19035,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19036,plain,
% 87.93/88.13 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16))),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19035, 18690, 18794])).
% 87.93/88.13 tff(19037,plain,
% 87.93/88.13 (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19036, 18683, 18671])).
% 87.93/88.13 tff(19038,assumption,(m_user_v_ack(c_e_h_1, c_u, s19)), introduced(assumption)).
% 87.93/88.13 tff(19039,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s19)), introduced(assumption)).
% 87.93/88.13 tff(19040,plain,
% 87.93/88.13 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19041,plain,
% 87.93/88.13 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19042,plain,
% 87.93/88.13 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19041, 19040])).
% 87.93/88.13 tff(19043,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19042, 4481, 19039, 19038])).
% 87.93/88.13 tff(19044,plain,((~m_user_v_ack(c_e_h_1, c_u, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19045,plain,
% 87.93/88.13 (~m_user_v_ack(c_e_h_1, c_u, s19)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19044, 19037])).
% 87.93/88.13 tff(19046,assumption,(node24(s19)), introduced(assumption)).
% 87.93/88.13 tff(19047,assumption,(~m_user_v_ack(c_e_h_1, c_u, s19)), introduced(assumption)).
% 87.93/88.13 tff(19048,plain,
% 87.93/88.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s19) | (~node24(s19)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s19) | (~node24(s19)))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19049,plain,
% 87.93/88.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s19) | (~node24(s19)))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19050,plain,
% 87.93/88.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s19) | (~node24(s19))),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19049, 19048])).
% 87.93/88.13 tff(19051,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19050, 8407, 19047, 19046])).
% 87.93/88.13 tff(19052,plain,(m_user_v_ack(c_e_h_1, c_u, s19) | (~node24(s19))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19053,plain,
% 87.93/88.13 (~node24(s19)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19052, 19045])).
% 87.93/88.13 tff(19054,plain,
% 87.93/88.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s19)) | m_user_v_ack(c_e_h_1, c_u, s19))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s19)) | m_user_v_ack(c_e_h_1, c_u, s19))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19055,plain,
% 87.93/88.13 ((m_user_v_ack(c_e_h_1, c_u, s19) | (~node23(s19))) <=> ((~node23(s19)) | m_user_v_ack(c_e_h_1, c_u, s19))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19056,plain,
% 87.93/88.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s19) | (~node23(s19)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s19)) | m_user_v_ack(c_e_h_1, c_u, s19)))),
% 87.93/88.13 inference(monotonicity,[status(thm)],[19055])).
% 87.93/88.13 tff(19057,plain,
% 87.93/88.13 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s19) | (~node23(s19)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s19)) | m_user_v_ack(c_e_h_1, c_u, s19))),
% 87.93/88.13 inference(transitivity,[status(thm)],[19056, 19054])).
% 87.93/88.13 tff(19058,plain,
% 87.93/88.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s19) | (~node23(s19)))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19059,plain,
% 87.93/88.13 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s19)) | m_user_v_ack(c_e_h_1, c_u, s19)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19058, 19057])).
% 87.93/88.13 tff(19060,plain,
% 87.93/88.13 (~node23(s19)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19059, 8418, 19045])).
% 87.93/88.13 tff(19061,plain,
% 87.93/88.13 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s19) | node24(s19) | node25(s19) | (~node26(s19)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s19) | node24(s19) | node25(s19) | (~node26(s19)))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19062,plain,
% 87.93/88.13 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s19) | node24(s19) | node25(s19) | (~node26(s19)))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19063,plain,
% 87.93/88.13 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s19) | node24(s19) | node25(s19) | (~node26(s19))),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19062, 19061])).
% 87.93/88.13 tff(19064,plain,
% 87.93/88.13 (node25(s19) | (~node26(s19))),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19063, 8435, 19060, 19053])).
% 87.93/88.13 tff(19065,plain,
% 87.93/88.13 (~node26(s19)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19064, 15846])).
% 87.93/88.13 tff(19066,plain,
% 87.93/88.13 (~m_and_h_gate_v_out(c_e_h_2, c_l, s8)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9242, 9237])).
% 87.93/88.13 tff(19067,plain,
% 87.93/88.13 (~m_and_h_gate_v_out(c_e_h_2, c_l, s9)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9645, 19066])).
% 87.93/88.13 tff(19068,plain,
% 87.93/88.13 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s9)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9650, 19067])).
% 87.93/88.13 tff(19069,plain,
% 87.93/88.13 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s8)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9250, 19066])).
% 87.93/88.13 tff(19070,plain,
% 87.93/88.13 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[8518, 801, 9237])).
% 87.93/88.13 tff(19071,plain,
% 87.93/88.13 (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[8828, 19070, 8795])).
% 87.93/88.13 tff(19072,plain,
% 87.93/88.13 (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9404, 19071, 19069])).
% 87.93/88.13 tff(19073,plain,
% 87.93/88.13 (~m_or_h_gate_v_out(c_e_h_2, c_j, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9812, 19072, 19068])).
% 87.93/88.13 tff(19074,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_h, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9816, 309, 19073])).
% 87.93/88.13 tff(19075,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[8832, 309, 19071])).
% 87.93/88.13 tff(19076,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_h, s9)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9000, 19075, 8922])).
% 87.93/88.13 tff(19077,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_h, s9)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9408, 309, 19072])).
% 87.93/88.13 tff(19078,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_h, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9471, 19077, 19076])).
% 87.93/88.13 tff(19079,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_h, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9877, 19078, 19074])).
% 87.93/88.13 tff(19080,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16)), introduced(assumption)).
% 87.93/88.13 tff(19081,plain,
% 87.93/88.13 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9891, 19079])).
% 87.93/88.13 tff(19082,plain,
% 87.93/88.13 (~node20(c_e_h_2, c_i, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9899, 19081])).
% 87.93/88.13 tff(19083,plain,
% 87.93/88.13 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9006, 23, 19076])).
% 87.93/88.13 tff(19084,plain,
% 87.93/88.13 (~node20(c_e_h_2, c_i, s9)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9010, 37, 19083])).
% 87.93/88.13 tff(19085,plain,
% 87.93/88.13 (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9066, 19084, 9047])).
% 87.93/88.13 tff(19086,plain,
% 87.93/88.13 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9475, 23, 19078])).
% 87.93/88.13 tff(19087,plain,
% 87.93/88.13 (~node20(c_e_h_2, c_i, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9479, 37, 19086])).
% 87.93/88.13 tff(19088,plain,
% 87.93/88.13 (~m_and_h_gate_v_out(c_e_h_2, c_i, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9503, 19087, 19085])).
% 87.93/88.13 tff(19089,plain,
% 87.93/88.13 (~m_and_h_gate_v_out(c_e_h_2, c_i, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9922, 19088, 19082])).
% 87.93/88.13 tff(19090,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_e, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9930, 19089])).
% 87.93/88.13 tff(19091,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_e, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9074, 19085])).
% 87.93/88.13 tff(19092,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_e, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9211, 19091, 9153])).
% 87.93/88.13 tff(19093,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_e, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9511, 19088])).
% 87.93/88.13 tff(19094,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_e, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[9573, 19093, 19092])).
% 87.93/88.13 tff(19095,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_e, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10001, 19094, 19090])).
% 87.93/88.13 tff(19096,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[3749, 3705])).
% 87.93/88.13 tff(19097,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[4399, 1048, 12473])).
% 87.93/88.13 tff(19098,plain,
% 87.93/88.13 (~node9(c_e_h_2, c_m, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[4428, 1062, 19097])).
% 87.93/88.13 tff(19099,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[4424, 19098, 19096])).
% 87.93/88.13 tff(19100,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12460, 19096])).
% 87.93/88.13 tff(19101,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12513, 12484, 19100, 12473])).
% 87.93/88.13 tff(19102,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12648, 1048, 19101])).
% 87.93/88.13 tff(19103,plain,
% 87.93/88.13 (~node9(c_e_h_2, c_m, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12652, 1062, 19102])).
% 87.93/88.13 tff(19104,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12643, 19103, 19099])).
% 87.93/88.13 tff(19105,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12571, 19091, 12473, 12484, 19100, 19099])).
% 87.93/88.13 tff(19106,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12696, 1048, 19105])).
% 87.93/88.13 tff(19107,plain,
% 87.93/88.13 (~node9(c_e_h_2, c_m, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12700, 1062, 19106])).
% 87.93/88.13 tff(19108,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12725, 19107, 19104])).
% 87.93/88.13 tff(19109,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12617, 19104])).
% 87.93/88.13 tff(19110,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12609, 19093, 9153, 12473, 19109, 19091, 19100, 19099])).
% 87.93/88.13 tff(19111,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12794, 1048, 19110])).
% 87.93/88.13 tff(19112,plain,
% 87.93/88.13 (~node9(c_e_h_2, c_m, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12798, 1062, 19111])).
% 87.93/88.13 tff(19113,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s14)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12821, 19112, 19108])).
% 87.93/88.13 tff(19114,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12468, 19095])).
% 87.93/88.13 tff(19115,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12691, 19108])).
% 87.93/88.13 tff(19116,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s14)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12683, 19115, 19114, 19110])).
% 87.93/88.13 tff(19117,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s14)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12731, 1048, 19116])).
% 87.93/88.13 tff(19118,plain,
% 87.93/88.13 (~node9(c_e_h_2, c_m, s14)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12739, 19117])).
% 87.93/88.13 tff(19119,plain,
% 87.93/88.13 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12842, 19118, 19113])).
% 87.93/88.13 tff(19120,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)), introduced(assumption)).
% 87.93/88.13 tff(19121,plain,
% 87.93/88.13 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19122,plain,
% 87.93/88.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19123,plain,
% 87.93/88.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19122, 19121])).
% 87.93/88.13 tff(19124,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19123, 1142, 14054, 19120])).
% 87.93/88.13 tff(19125,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s15) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19126,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19125, 19119])).
% 87.93/88.13 tff(19127,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12607, 19094])).
% 87.93/88.13 tff(19128,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)), introduced(assumption)).
% 87.93/88.13 tff(19129,plain,
% 87.93/88.13 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10095, 10089])).
% 87.93/88.13 tff(19130,plain,
% 87.93/88.13 (~m_or_h_gate_v_out(c_e_h_2, c_j, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10257, 19129, 10097])).
% 87.93/88.13 tff(19131,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_h, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10267, 19130])).
% 87.93/88.13 tff(19132,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_h, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10344, 19131, 9886])).
% 87.93/88.13 tff(19133,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[12468, 10004])).
% 87.93/88.13 tff(19134,plain,
% 87.93/88.13 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10348, 23, 14420])).
% 87.93/88.13 tff(19135,plain,
% 87.93/88.13 (~node20(c_e_h_2, c_i, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10352, 37, 19134])).
% 87.93/88.13 tff(19136,plain,
% 87.93/88.13 (~m_and_h_gate_v_out(c_e_h_2, c_i, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10375, 19135, 9925])).
% 87.93/88.13 tff(19137,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_e, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10383, 19136])).
% 87.93/88.13 tff(19138,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_e, s14)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[10462, 19137, 10004])).
% 87.93/88.13 tff(19139,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_h, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14485, 14420, 14419])).
% 87.93/88.13 tff(19140,plain,
% 87.93/88.13 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14489, 23, 19139])).
% 87.93/88.13 tff(19141,plain,
% 87.93/88.13 (~node20(c_e_h_2, c_i, s13)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14493, 37, 19140])).
% 87.93/88.13 tff(19142,plain,
% 87.93/88.13 (~m_and_h_gate_v_out(c_e_h_2, c_i, s14)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14516, 19136, 19141])).
% 87.93/88.13 tff(19143,plain,
% 87.93/88.13 (~m_c_h_element_v_in2(c_e_h_2, c_e, s14)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14695, 19142])).
% 87.93/88.13 tff(19144,plain,
% 87.93/88.13 (~m_c_h_element_v_out(c_e_h_2, c_e, s15)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14784, 10465, 14720])).
% 87.93/88.13 tff(19145,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s14)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[13972, 10465])).
% 87.93/88.13 tff(19146,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14030, 19145, 12471, 12473, 19100, 9152, 12486, 12573, 19099, 3705, 4335])).
% 87.93/88.13 tff(19147,plain,
% 87.93/88.13 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15) | m_c_h_element_v_out(c_e_h_2, c_e, s15))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15) | m_c_h_element_v_out(c_e_h_2, c_e, s15))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19148,plain,
% 87.93/88.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15) | m_c_h_element_v_out(c_e_h_2, c_e, s15))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19149,plain,
% 87.93/88.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15) | m_c_h_element_v_out(c_e_h_2, c_e, s15)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19148, 19147])).
% 87.93/88.13 tff(19150,plain,
% 87.93/88.13 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19149, 976, 14786])).
% 87.93/88.13 tff(19151,assumption,(node10(c_e_h_2, c_n, s15, s16)), introduced(assumption)).
% 87.93/88.13 tff(19152,plain,
% 87.93/88.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~node10(c_e_h_2, c_n, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~node10(c_e_h_2, c_n, s15, s16)))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19153,plain,
% 87.93/88.13 (((~node10(c_e_h_2, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~node10(c_e_h_2, c_n, s15, s16)))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19154,plain,
% 87.93/88.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~node10(c_e_h_2, c_n, s15, s16))))),
% 87.93/88.13 inference(monotonicity,[status(thm)],[19153])).
% 87.93/88.13 tff(19155,plain,
% 87.93/88.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~node10(c_e_h_2, c_n, s15, s16)))),
% 87.93/88.13 inference(transitivity,[status(thm)],[19154, 19152])).
% 87.93/88.13 tff(19156,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19157,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~node10(c_e_h_2, c_n, s15, s16))),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19156, 19155])).
% 87.93/88.13 tff(19158,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19157, 1191, 19080, 19151, 19128, 19150])).
% 87.93/88.13 tff(19159,plain,((~node10(c_e_h_2, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19160,plain,
% 87.93/88.13 (~node10(c_e_h_2, c_n, s15, s16)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19159, 19080, 14786, 19128])).
% 87.93/88.13 tff(19161,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)), introduced(assumption)).
% 87.93/88.13 tff(19162,assumption,(node11(c_e_h_2, c_n, s15, s16)), introduced(assumption)).
% 87.93/88.13 tff(19163,plain,
% 87.93/88.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~node11(c_e_h_2, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~node11(c_e_h_2, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19164,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~node11(c_e_h_2, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19165,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~node11(c_e_h_2, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15))),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19164, 19163])).
% 87.93/88.13 tff(19166,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19165, 1161, 19080, 19161, 19162])).
% 87.93/88.13 tff(19167,plain,((~node11(c_e_h_2, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19168,plain,
% 87.93/88.13 (~node11(c_e_h_2, c_n, s15, s16)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19167, 19080, 19161])).
% 87.93/88.13 tff(19169,plain,
% 87.93/88.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_2, c_n, s15, s16) | node11(c_e_h_2, c_n, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_2, c_n, s15, s16) | node11(c_e_h_2, c_n, s15, s16))),
% 87.93/88.13 inference(rewrite,[status(thm)],[])).
% 87.93/88.13 tff(19170,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_2, c_n, s15, s16) | node11(c_e_h_2, c_n, s15, s16))),
% 87.93/88.13 inference(quant_inst,[status(thm)],[])).
% 87.93/88.13 tff(19171,plain,
% 87.93/88.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_2, c_n, s15, s16) | node11(c_e_h_2, c_n, s15, s16)),
% 87.93/88.13 inference(modus_ponens,[status(thm)],[19170, 19169])).
% 87.93/88.13 tff(19172,plain,
% 87.93/88.13 (node10(c_e_h_2, c_n, s15, s16) | node11(c_e_h_2, c_n, s15, s16)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19171, 1092, 12879])).
% 87.93/88.13 tff(19173,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19172, 19168, 19160])).
% 87.93/88.13 tff(19174,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s15)) | m_c_h_element_v_out(c_e_h_2, c_e, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19175,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19174, 19146, 19144, 19128, 19080])).
% 87.93/88.13 tff(19176,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_c_h_element_v_in2(c_e_h_2, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19177,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19176, 19143, 19138, 19080, 3705, 12473, 9152, 12486, 12573, 19128, 4335, 19133])).
% 87.93/88.13 tff(19178,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s12) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | m_and_h_gate_v_out(c_e_h_2, c_i, s12) | m_c_h_element_v_in2(c_e_h_2, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.13 tff(19179,plain,
% 87.93/88.13 (m_c_h_element_v_in2(c_e_h_2, c_h, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[19178, 19132, 3705, 12473, 9152, 12486, 12573, 19128, 4335, 10004, 9925, 19080])).
% 87.93/88.13 tff(19180,plain,
% 87.93/88.13 (m_or_h_gate_v_out(c_e_h_2, c_j, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14416, 309, 19179])).
% 87.93/88.13 tff(19181,plain,
% 87.93/88.13 (~node6(c_e_h_2, c_j, s11, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14262, 19180, 19130])).
% 87.93/88.13 tff(19182,plain,
% 87.93/88.13 (node5(c_e_h_2, c_j, s11, s12)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14410, 19181])).
% 87.93/88.13 tff(19183,plain,
% 87.93/88.13 (m_or_h_gate_v_in1(c_e_h_2, c_j, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14402, 19182, 19180])).
% 87.93/88.13 tff(19184,plain,
% 87.93/88.13 (m_and_h_gate_v_out(c_e_h_2, c_l, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14249, 801, 19183])).
% 87.93/88.13 tff(19185,plain,
% 87.93/88.13 (~node22(c_e_h_2, c_l, s10, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14168, 19184, 10089])).
% 87.93/88.13 tff(19186,plain,
% 87.93/88.13 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14156, 19096])).
% 87.93/88.13 tff(19187,plain,
% 87.93/88.13 (~node20(c_e_h_2, c_l, s10)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14160, 1535, 19186])).
% 87.93/88.13 tff(19188,plain,
% 87.93/88.13 (~node21(c_e_h_2, c_l, s10, s11)),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14176, 19184, 19187])).
% 87.93/88.13 tff(19189,plain,
% 87.93/88.13 ($false),
% 87.93/88.13 inference(unit_resolution,[status(thm)],[14181, 19188, 19185])).
% 87.93/88.13 tff(19190,plain,(m_and_h_gate_v_out(c_e_h_2, c_l, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | m_c_h_element_v_in2(c_e_h_2, c_e, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_c_h_element_v_out(c_e_h_2, c_e, s13) | m_and_h_gate_v_out(c_e_h_2, c_i, s12) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | m_c_h_element_v_out(c_e_h_2, c_h, s11) | m_or_h_gate_v_out(c_e_h_2, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19191,plain,
% 87.93/88.14 (m_and_h_gate_v_out(c_e_h_2, c_l, s10)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19190, 19091, 12473, 3705, 12484, 19127, 19126, 4335, 19095, 19089, 19080, 19079, 19073])).
% 87.93/88.14 tff(19192,plain,
% 87.93/88.14 (~node21(c_e_h_2, c_l, s9, s10)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[10073, 19191])).
% 87.93/88.14 tff(19193,plain,
% 87.93/88.14 (~node22(c_e_h_2, c_l, s9, s10)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[10080, 19191, 19067])).
% 87.93/88.14 tff(19194,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[10085, 19193, 19192])).
% 87.93/88.14 tff(19195,plain,(m_and_h_gate_v_out(c_e_h_2, c_l, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16) | m_c_h_element_v_out(c_e_h_2, c_e, s10) | m_and_h_gate_v_out(c_e_h_2, c_i, s9) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | m_or_h_gate_v_out(c_e_h_2, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19196,plain,
% 87.93/88.14 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19195, 12745, 9214, 9012, 9046, 12462, 3676, 9150, 9015])).
% 87.93/88.14 tff(19197,plain,
% 87.93/88.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16)))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19198,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16)))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19199,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s16))),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19198, 19197])).
% 87.93/88.14 tff(19200,plain,
% 87.93/88.14 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19199, 1048, 19196])).
% 87.93/88.14 tff(19201,plain,
% 87.93/88.14 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19202,plain,
% 87.93/88.14 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19203,plain,
% 87.93/88.14 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s16)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19202, 19201])).
% 87.93/88.14 tff(19204,plain,
% 87.93/88.14 (~node9(c_e_h_2, c_m, s16)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19203, 1062, 19200])).
% 87.93/88.14 tff(19205,assumption,(~node9(c_e_h_2, c_m, s16)), introduced(assumption)).
% 87.93/88.14 tff(19206,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)), introduced(assumption)).
% 87.93/88.14 tff(19207,assumption,(node11(c_e_h_2, c_m, s16, s17)), introduced(assumption)).
% 87.93/88.14 tff(19208,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | (~node11(c_e_h_2, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | (~node11(c_e_h_2, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19209,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | (~node11(c_e_h_2, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19210,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | (~node11(c_e_h_2, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19209, 19208])).
% 87.93/88.14 tff(19211,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19210, 1130, 19206, 19207, 14062])).
% 87.93/88.14 tff(19212,plain,((~node11(c_e_h_2, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19213,plain,
% 87.93/88.14 (~node11(c_e_h_2, c_m, s16, s17)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19212, 19206, 14062])).
% 87.93/88.14 tff(19214,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_2, c_m, s16, s17) | node11(c_e_h_2, c_m, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_2, c_m, s16, s17) | node11(c_e_h_2, c_m, s16, s17))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19215,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_2, c_m, s16, s17) | node11(c_e_h_2, c_m, s16, s17))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19216,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_2, c_m, s16, s17) | node11(c_e_h_2, c_m, s16, s17)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19215, 19214])).
% 87.93/88.14 tff(19217,plain,
% 87.93/88.14 (node10(c_e_h_2, c_m, s16, s17) | node11(c_e_h_2, c_m, s16, s17)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19216, 1092, 14096])).
% 87.93/88.14 tff(19218,plain,
% 87.93/88.14 (node10(c_e_h_2, c_m, s16, s17)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19217, 19213])).
% 87.93/88.14 tff(19219,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | node9(c_e_h_2, c_m, s16) | (~node10(c_e_h_2, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | node9(c_e_h_2, c_m, s16) | (~node10(c_e_h_2, c_m, s16, s17)))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19220,plain,
% 87.93/88.14 ((node9(c_e_h_2, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | (~node10(c_e_h_2, c_m, s16, s17))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | node9(c_e_h_2, c_m, s16) | (~node10(c_e_h_2, c_m, s16, s17)))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19221,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | (~node10(c_e_h_2, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | node9(c_e_h_2, c_m, s16) | (~node10(c_e_h_2, c_m, s16, s17))))),
% 87.93/88.14 inference(monotonicity,[status(thm)],[19220])).
% 87.93/88.14 tff(19222,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | (~node10(c_e_h_2, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | node9(c_e_h_2, c_m, s16) | (~node10(c_e_h_2, c_m, s16, s17)))),
% 87.93/88.14 inference(transitivity,[status(thm)],[19221, 19219])).
% 87.93/88.14 tff(19223,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | (~node10(c_e_h_2, c_m, s16, s17)))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19224,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | node9(c_e_h_2, c_m, s16) | (~node10(c_e_h_2, c_m, s16, s17))),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19223, 19222])).
% 87.93/88.14 tff(19225,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19224, 1076, 19206, 19218, 19205])).
% 87.93/88.14 tff(19226,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)) | node9(c_e_h_2, c_m, s16) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s16)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19227,plain,
% 87.93/88.14 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19226, 14060, 19204])).
% 87.93/88.14 tff(19228,assumption,(m_and_h_gate_v_in2(c_e_h_2, c_r, s17)), introduced(assumption)).
% 87.93/88.14 tff(19229,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)), introduced(assumption)).
% 87.93/88.14 tff(19230,plain,
% 87.93/88.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19231,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19232,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19231, 19230])).
% 87.93/88.14 tff(19233,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19232, 1521, 19229, 19228])).
% 87.93/88.14 tff(19234,plain,((~m_and_h_gate_v_in2(c_e_h_2, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s17)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19235,plain,
% 87.93/88.14 (~m_and_h_gate_v_in2(c_e_h_2, c_r, s17)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19234, 19227])).
% 87.93/88.14 tff(19236,assumption,(~m_and_h_gate_v_in2(c_e_h_2, c_r, s17)), introduced(assumption)).
% 87.93/88.14 tff(19237,plain,
% 87.93/88.14 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s17))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19238,plain,
% 87.93/88.14 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s17))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19239,plain,
% 87.93/88.14 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s17)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19238, 19237])).
% 87.93/88.14 tff(19240,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19239, 1535, 19236, 15676])).
% 87.93/88.14 tff(19241,plain,((~node20(c_e_h_2, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_2, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19242,plain,
% 87.93/88.14 (~node20(c_e_h_2, c_r, s17)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19241, 19235])).
% 87.93/88.14 tff(19243,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s10)), introduced(assumption)).
% 87.93/88.14 tff(19244,plain,
% 87.93/88.14 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19245,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19246,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19245, 19244])).
% 87.93/88.14 tff(19247,plain,
% 87.93/88.14 (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19246, 365, 16283])).
% 87.93/88.14 tff(19248,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s3)), introduced(assumption)).
% 87.93/88.14 tff(19249,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s2)), introduced(assumption)).
% 87.93/88.14 tff(19250,plain,
% 87.93/88.14 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19251,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19252,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19251, 19250])).
% 87.93/88.14 tff(19253,plain,
% 87.93/88.14 (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19252, 365, 7706])).
% 87.93/88.14 tff(19254,plain,
% 87.93/88.14 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19255,plain,
% 87.93/88.14 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19256,plain,
% 87.93/88.14 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19255, 19254])).
% 87.93/88.14 tff(19257,plain,
% 87.93/88.14 ((~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19256, 228, 19253])).
% 87.93/88.14 tff(19258,plain,
% 87.93/88.14 (~node16(c_e_h_3, c_e, s2)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19257, 19249])).
% 87.93/88.14 tff(19259,assumption,(node14(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 87.93/88.14 tff(19260,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19261,plain,
% 87.93/88.14 (((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~node14(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19262,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2)))),
% 87.93/88.14 inference(monotonicity,[status(thm)],[19261])).
% 87.93/88.14 tff(19263,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 87.93/88.14 inference(transitivity,[status(thm)],[19262, 19260])).
% 87.93/88.14 tff(19264,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19265,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19264, 19263])).
% 87.93/88.14 tff(19266,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19265, 283, 19248, 19259, 19249])).
% 87.93/88.14 tff(19267,plain,((~node14(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19268,plain,
% 87.93/88.14 (~node14(c_e_h_3, c_e, s2, s3)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19267, 19248, 19249])).
% 87.93/88.14 tff(19269,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 87.93/88.14 tff(19270,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s1)), introduced(assumption)).
% 87.93/88.14 tff(19271,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s1)), introduced(assumption)).
% 87.93/88.14 tff(19272,plain,
% 87.93/88.14 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19273,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19274,plain,
% 87.93/88.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19273, 19272])).
% 87.93/88.14 tff(19275,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19274, 365, 19271, 7668])).
% 87.93/88.14 tff(19276,plain,(~m_c_h_element_v_in2(c_e_h_3, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19277,plain,
% 87.93/88.14 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | m_c_h_element_v_in2(c_e_h_3, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | m_c_h_element_v_in2(c_e_h_3, c_e, s1))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19278,plain,
% 87.93/88.14 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | m_c_h_element_v_in2(c_e_h_3, c_e, s1))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19279,plain,
% 87.93/88.14 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | m_c_h_element_v_in2(c_e_h_3, c_e, s1)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19278, 19277])).
% 87.93/88.14 tff(19280,plain,
% 87.93/88.14 ((~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19279, 228, 19276])).
% 87.93/88.14 tff(19281,plain,
% 87.93/88.14 (~node16(c_e_h_3, c_e, s1)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19280, 19270])).
% 87.93/88.14 tff(19282,assumption,(node15(c_e_h_3, c_e, s1, s2)), introduced(assumption)).
% 87.93/88.14 tff(19283,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s1)), introduced(assumption)).
% 87.93/88.14 tff(19284,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s0)), introduced(assumption)).
% 87.93/88.14 tff(19285,plain,
% 87.93/88.14 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19286,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19285, 13, 19284])).
% 87.93/88.14 tff(19287,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19288,assumption,(node18(c_e_h_3, c_e, s0, s1)), introduced(assumption)).
% 87.93/88.14 tff(19289,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node18(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node18(c_e_h_3, c_e, s0, s1)))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19290,plain,
% 87.93/88.14 (((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~node18(c_e_h_3, c_e, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node18(c_e_h_3, c_e, s0, s1)))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19291,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~node18(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node18(c_e_h_3, c_e, s0, s1))))),
% 87.93/88.14 inference(monotonicity,[status(thm)],[19290])).
% 87.93/88.14 tff(19292,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~node18(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node18(c_e_h_3, c_e, s0, s1)))),
% 87.93/88.14 inference(transitivity,[status(thm)],[19291, 19289])).
% 87.93/88.14 tff(19293,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~node18(c_e_h_3, c_e, s0, s1)))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19294,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node18(c_e_h_3, c_e, s0, s1))),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19293, 19292])).
% 87.93/88.14 tff(19295,plain,
% 87.93/88.14 ($false),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19294, 124, 19288, 19287, 19283])).
% 87.93/88.14 tff(19296,plain,((~node18(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.14 tff(19297,plain,
% 87.93/88.14 (~node18(c_e_h_3, c_e, s0, s1)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19296, 19283])).
% 87.93/88.14 tff(19298,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_e, s0, s1))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19299,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_e, s0, s1))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19300,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_e, s0, s1)),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19299, 19298])).
% 87.93/88.14 tff(19301,plain,
% 87.93/88.14 (node19(c_e_h_3, c_e, s0, s1)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19300, 141, 71])).
% 87.93/88.14 tff(19302,plain,
% 87.93/88.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s0) | node18(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s0) | node18(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))),
% 87.93/88.14 inference(rewrite,[status(thm)],[])).
% 87.93/88.14 tff(19303,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s0) | node18(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))),
% 87.93/88.14 inference(quant_inst,[status(thm)],[])).
% 87.93/88.14 tff(19304,plain,
% 87.93/88.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s0) | node18(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1))),
% 87.93/88.14 inference(modus_ponens,[status(thm)],[19303, 19302])).
% 87.93/88.14 tff(19305,plain,
% 87.93/88.14 (node17(c_e_h_3, c_e, s0) | node18(c_e_h_3, c_e, s0, s1)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19304, 156, 19301])).
% 87.93/88.14 tff(19306,plain,
% 87.93/88.14 (node17(c_e_h_3, c_e, s0)),
% 87.93/88.14 inference(unit_resolution,[status(thm)],[19305, 19297])).
% 87.93/88.14 tff(19307,assumption,(node17(c_e_h_3, c_e, s0)), introduced(assumption)).
% 87.93/88.14 tff(19308,assumption,(node16(c_e_h_3, c_e, s0)), introduced(assumption)).
% 87.93/88.14 tff(19309,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s0)), introduced(assumption)).
% 87.93/88.14 tff(19310,plain,
% 87.93/88.14 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19311,plain,
% 87.93/88.15 ((m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19312,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(monotonicity,[status(thm)],[19311])).
% 87.93/88.15 tff(19313,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(transitivity,[status(thm)],[19312, 19310])).
% 87.93/88.15 tff(19314,plain,
% 87.93/88.15 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19315,plain,
% 87.93/88.15 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19314, 19313])).
% 87.93/88.15 tff(19316,plain,
% 87.93/88.15 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19315, 245, 19307])).
% 87.93/88.15 tff(19317,plain,
% 87.93/88.15 (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19316, 19309])).
% 87.93/88.15 tff(19318,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19319,plain,
% 87.93/88.15 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19320,plain,
% 87.93/88.15 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19319, 19318])).
% 87.93/88.15 tff(19321,plain,
% 87.93/88.15 (m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19320, 228, 19308])).
% 87.93/88.15 tff(19322,plain,
% 87.93/88.15 ($false),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19321, 19317, 19309])).
% 87.93/88.15 tff(19323,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node16(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.15 tff(19324,plain,
% 87.93/88.15 (m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19323, 19308, 19307])).
% 87.93/88.15 tff(19325,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19326,plain,
% 87.93/88.15 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0) | (~node17(c_e_h_3, c_e, s0))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19327,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0) | (~node17(c_e_h_3, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(monotonicity,[status(thm)],[19326])).
% 87.93/88.15 tff(19328,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0) | (~node17(c_e_h_3, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(transitivity,[status(thm)],[19327, 19325])).
% 87.93/88.15 tff(19329,plain,
% 87.93/88.15 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0) | (~node17(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19330,plain,
% 87.93/88.15 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19329, 19328])).
% 87.93/88.15 tff(19331,plain,
% 87.93/88.15 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19330, 209, 19307])).
% 87.93/88.15 tff(19332,plain,
% 87.93/88.15 (m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19331, 19324])).
% 87.93/88.15 tff(19333,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node16(c_e_h_3, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node16(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19334,plain,
% 87.93/88.15 (((~node16(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node16(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19335,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node16(c_e_h_3, c_e, s0))))),
% 87.93/88.15 inference(monotonicity,[status(thm)],[19334])).
% 87.93/88.15 tff(19336,plain,
% 87.93/88.15 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node16(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(transitivity,[status(thm)],[19335, 19333])).
% 87.93/88.15 tff(19337,plain,
% 87.93/88.15 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19338,plain,
% 87.93/88.15 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node16(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19337, 19336])).
% 87.93/88.15 tff(19339,plain,
% 87.93/88.15 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19338, 263, 19308])).
% 87.93/88.15 tff(19340,plain,
% 87.93/88.15 ($false),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19339, 19332, 19324])).
% 87.93/88.15 tff(19341,plain,((~node16(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.15 tff(19342,plain,
% 87.93/88.15 (~node16(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19341, 19306])).
% 87.93/88.15 tff(19343,plain,
% 87.93/88.15 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19344,plain,
% 87.93/88.15 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19345,plain,
% 87.93/88.15 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19344, 19343])).
% 87.93/88.15 tff(19346,plain,
% 87.93/88.15 (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19345, 365, 7653])).
% 87.93/88.15 tff(19347,plain,
% 87.93/88.15 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | (~node17(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19330, 209, 19346])).
% 87.93/88.15 tff(19348,plain,
% 87.93/88.15 (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19347, 19306])).
% 87.93/88.15 tff(19349,assumption,(node14(c_e_h_3, c_e, s0, s1)), introduced(assumption)).
% 87.93/88.15 tff(19350,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19351,plain,
% 87.93/88.15 (((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1))) <=> ((~node14(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19352,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(monotonicity,[status(thm)],[19351])).
% 87.93/88.15 tff(19353,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(transitivity,[status(thm)],[19352, 19350])).
% 87.93/88.15 tff(19354,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19355,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19354, 19353])).
% 87.93/88.15 tff(19356,plain,
% 87.93/88.15 ($false),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19355, 283, 19349, 19348, 19283])).
% 87.93/88.15 tff(19357,plain,((~node14(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.15 tff(19358,plain,
% 87.93/88.15 (~node14(c_e_h_3, c_e, s0, s1)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19357, 19283])).
% 87.93/88.15 tff(19359,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node14(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node14(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19360,plain,
% 87.93/88.15 ((node16(c_e_h_3, c_e, s0) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1))) <=> (node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node14(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19361,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s0) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node14(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0)))),
% 87.93/88.15 inference(monotonicity,[status(thm)],[19360])).
% 87.93/88.15 tff(19362,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s0) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node14(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(transitivity,[status(thm)],[19361, 19359])).
% 87.93/88.15 tff(19363,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s0) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19364,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node14(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19363, 19362])).
% 87.93/88.15 tff(19365,plain,
% 87.93/88.15 (node15(c_e_h_3, c_e, s0, s1) | node14(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19364, 189, 19301])).
% 87.93/88.15 tff(19366,plain,
% 87.93/88.15 (node15(c_e_h_3, c_e, s0, s1)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19365, 19358, 19342])).
% 87.93/88.15 tff(19367,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19368,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19369,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19368, 19367])).
% 87.93/88.15 tff(19370,plain,
% 87.93/88.15 ($false),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19369, 173, 19366, 19287, 19283])).
% 87.93/88.15 tff(19371,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.15 tff(19372,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19373,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19374,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19373, 19372])).
% 87.93/88.15 tff(19375,plain,
% 87.93/88.15 ($false),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19374, 173, 19371, 19269, 19282])).
% 87.93/88.15 tff(19376,plain,((~node15(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.15 tff(19377,plain,
% 87.93/88.15 (~node15(c_e_h_3, c_e, s1, s2)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19376, 19269])).
% 87.93/88.15 tff(19378,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_e, s1, s2))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19379,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_e, s1, s2))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19380,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_e, s1, s2)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19379, 19378])).
% 87.93/88.15 tff(19381,plain,
% 87.93/88.15 (node19(c_e_h_3, c_e, s1, s2)),
% 87.93/88.15 inference(unit_resolution,[status(thm)],[19380, 141, 344])).
% 87.93/88.15 tff(19382,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19383,plain,
% 87.93/88.15 ((node16(c_e_h_3, c_e, s1) | node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2))) <=> (node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1))),
% 87.93/88.15 inference(rewrite,[status(thm)],[])).
% 87.93/88.15 tff(19384,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s1) | node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1)))),
% 87.93/88.15 inference(monotonicity,[status(thm)],[19383])).
% 87.93/88.15 tff(19385,plain,
% 87.93/88.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s1) | node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1))),
% 87.93/88.15 inference(transitivity,[status(thm)],[19384, 19382])).
% 87.93/88.15 tff(19386,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s1) | node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))),
% 87.93/88.15 inference(quant_inst,[status(thm)],[])).
% 87.93/88.15 tff(19387,plain,
% 87.93/88.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1)),
% 87.93/88.15 inference(modus_ponens,[status(thm)],[19386, 19385])).
% 87.93/88.16 tff(19388,plain,
% 87.93/88.16 (node15(c_e_h_3, c_e, s1, s2) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19387, 189, 19381])).
% 87.93/88.16 tff(19389,plain,
% 87.93/88.16 (node14(c_e_h_3, c_e, s1, s2)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19388, 19377, 19281])).
% 87.93/88.16 tff(19390,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19391,plain,
% 87.93/88.16 (((~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19392,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2))))),
% 87.93/88.16 inference(monotonicity,[status(thm)],[19391])).
% 87.93/88.16 tff(19393,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 87.93/88.16 inference(transitivity,[status(thm)],[19392, 19390])).
% 87.93/88.16 tff(19394,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19395,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node14(c_e_h_3, c_e, s1, s2))),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19394, 19393])).
% 87.93/88.16 tff(19396,plain,
% 87.93/88.16 ($false),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19395, 283, 19269, 19389, 19270])).
% 87.93/88.16 tff(19397,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.16 tff(19398,plain,
% 87.93/88.16 (m_c_h_element_v_in1(c_e_h_3, c_e, s1)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19397, 19269])).
% 87.93/88.16 tff(19399,assumption,(node18(c_e_h_3, c_e, s1, s2)), introduced(assumption)).
% 87.93/88.16 tff(19400,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s1)), introduced(assumption)).
% 87.93/88.16 tff(19401,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19402,plain,
% 87.93/88.16 (((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19403,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))))),
% 87.93/88.16 inference(monotonicity,[status(thm)],[19402])).
% 87.93/88.16 tff(19404,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))),
% 87.93/88.16 inference(transitivity,[status(thm)],[19403, 19401])).
% 87.93/88.16 tff(19405,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19406,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~node18(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19405, 19404])).
% 87.93/88.16 tff(19407,plain,
% 87.93/88.16 ($false),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19406, 124, 19400, 19269, 19399])).
% 87.93/88.16 tff(19408,plain,((~node18(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.16 tff(19409,plain,
% 87.93/88.16 ((~node18(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19408, 19371])).
% 87.93/88.16 tff(19410,plain,
% 87.93/88.16 (~node18(c_e_h_3, c_e, s1, s2)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19409, 19269])).
% 87.93/88.16 tff(19411,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s1) | (~node19(c_e_h_3, c_e, s1, s2)) | node18(c_e_h_3, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s1) | (~node19(c_e_h_3, c_e, s1, s2)) | node18(c_e_h_3, c_e, s1, s2))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19412,plain,
% 87.93/88.16 ((node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2))) <=> (node17(c_e_h_3, c_e, s1) | (~node19(c_e_h_3, c_e, s1, s2)) | node18(c_e_h_3, c_e, s1, s2))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19413,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s1) | (~node19(c_e_h_3, c_e, s1, s2)) | node18(c_e_h_3, c_e, s1, s2)))),
% 87.93/88.16 inference(monotonicity,[status(thm)],[19412])).
% 87.93/88.16 tff(19414,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s1) | (~node19(c_e_h_3, c_e, s1, s2)) | node18(c_e_h_3, c_e, s1, s2))),
% 87.93/88.16 inference(transitivity,[status(thm)],[19413, 19411])).
% 87.93/88.16 tff(19415,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19416,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s1) | (~node19(c_e_h_3, c_e, s1, s2)) | node18(c_e_h_3, c_e, s1, s2)),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19415, 19414])).
% 87.93/88.16 tff(19417,plain,
% 87.93/88.16 (node17(c_e_h_3, c_e, s1) | node18(c_e_h_3, c_e, s1, s2)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19416, 156, 19381])).
% 87.93/88.16 tff(19418,plain,
% 87.93/88.16 (node17(c_e_h_3, c_e, s1)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19417, 19410])).
% 87.93/88.16 tff(19419,plain,
% 87.93/88.16 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19420,plain,
% 87.93/88.16 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1))) <=> ((~node17(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19421,plain,
% 87.93/88.16 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1))))),
% 87.93/88.16 inference(monotonicity,[status(thm)],[19420])).
% 87.93/88.16 tff(19422,plain,
% 87.93/88.16 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)))),
% 87.93/88.16 inference(transitivity,[status(thm)],[19421, 19419])).
% 87.93/88.16 tff(19423,plain,
% 87.93/88.16 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~node17(c_e_h_3, c_e, s1)))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19424,plain,
% 87.93/88.16 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s1)) | m_c_h_element_v_in2(c_e_h_3, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1))),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19423, 19422])).
% 87.93/88.16 tff(19425,plain,
% 87.93/88.16 ((~node17(c_e_h_3, c_e, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1))),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19424, 209, 19276])).
% 87.93/88.16 tff(19426,plain,
% 87.93/88.16 ($false),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19425, 19418, 19398])).
% 87.93/88.16 tff(19427,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.16 tff(19428,assumption,(node15(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 87.93/88.16 tff(19429,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 87.93/88.16 tff(19430,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19431,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19432,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19431, 19430])).
% 87.93/88.16 tff(19433,plain,
% 87.93/88.16 ($false),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19432, 173, 19248, 19429, 19428])).
% 87.93/88.16 tff(19434,plain,((~node15(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.16 tff(19435,plain,
% 87.93/88.16 ((~node15(c_e_h_3, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19434, 19427])).
% 87.93/88.16 tff(19436,plain,
% 87.93/88.16 (~node15(c_e_h_3, c_e, s2, s3)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19435, 19248])).
% 87.93/88.16 tff(19437,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19438,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19439,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3)),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19438, 19437])).
% 87.93/88.16 tff(19440,plain,
% 87.93/88.16 (node19(c_e_h_3, c_e, s2, s3)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19439, 141, 582])).
% 87.93/88.16 tff(19441,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19442,plain,
% 87.93/88.16 ((node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))) <=> (node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19443,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3))))),
% 87.93/88.16 inference(monotonicity,[status(thm)],[19442])).
% 87.93/88.16 tff(19444,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(transitivity,[status(thm)],[19443, 19441])).
% 87.93/88.16 tff(19445,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19446,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3))),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19445, 19444])).
% 87.93/88.16 tff(19447,plain,
% 87.93/88.16 (node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19446, 189, 19440])).
% 87.93/88.16 tff(19448,plain,
% 87.93/88.16 ($false),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19447, 19436, 19268, 19258])).
% 87.93/88.16 tff(19449,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.16 tff(19450,plain,
% 87.93/88.16 (m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19449, 19248])).
% 87.93/88.16 tff(19451,plain,
% 87.93/88.16 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19452,plain,
% 87.93/88.16 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2))) <=> ((~node17(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19453,plain,
% 87.93/88.16 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2))))),
% 87.93/88.16 inference(monotonicity,[status(thm)],[19452])).
% 87.93/88.16 tff(19454,plain,
% 87.93/88.16 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)))),
% 87.93/88.16 inference(transitivity,[status(thm)],[19453, 19451])).
% 87.93/88.16 tff(19455,plain,
% 87.93/88.16 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19456,plain,
% 87.93/88.16 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19455, 19454])).
% 87.93/88.16 tff(19457,plain,
% 87.93/88.16 ((~node17(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2))),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19456, 209, 19253])).
% 87.93/88.16 tff(19458,plain,
% 87.93/88.16 (~node17(c_e_h_3, c_e, s2)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19457, 19450])).
% 87.93/88.16 tff(19459,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19460,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(quant_inst,[status(thm)],[])).
% 87.93/88.16 tff(19461,plain,
% 87.93/88.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))),
% 87.93/88.16 inference(modus_ponens,[status(thm)],[19460, 19459])).
% 87.93/88.16 tff(19462,plain,
% 87.93/88.16 (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19461, 156, 19440])).
% 87.93/88.16 tff(19463,plain,
% 87.93/88.16 (node18(c_e_h_3, c_e, s2, s3)),
% 87.93/88.16 inference(unit_resolution,[status(thm)],[19462, 19458])).
% 87.93/88.16 tff(19464,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node18(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node18(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19465,plain,
% 87.93/88.16 (((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node18(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(rewrite,[status(thm)],[])).
% 87.93/88.16 tff(19466,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node18(c_e_h_3, c_e, s2, s3))))),
% 87.93/88.16 inference(monotonicity,[status(thm)],[19465])).
% 87.93/88.16 tff(19467,plain,
% 87.93/88.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node18(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.16 inference(transitivity,[status(thm)],[19466, 19464])).
% 87.93/88.17 tff(19468,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19469,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node18(c_e_h_3, c_e, s2, s3))),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19468, 19467])).
% 87.93/88.17 tff(19470,plain,
% 87.93/88.17 ($false),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19469, 124, 19248, 19427, 19463])).
% 87.93/88.17 tff(19471,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.17 tff(19472,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s4)), introduced(assumption)).
% 87.93/88.17 tff(19473,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s3)), introduced(assumption)).
% 87.93/88.17 tff(19474,assumption,(node15(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 87.93/88.17 tff(19475,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19476,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19477,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19476, 19475])).
% 87.93/88.17 tff(19478,plain,
% 87.93/88.17 ($false),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19477, 173, 19473, 19472, 19474])).
% 87.93/88.17 tff(19479,plain,((~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.17 tff(19480,plain,
% 87.93/88.17 (~node15(c_e_h_3, c_e, s3, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19479, 19473, 19472])).
% 87.93/88.17 tff(19481,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s3)), introduced(assumption)).
% 87.93/88.17 tff(19482,assumption,(~node15(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 87.93/88.17 tff(19483,plain,
% 87.93/88.17 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19484,plain,
% 87.93/88.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19485,plain,
% 87.93/88.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19484, 19483])).
% 87.93/88.17 tff(19486,plain,
% 87.93/88.17 (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19485, 365, 7723])).
% 87.93/88.17 tff(19487,plain,
% 87.93/88.17 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19488,plain,
% 87.93/88.17 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19489,plain,
% 87.93/88.17 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19488, 19487])).
% 87.93/88.17 tff(19490,plain,
% 87.93/88.17 ((~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19489, 228, 19486])).
% 87.93/88.17 tff(19491,plain,
% 87.93/88.17 (~node16(c_e_h_3, c_e, s3)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19490, 19481])).
% 87.93/88.17 tff(19492,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19493,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19494,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19493, 19492])).
% 87.93/88.17 tff(19495,plain,
% 87.93/88.17 (node19(c_e_h_3, c_e, s3, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19494, 141, 679])).
% 87.93/88.17 tff(19496,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s3) | node15(c_e_h_3, c_e, s3, s4) | node14(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s3) | node15(c_e_h_3, c_e, s3, s4) | node14(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19497,plain,
% 87.93/88.17 ((node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4))) <=> (node16(c_e_h_3, c_e, s3) | node15(c_e_h_3, c_e, s3, s4) | node14(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19498,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s3) | node15(c_e_h_3, c_e, s3, s4) | node14(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4))))),
% 87.93/88.17 inference(monotonicity,[status(thm)],[19497])).
% 87.93/88.17 tff(19499,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s3) | node15(c_e_h_3, c_e, s3, s4) | node14(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(transitivity,[status(thm)],[19498, 19496])).
% 87.93/88.17 tff(19500,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19501,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s3) | node15(c_e_h_3, c_e, s3, s4) | node14(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4))),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19500, 19499])).
% 87.93/88.17 tff(19502,plain,
% 87.93/88.17 (node16(c_e_h_3, c_e, s3) | node15(c_e_h_3, c_e, s3, s4) | node14(c_e_h_3, c_e, s3, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19501, 189, 19495])).
% 87.93/88.17 tff(19503,plain,
% 87.93/88.17 (node14(c_e_h_3, c_e, s3, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19502, 19491, 19482])).
% 87.93/88.17 tff(19504,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~node14(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~node14(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19505,plain,
% 87.93/88.17 (((~node14(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~node14(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19506,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~node14(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))))),
% 87.93/88.17 inference(monotonicity,[status(thm)],[19505])).
% 87.93/88.17 tff(19507,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~node14(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))),
% 87.93/88.17 inference(transitivity,[status(thm)],[19506, 19504])).
% 87.93/88.17 tff(19508,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19509,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~node14(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19508, 19507])).
% 87.93/88.17 tff(19510,plain,
% 87.93/88.17 ($false),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19509, 283, 19472, 19503, 19481])).
% 87.93/88.17 tff(19511,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | node15(c_e_h_3, c_e, s3, s4)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.17 tff(19512,plain,
% 87.93/88.17 (m_c_h_element_v_in1(c_e_h_3, c_e, s3)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19511, 19480, 19472])).
% 87.93/88.17 tff(19513,plain,
% 87.93/88.17 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19514,plain,
% 87.93/88.17 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3))) <=> ((~node17(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19515,plain,
% 87.93/88.17 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3))))),
% 87.93/88.17 inference(monotonicity,[status(thm)],[19514])).
% 87.93/88.17 tff(19516,plain,
% 87.93/88.17 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)))),
% 87.93/88.17 inference(transitivity,[status(thm)],[19515, 19513])).
% 87.93/88.17 tff(19517,plain,
% 87.93/88.17 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3)))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19518,plain,
% 87.93/88.17 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3))),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19517, 19516])).
% 87.93/88.17 tff(19519,plain,
% 87.93/88.17 ((~node17(c_e_h_3, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3))),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19518, 209, 19486])).
% 87.93/88.17 tff(19520,plain,
% 87.93/88.17 (~node17(c_e_h_3, c_e, s3)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19519, 19512])).
% 87.93/88.17 tff(19521,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19522,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19523,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4))),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19522, 19521])).
% 87.93/88.17 tff(19524,plain,
% 87.93/88.17 (node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19523, 156, 19495])).
% 87.93/88.17 tff(19525,plain,
% 87.93/88.17 (node18(c_e_h_3, c_e, s3, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19524, 19520])).
% 87.93/88.17 tff(19526,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node18(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node18(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19527,plain,
% 87.93/88.17 (((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~node18(c_e_h_3, c_e, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node18(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19528,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~node18(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node18(c_e_h_3, c_e, s3, s4))))),
% 87.93/88.17 inference(monotonicity,[status(thm)],[19527])).
% 87.93/88.17 tff(19529,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~node18(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node18(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(transitivity,[status(thm)],[19528, 19526])).
% 87.93/88.17 tff(19530,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~node18(c_e_h_3, c_e, s3, s4)))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19531,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node18(c_e_h_3, c_e, s3, s4))),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19530, 19529])).
% 87.93/88.17 tff(19532,plain,
% 87.93/88.17 ($false),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19531, 124, 19473, 19472, 19525])).
% 87.93/88.17 tff(19533,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.17 tff(19534,plain,
% 87.93/88.17 (~m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19533, 19471])).
% 87.93/88.17 tff(19535,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s4)), introduced(assumption)).
% 87.93/88.17 tff(19536,plain,
% 87.93/88.17 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19537,plain,
% 87.93/88.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19538,plain,
% 87.93/88.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19537, 19536])).
% 87.93/88.17 tff(19539,plain,
% 87.93/88.17 ($false),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19538, 365, 10741, 19535])).
% 87.93/88.17 tff(19540,plain,(~m_c_h_element_v_in2(c_e_h_3, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.17 tff(19541,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s4)), introduced(assumption)).
% 87.93/88.17 tff(19542,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s5)), introduced(assumption)).
% 87.93/88.17 tff(19543,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s4)), introduced(assumption)).
% 87.93/88.17 tff(19544,assumption,(node15(c_e_h_3, c_e, s4, s5)), introduced(assumption)).
% 87.93/88.17 tff(19545,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19546,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19547,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19546, 19545])).
% 87.93/88.17 tff(19548,plain,
% 87.93/88.17 ($false),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19547, 173, 19543, 19542, 19544])).
% 87.93/88.17 tff(19549,plain,((~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.17 tff(19550,plain,
% 87.93/88.17 (~node15(c_e_h_3, c_e, s4, s5)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19549, 19543, 19542])).
% 87.93/88.17 tff(19551,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s4)), introduced(assumption)).
% 87.93/88.17 tff(19552,assumption,(~node15(c_e_h_3, c_e, s4, s5)), introduced(assumption)).
% 87.93/88.17 tff(19553,plain,
% 87.93/88.17 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s4))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19554,plain,
% 87.93/88.17 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s4))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19555,plain,
% 87.93/88.17 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s4)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19554, 19553])).
% 87.93/88.17 tff(19556,plain,
% 87.93/88.17 ((~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19555, 228, 19541])).
% 87.93/88.17 tff(19557,plain,
% 87.93/88.17 (~node16(c_e_h_3, c_e, s4)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19556, 19551])).
% 87.93/88.17 tff(19558,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_e, s4, s5))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19559,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_e, s4, s5))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19560,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_e, s4, s5)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19559, 19558])).
% 87.93/88.17 tff(19561,plain,
% 87.93/88.17 (node19(c_e_h_3, c_e, s4, s5)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19560, 141, 1432])).
% 87.93/88.17 tff(19562,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s4, s5)) | node16(c_e_h_3, c_e, s4) | node15(c_e_h_3, c_e, s4, s5) | node14(c_e_h_3, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s4, s5)) | node16(c_e_h_3, c_e, s4) | node15(c_e_h_3, c_e, s4, s5) | node14(c_e_h_3, c_e, s4, s5))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19563,plain,
% 87.93/88.17 ((node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5))) <=> ((~node19(c_e_h_3, c_e, s4, s5)) | node16(c_e_h_3, c_e, s4) | node15(c_e_h_3, c_e, s4, s5) | node14(c_e_h_3, c_e, s4, s5))),
% 87.93/88.17 inference(rewrite,[status(thm)],[])).
% 87.93/88.17 tff(19564,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s4, s5)) | node16(c_e_h_3, c_e, s4) | node15(c_e_h_3, c_e, s4, s5) | node14(c_e_h_3, c_e, s4, s5)))),
% 87.93/88.17 inference(monotonicity,[status(thm)],[19563])).
% 87.93/88.17 tff(19565,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s4, s5)) | node16(c_e_h_3, c_e, s4) | node15(c_e_h_3, c_e, s4, s5) | node14(c_e_h_3, c_e, s4, s5))),
% 87.93/88.17 inference(transitivity,[status(thm)],[19564, 19562])).
% 87.93/88.17 tff(19566,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))),
% 87.93/88.17 inference(quant_inst,[status(thm)],[])).
% 87.93/88.17 tff(19567,plain,
% 87.93/88.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s4, s5)) | node16(c_e_h_3, c_e, s4) | node15(c_e_h_3, c_e, s4, s5) | node14(c_e_h_3, c_e, s4, s5)),
% 87.93/88.17 inference(modus_ponens,[status(thm)],[19566, 19565])).
% 87.93/88.17 tff(19568,plain,
% 87.93/88.17 (node16(c_e_h_3, c_e, s4) | node15(c_e_h_3, c_e, s4, s5) | node14(c_e_h_3, c_e, s4, s5)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19567, 189, 19561])).
% 87.93/88.17 tff(19569,plain,
% 87.93/88.17 (node14(c_e_h_3, c_e, s4, s5)),
% 87.93/88.17 inference(unit_resolution,[status(thm)],[19568, 19557, 19552])).
% 87.93/88.17 tff(19570,plain,
% 87.93/88.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19571,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19572,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19571, 19570])).
% 87.93/88.18 tff(19573,plain,
% 87.93/88.18 ($false),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19572, 283, 19542, 19569, 19551])).
% 87.93/88.18 tff(19574,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | node15(c_e_h_3, c_e, s4, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.18 tff(19575,plain,
% 87.93/88.18 (m_c_h_element_v_in1(c_e_h_3, c_e, s4)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19574, 19550, 19542, 19541])).
% 87.93/88.18 tff(19576,plain,
% 87.93/88.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4)))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19577,plain,
% 87.93/88.18 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4)))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19578,plain,
% 87.93/88.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4))))),
% 87.93/88.18 inference(monotonicity,[status(thm)],[19577])).
% 87.93/88.18 tff(19579,plain,
% 87.93/88.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4)))),
% 87.93/88.18 inference(transitivity,[status(thm)],[19578, 19576])).
% 87.93/88.18 tff(19580,plain,
% 87.93/88.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19581,plain,
% 87.93/88.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4))),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19580, 19579])).
% 87.93/88.18 tff(19582,plain,
% 87.93/88.18 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4))),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19581, 209, 19541])).
% 87.93/88.18 tff(19583,plain,
% 87.93/88.18 (~node17(c_e_h_3, c_e, s4)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19582, 19575])).
% 87.93/88.18 tff(19584,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node18(c_e_h_3, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node18(c_e_h_3, c_e, s4, s5))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19585,plain,
% 87.93/88.18 ((node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5))) <=> (node17(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node18(c_e_h_3, c_e, s4, s5))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19586,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node18(c_e_h_3, c_e, s4, s5)))),
% 87.93/88.18 inference(monotonicity,[status(thm)],[19585])).
% 87.93/88.18 tff(19587,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node18(c_e_h_3, c_e, s4, s5))),
% 87.93/88.18 inference(transitivity,[status(thm)],[19586, 19584])).
% 87.93/88.18 tff(19588,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19589,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s4) | (~node19(c_e_h_3, c_e, s4, s5)) | node18(c_e_h_3, c_e, s4, s5)),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19588, 19587])).
% 87.93/88.18 tff(19590,plain,
% 87.93/88.18 (node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19589, 156, 19561])).
% 87.93/88.18 tff(19591,plain,
% 87.93/88.18 (node18(c_e_h_3, c_e, s4, s5)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19590, 19583])).
% 87.93/88.18 tff(19592,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19593,plain,
% 87.93/88.18 (((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19594,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))))),
% 87.93/88.18 inference(monotonicity,[status(thm)],[19593])).
% 87.93/88.18 tff(19595,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 87.93/88.18 inference(transitivity,[status(thm)],[19594, 19592])).
% 87.93/88.18 tff(19596,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19597,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19596, 19595])).
% 87.93/88.18 tff(19598,plain,
% 87.93/88.18 ($false),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19597, 124, 19543, 19542, 19591])).
% 87.93/88.18 tff(19599,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.18 tff(19600,plain,
% 87.93/88.18 (m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19599, 19540])).
% 87.93/88.18 tff(19601,plain,
% 87.93/88.18 (~m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19600, 19534])).
% 87.93/88.18 tff(19602,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s5)), introduced(assumption)).
% 87.93/88.18 tff(19603,plain,
% 87.93/88.18 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19604,plain,
% 87.93/88.18 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19605,plain,
% 87.93/88.18 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19604, 19603])).
% 87.93/88.18 tff(19606,plain,
% 87.93/88.18 ($false),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19605, 365, 13312, 19602])).
% 87.93/88.18 tff(19607,plain,(m_and_h_gate_v_out(c_e_h_3, c_i, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.18 tff(19608,plain,
% 87.93/88.18 (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19607, 13310])).
% 87.93/88.18 tff(19609,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s6)), introduced(assumption)).
% 87.93/88.18 tff(19610,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s5)), introduced(assumption)).
% 87.93/88.18 tff(19611,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s5)), introduced(assumption)).
% 87.93/88.18 tff(19612,assumption,(node15(c_e_h_3, c_e, s5, s6)), introduced(assumption)).
% 87.93/88.18 tff(19613,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19614,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19615,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19614, 19613])).
% 87.93/88.18 tff(19616,plain,
% 87.93/88.18 ($false),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19615, 173, 19611, 19612, 19609])).
% 87.93/88.18 tff(19617,plain,((~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 87.93/88.18 tff(19618,plain,
% 87.93/88.18 (~node15(c_e_h_3, c_e, s5, s6)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19617, 19611, 19609])).
% 87.93/88.18 tff(19619,assumption,(~node15(c_e_h_3, c_e, s5, s6)), introduced(assumption)).
% 87.93/88.18 tff(19620,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s5)), introduced(assumption)).
% 87.93/88.18 tff(19621,plain,
% 87.93/88.18 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s5))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19622,plain,
% 87.93/88.18 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s5))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19623,plain,
% 87.93/88.18 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s5)),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19622, 19621])).
% 87.93/88.18 tff(19624,plain,
% 87.93/88.18 ((~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19623, 228, 19610])).
% 87.93/88.18 tff(19625,plain,
% 87.93/88.18 (~node16(c_e_h_3, c_e, s5)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19624, 19620])).
% 87.93/88.18 tff(19626,assumption,(node14(c_e_h_3, c_e, s5, s6)), introduced(assumption)).
% 87.93/88.18 tff(19627,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~node14(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19628,plain,
% 87.93/88.18 (((~node14(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19629,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~node14(c_e_h_3, c_e, s5, s6))))),
% 87.93/88.18 inference(monotonicity,[status(thm)],[19628])).
% 87.93/88.18 tff(19630,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 87.93/88.18 inference(transitivity,[status(thm)],[19629, 19627])).
% 87.93/88.18 tff(19631,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19632,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~node14(c_e_h_3, c_e, s5, s6))),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19631, 19630])).
% 87.93/88.18 tff(19633,plain,
% 87.93/88.18 ($false),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19632, 283, 19626, 19609, 19620])).
% 87.93/88.18 tff(19634,plain,((~node14(c_e_h_3, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 87.93/88.18 tff(19635,plain,
% 87.93/88.18 (~node14(c_e_h_3, c_e, s5, s6)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19634, 19620, 19609])).
% 87.93/88.18 tff(19636,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_e, s5, s6))),
% 87.93/88.18 inference(rewrite,[status(thm)],[])).
% 87.93/88.18 tff(19637,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_e, s5, s6))),
% 87.93/88.18 inference(quant_inst,[status(thm)],[])).
% 87.93/88.18 tff(19638,plain,
% 87.93/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_e, s5, s6)),
% 87.93/88.18 inference(modus_ponens,[status(thm)],[19637, 19636])).
% 87.93/88.18 tff(19639,plain,
% 87.93/88.18 (node19(c_e_h_3, c_e, s5, s6)),
% 87.93/88.18 inference(unit_resolution,[status(thm)],[19638, 141, 1499])).
% 87.93/88.18 tff(19640,plain,
% 87.93/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6))),
% 88.01/88.18 inference(rewrite,[status(thm)],[])).
% 88.01/88.18 tff(19641,plain,
% 88.01/88.18 ((node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6))) <=> (node16(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6))),
% 88.01/88.18 inference(rewrite,[status(thm)],[])).
% 88.01/88.18 tff(19642,plain,
% 88.01/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6)))),
% 88.01/88.18 inference(monotonicity,[status(thm)],[19641])).
% 88.01/88.18 tff(19643,plain,
% 88.01/88.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6))),
% 88.01/88.18 inference(transitivity,[status(thm)],[19642, 19640])).
% 88.01/88.18 tff(19644,plain,
% 88.01/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))),
% 88.01/88.18 inference(quant_inst,[status(thm)],[])).
% 88.01/88.18 tff(19645,plain,
% 88.01/88.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6)),
% 88.01/88.18 inference(modus_ponens,[status(thm)],[19644, 19643])).
% 88.01/88.18 tff(19646,plain,
% 88.01/88.18 (node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6)),
% 88.01/88.18 inference(unit_resolution,[status(thm)],[19645, 189, 19639])).
% 88.01/88.18 tff(19647,plain,
% 88.01/88.18 ($false),
% 88.01/88.18 inference(unit_resolution,[status(thm)],[19646, 19635, 19625, 19619])).
% 88.01/88.18 tff(19648,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s5) | node15(c_e_h_3, c_e, s5, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.18 tff(19649,plain,
% 88.01/88.18 (m_c_h_element_v_in1(c_e_h_3, c_e, s5)),
% 88.01/88.18 inference(unit_resolution,[status(thm)],[19648, 19618, 19609, 19610])).
% 88.01/88.18 tff(19650,plain,
% 88.01/88.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)))),
% 88.01/88.18 inference(rewrite,[status(thm)],[])).
% 88.01/88.18 tff(19651,plain,
% 88.01/88.18 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5))) <=> ((~node17(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)))),
% 88.01/88.18 inference(rewrite,[status(thm)],[])).
% 88.01/88.18 tff(19652,plain,
% 88.01/88.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5))))),
% 88.01/88.18 inference(monotonicity,[status(thm)],[19651])).
% 88.01/88.18 tff(19653,plain,
% 88.01/88.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)))),
% 88.01/88.18 inference(transitivity,[status(thm)],[19652, 19650])).
% 88.01/88.18 tff(19654,plain,
% 88.01/88.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5)))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19655,plain,
% 88.01/88.19 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5))),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19654, 19653])).
% 88.01/88.19 tff(19656,plain,
% 88.01/88.19 ((~node17(c_e_h_3, c_e, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5))),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19655, 209, 19610])).
% 88.01/88.19 tff(19657,plain,
% 88.01/88.19 (~node17(c_e_h_3, c_e, s5)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19656, 19649])).
% 88.01/88.19 tff(19658,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s5, s6)) | node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s5, s6)) | node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19659,plain,
% 88.01/88.19 ((node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6))) <=> ((~node19(c_e_h_3, c_e, s5, s6)) | node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19660,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s5, s6)) | node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6)))),
% 88.01/88.19 inference(monotonicity,[status(thm)],[19659])).
% 88.01/88.19 tff(19661,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s5, s6)) | node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6))),
% 88.01/88.19 inference(transitivity,[status(thm)],[19660, 19658])).
% 88.01/88.19 tff(19662,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19663,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s5, s6)) | node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6)),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19662, 19661])).
% 88.01/88.19 tff(19664,plain,
% 88.01/88.19 (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19663, 156, 19639])).
% 88.01/88.19 tff(19665,plain,
% 88.01/88.19 (node18(c_e_h_3, c_e, s5, s6)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19664, 19657])).
% 88.01/88.19 tff(19666,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6)))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19667,plain,
% 88.01/88.19 (((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~node18(c_e_h_3, c_e, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6)))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19668,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~node18(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6))))),
% 88.01/88.19 inference(monotonicity,[status(thm)],[19667])).
% 88.01/88.19 tff(19669,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~node18(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6)))),
% 88.01/88.19 inference(transitivity,[status(thm)],[19668, 19666])).
% 88.01/88.19 tff(19670,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~node18(c_e_h_3, c_e, s5, s6)))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19671,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6))),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19670, 19669])).
% 88.01/88.19 tff(19672,plain,
% 88.01/88.19 ($false),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19671, 124, 19611, 19665, 19609])).
% 88.01/88.19 tff(19673,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.19 tff(19674,plain,
% 88.01/88.19 (m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19673, 19608])).
% 88.01/88.19 tff(19675,plain,
% 88.01/88.19 (~m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19674, 19601])).
% 88.01/88.19 tff(19676,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s7)), introduced(assumption)).
% 88.01/88.19 tff(19677,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s6)), introduced(assumption)).
% 88.01/88.19 tff(19678,assumption,(node18(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 88.01/88.19 tff(19679,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19680,plain,
% 88.01/88.19 (((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7))) <=> ((~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19681,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(monotonicity,[status(thm)],[19680])).
% 88.01/88.19 tff(19682,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(transitivity,[status(thm)],[19681, 19679])).
% 88.01/88.19 tff(19683,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19684,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19683, 19682])).
% 88.01/88.19 tff(19685,plain,
% 88.01/88.19 ($false),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19684, 124, 19676, 19678, 19677])).
% 88.01/88.19 tff(19686,plain,((~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.19 tff(19687,plain,
% 88.01/88.19 (~node18(c_e_h_3, c_e, s6, s7)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19686, 19676, 19677])).
% 88.01/88.19 tff(19688,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_e, s6, s7))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19689,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_e, s6, s7))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19690,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_e, s6, s7)),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19689, 19688])).
% 88.01/88.19 tff(19691,plain,
% 88.01/88.19 (node19(c_e_h_3, c_e, s6, s7)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19690, 141, 1552])).
% 88.01/88.19 tff(19692,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s6, s7)) | node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s6, s7)) | node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19693,plain,
% 88.01/88.19 ((node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7))) <=> ((~node19(c_e_h_3, c_e, s6, s7)) | node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19694,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s6, s7)) | node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7)))),
% 88.01/88.19 inference(monotonicity,[status(thm)],[19693])).
% 88.01/88.19 tff(19695,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s6, s7)) | node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7))),
% 88.01/88.19 inference(transitivity,[status(thm)],[19694, 19692])).
% 88.01/88.19 tff(19696,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19697,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s6, s7)) | node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7)),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19696, 19695])).
% 88.01/88.19 tff(19698,plain,
% 88.01/88.19 (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19697, 156, 19691])).
% 88.01/88.19 tff(19699,plain,
% 88.01/88.19 (node17(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19698, 19687])).
% 88.01/88.19 tff(19700,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s6)), introduced(assumption)).
% 88.01/88.19 tff(19701,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19702,plain,
% 88.01/88.19 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19703,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6))))),
% 88.01/88.19 inference(monotonicity,[status(thm)],[19702])).
% 88.01/88.19 tff(19704,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(transitivity,[status(thm)],[19703, 19701])).
% 88.01/88.19 tff(19705,plain,
% 88.01/88.19 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19706,plain,
% 88.01/88.19 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19705, 19704])).
% 88.01/88.19 tff(19707,plain,
% 88.01/88.19 ((~node17(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19706, 209, 19700])).
% 88.01/88.19 tff(19708,plain,
% 88.01/88.19 (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19707, 19699])).
% 88.01/88.19 tff(19709,assumption,(node15(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 88.01/88.19 tff(19710,plain,
% 88.01/88.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19711,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19712,plain,
% 88.01/88.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19711, 19710])).
% 88.01/88.19 tff(19713,plain,
% 88.01/88.19 ($false),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19712, 173, 19676, 19709, 19677])).
% 88.01/88.19 tff(19714,plain,((~node15(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.19 tff(19715,plain,
% 88.01/88.19 (~node15(c_e_h_3, c_e, s6, s7)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19714, 19676, 19677])).
% 88.01/88.19 tff(19716,assumption,(node16(c_e_h_3, c_e, s6)), introduced(assumption)).
% 88.01/88.19 tff(19717,assumption,(node17(c_e_h_3, c_e, s6)), introduced(assumption)).
% 88.01/88.19 tff(19718,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s6)), introduced(assumption)).
% 88.01/88.19 tff(19719,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19720,plain,
% 88.01/88.19 (((~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19721,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6))))),
% 88.01/88.19 inference(monotonicity,[status(thm)],[19720])).
% 88.01/88.19 tff(19722,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(transitivity,[status(thm)],[19721, 19719])).
% 88.01/88.19 tff(19723,plain,
% 88.01/88.19 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19724,plain,
% 88.01/88.19 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19723, 19722])).
% 88.01/88.19 tff(19725,plain,
% 88.01/88.19 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19724, 263, 19716])).
% 88.01/88.19 tff(19726,plain,
% 88.01/88.19 (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19725, 19718])).
% 88.01/88.19 tff(19727,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19728,plain,
% 88.01/88.19 ((m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(rewrite,[status(thm)],[])).
% 88.01/88.19 tff(19729,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(monotonicity,[status(thm)],[19728])).
% 88.01/88.19 tff(19730,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 88.01/88.19 inference(transitivity,[status(thm)],[19729, 19727])).
% 88.01/88.19 tff(19731,plain,
% 88.01/88.19 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))),
% 88.01/88.19 inference(quant_inst,[status(thm)],[])).
% 88.01/88.19 tff(19732,plain,
% 88.01/88.19 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(modus_ponens,[status(thm)],[19731, 19730])).
% 88.01/88.19 tff(19733,plain,
% 88.01/88.19 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19732, 245, 19717])).
% 88.01/88.19 tff(19734,plain,
% 88.01/88.19 ($false),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19733, 19726, 19718])).
% 88.01/88.19 tff(19735,plain,((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.19 tff(19736,plain,
% 88.01/88.19 (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 88.01/88.19 inference(unit_resolution,[status(thm)],[19735, 19717, 19716])).
% 88.01/88.19 tff(19737,plain,
% 88.01/88.19 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19738,plain,
% 88.01/88.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19739,plain,
% 88.01/88.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19738, 19737])).
% 88.01/88.20 tff(19740,plain,
% 88.01/88.20 (m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19739, 228, 19716])).
% 88.01/88.20 tff(19741,plain,
% 88.01/88.20 (m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19740, 19736])).
% 88.01/88.20 tff(19742,plain,
% 88.01/88.20 (m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19706, 209, 19717])).
% 88.01/88.20 tff(19743,plain,
% 88.01/88.20 ($false),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19742, 19741, 19736])).
% 88.01/88.20 tff(19744,plain,((~node17(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.20 tff(19745,plain,
% 88.01/88.20 (~node16(c_e_h_3, c_e, s6)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19744, 19699])).
% 88.01/88.20 tff(19746,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19747,plain,
% 88.01/88.20 ((node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7))) <=> ((~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19748,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7)))),
% 88.01/88.20 inference(monotonicity,[status(thm)],[19747])).
% 88.01/88.20 tff(19749,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7))),
% 88.01/88.20 inference(transitivity,[status(thm)],[19748, 19746])).
% 88.01/88.20 tff(19750,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19751,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7)),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19750, 19749])).
% 88.01/88.20 tff(19752,plain,
% 88.01/88.20 (node15(c_e_h_3, c_e, s6, s7) | node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19751, 189, 19691])).
% 88.01/88.20 tff(19753,plain,
% 88.01/88.20 (node14(c_e_h_3, c_e, s6, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19752, 19745, 19715])).
% 88.01/88.20 tff(19754,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s6)), introduced(assumption)).
% 88.01/88.20 tff(19755,assumption,(node14(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 88.01/88.20 tff(19756,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19757,plain,
% 88.01/88.20 (((~node14(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19758,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7))))),
% 88.01/88.20 inference(monotonicity,[status(thm)],[19757])).
% 88.01/88.20 tff(19759,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 88.01/88.20 inference(transitivity,[status(thm)],[19758, 19756])).
% 88.01/88.20 tff(19760,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19761,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7))),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19760, 19759])).
% 88.01/88.20 tff(19762,plain,
% 88.01/88.20 ($false),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19761, 283, 19676, 19755, 19754])).
% 88.01/88.20 tff(19763,plain,((~node14(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.20 tff(19764,plain,
% 88.01/88.20 ($false),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19763, 19753, 19708, 19676])).
% 88.01/88.20 tff(19765,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | m_c_h_element_v_out(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.20 tff(19766,plain,
% 88.01/88.20 ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19765, 19675])).
% 88.01/88.20 tff(19767,plain,
% 88.01/88.20 (~m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19766, 19247])).
% 88.01/88.20 tff(19768,plain,
% 88.01/88.20 (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[17002, 16974, 16283])).
% 88.01/88.20 tff(19769,plain,
% 88.01/88.20 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19770,plain,
% 88.01/88.20 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19771,plain,
% 88.01/88.20 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19770, 19769])).
% 88.01/88.20 tff(19772,plain,
% 88.01/88.20 (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19771, 365, 19768])).
% 88.01/88.20 tff(19773,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s8)), introduced(assumption)).
% 88.01/88.20 tff(19774,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s7)), introduced(assumption)).
% 88.01/88.20 tff(19775,assumption,(node18(c_e_h_3, c_e, s7, s8)), introduced(assumption)).
% 88.01/88.20 tff(19776,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19777,plain,
% 88.01/88.20 (((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19778,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))))),
% 88.01/88.20 inference(monotonicity,[status(thm)],[19777])).
% 88.01/88.20 tff(19779,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))),
% 88.01/88.20 inference(transitivity,[status(thm)],[19778, 19776])).
% 88.01/88.20 tff(19780,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19781,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19780, 19779])).
% 88.01/88.20 tff(19782,plain,
% 88.01/88.20 ($false),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19781, 124, 19774, 19773, 19775])).
% 88.01/88.20 tff(19783,plain,((~node18(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.20 tff(19784,plain,
% 88.01/88.20 (~node18(c_e_h_3, c_e, s7, s8)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19783, 19774, 19773])).
% 88.01/88.20 tff(19785,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_e, s7, s8))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19786,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_e, s7, s8))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19787,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_e, s7, s8)),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19786, 19785])).
% 88.01/88.20 tff(19788,plain,
% 88.01/88.20 (node19(c_e_h_3, c_e, s7, s8)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19787, 141, 2152])).
% 88.01/88.20 tff(19789,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s7) | (~node19(c_e_h_3, c_e, s7, s8)) | node18(c_e_h_3, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s7) | (~node19(c_e_h_3, c_e, s7, s8)) | node18(c_e_h_3, c_e, s7, s8))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19790,plain,
% 88.01/88.20 ((node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8))) <=> (node17(c_e_h_3, c_e, s7) | (~node19(c_e_h_3, c_e, s7, s8)) | node18(c_e_h_3, c_e, s7, s8))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19791,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s7) | (~node19(c_e_h_3, c_e, s7, s8)) | node18(c_e_h_3, c_e, s7, s8)))),
% 88.01/88.20 inference(monotonicity,[status(thm)],[19790])).
% 88.01/88.20 tff(19792,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s7) | (~node19(c_e_h_3, c_e, s7, s8)) | node18(c_e_h_3, c_e, s7, s8))),
% 88.01/88.20 inference(transitivity,[status(thm)],[19791, 19789])).
% 88.01/88.20 tff(19793,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19794,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s7) | (~node19(c_e_h_3, c_e, s7, s8)) | node18(c_e_h_3, c_e, s7, s8)),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19793, 19792])).
% 88.01/88.20 tff(19795,plain,
% 88.01/88.20 (node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19794, 156, 19788])).
% 88.01/88.20 tff(19796,plain,
% 88.01/88.20 (node17(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19795, 19784])).
% 88.01/88.20 tff(19797,assumption,(node15(c_e_h_3, c_e, s7, s8)), introduced(assumption)).
% 88.01/88.20 tff(19798,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19799,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19800,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19799, 19798])).
% 88.01/88.20 tff(19801,plain,
% 88.01/88.20 ($false),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19800, 173, 19774, 19773, 19797])).
% 88.01/88.20 tff(19802,plain,((~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.20 tff(19803,plain,
% 88.01/88.20 (~node15(c_e_h_3, c_e, s7, s8)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19802, 19774, 19773])).
% 88.01/88.20 tff(19804,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s7)), introduced(assumption)).
% 88.01/88.20 tff(19805,assumption,(~node15(c_e_h_3, c_e, s7, s8)), introduced(assumption)).
% 88.01/88.20 tff(19806,assumption,(node17(c_e_h_3, c_e, s7)), introduced(assumption)).
% 88.01/88.20 tff(19807,plain,
% 88.01/88.20 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19808,plain,
% 88.01/88.20 ((m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19809,plain,
% 88.01/88.20 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7)))),
% 88.01/88.20 inference(monotonicity,[status(thm)],[19808])).
% 88.01/88.20 tff(19810,plain,
% 88.01/88.20 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7))),
% 88.01/88.20 inference(transitivity,[status(thm)],[19809, 19807])).
% 88.01/88.20 tff(19811,plain,
% 88.01/88.20 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19812,plain,
% 88.01/88.20 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19811, 19810])).
% 88.01/88.20 tff(19813,plain,
% 88.01/88.20 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19812, 245, 19806])).
% 88.01/88.20 tff(19814,plain,
% 88.01/88.20 (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19813, 19804])).
% 88.01/88.20 tff(19815,plain,
% 88.01/88.20 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19816,plain,
% 88.01/88.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19817,plain,
% 88.01/88.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19816, 19815])).
% 88.01/88.20 tff(19818,plain,
% 88.01/88.20 (~node16(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19817, 228, 19804, 19814])).
% 88.01/88.20 tff(19819,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s7) | node15(c_e_h_3, c_e, s7, s8) | node14(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s7) | node15(c_e_h_3, c_e, s7, s8) | node14(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19820,plain,
% 88.01/88.20 ((node16(c_e_h_3, c_e, s7) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8))) <=> (node16(c_e_h_3, c_e, s7) | node15(c_e_h_3, c_e, s7, s8) | node14(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19821,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s7) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s7) | node15(c_e_h_3, c_e, s7, s8) | node14(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8))))),
% 88.01/88.20 inference(monotonicity,[status(thm)],[19820])).
% 88.01/88.20 tff(19822,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s7) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s7) | node15(c_e_h_3, c_e, s7, s8) | node14(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))),
% 88.01/88.20 inference(transitivity,[status(thm)],[19821, 19819])).
% 88.01/88.20 tff(19823,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s7) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19824,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s7) | node15(c_e_h_3, c_e, s7, s8) | node14(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8))),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19823, 19822])).
% 88.01/88.20 tff(19825,plain,
% 88.01/88.20 (node16(c_e_h_3, c_e, s7) | node15(c_e_h_3, c_e, s7, s8) | node14(c_e_h_3, c_e, s7, s8)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19824, 189, 19788])).
% 88.01/88.20 tff(19826,plain,
% 88.01/88.20 (node14(c_e_h_3, c_e, s7, s8)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19825, 19818, 19805])).
% 88.01/88.20 tff(19827,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~node14(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~node14(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19828,plain,
% 88.01/88.20 (((~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~node14(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))),
% 88.01/88.20 inference(rewrite,[status(thm)],[])).
% 88.01/88.20 tff(19829,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~node14(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))))),
% 88.01/88.20 inference(monotonicity,[status(thm)],[19828])).
% 88.01/88.20 tff(19830,plain,
% 88.01/88.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~node14(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))),
% 88.01/88.20 inference(transitivity,[status(thm)],[19829, 19827])).
% 88.01/88.20 tff(19831,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))),
% 88.01/88.20 inference(quant_inst,[status(thm)],[])).
% 88.01/88.20 tff(19832,plain,
% 88.01/88.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~node14(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 88.01/88.20 inference(modus_ponens,[status(thm)],[19831, 19830])).
% 88.01/88.20 tff(19833,plain,
% 88.01/88.20 ($false),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19832, 283, 19773, 19826, 19804])).
% 88.01/88.20 tff(19834,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | node15(c_e_h_3, c_e, s7, s8) | (~node17(c_e_h_3, c_e, s7))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.20 tff(19835,plain,
% 88.01/88.20 (m_c_h_element_v_in1(c_e_h_3, c_e, s7)),
% 88.01/88.20 inference(unit_resolution,[status(thm)],[19834, 19803, 19773, 19796])).
% 88.01/88.20 tff(19836,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s7)), introduced(assumption)).
% 88.01/88.20 tff(19837,plain,
% 88.01/88.20 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19838,plain,
% 88.01/88.21 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19839,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7))))),
% 88.01/88.21 inference(monotonicity,[status(thm)],[19838])).
% 88.01/88.21 tff(19840,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)))),
% 88.01/88.21 inference(transitivity,[status(thm)],[19839, 19837])).
% 88.01/88.21 tff(19841,plain,
% 88.01/88.21 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19842,plain,
% 88.01/88.21 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7))),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19841, 19840])).
% 88.01/88.21 tff(19843,plain,
% 88.01/88.21 ((~node17(c_e_h_3, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7))),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19842, 209, 19836])).
% 88.01/88.21 tff(19844,plain,
% 88.01/88.21 ($false),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19843, 19835, 19796])).
% 88.01/88.21 tff(19845,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.21 tff(19846,plain,
% 88.01/88.21 (~m_c_h_element_v_out(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19845, 19772, 19767])).
% 88.01/88.21 tff(19847,plain,
% 88.01/88.21 (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[18252, 18228, 19768])).
% 88.01/88.21 tff(19848,plain,
% 88.01/88.21 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19849,plain,
% 88.01/88.21 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19850,plain,
% 88.01/88.21 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19849, 19848])).
% 88.01/88.21 tff(19851,plain,
% 88.01/88.21 (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19850, 365, 19847])).
% 88.01/88.21 tff(19852,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s9)), introduced(assumption)).
% 88.01/88.21 tff(19853,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s8)), introduced(assumption)).
% 88.01/88.21 tff(19854,assumption,(node18(c_e_h_3, c_e, s8, s9)), introduced(assumption)).
% 88.01/88.21 tff(19855,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19856,plain,
% 88.01/88.21 (((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19857,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))))),
% 88.01/88.21 inference(monotonicity,[status(thm)],[19856])).
% 88.01/88.21 tff(19858,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))),
% 88.01/88.21 inference(transitivity,[status(thm)],[19857, 19855])).
% 88.01/88.21 tff(19859,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19860,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19859, 19858])).
% 88.01/88.21 tff(19861,plain,
% 88.01/88.21 ($false),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19860, 124, 19853, 19852, 19854])).
% 88.01/88.21 tff(19862,plain,((~node18(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.21 tff(19863,plain,
% 88.01/88.21 (~node18(c_e_h_3, c_e, s8, s9)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19862, 19853, 19852])).
% 88.01/88.21 tff(19864,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s8)), introduced(assumption)).
% 88.01/88.21 tff(19865,assumption,(node15(c_e_h_3, c_e, s8, s9)), introduced(assumption)).
% 88.01/88.21 tff(19866,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19867,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19868,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19867, 19866])).
% 88.01/88.21 tff(19869,plain,
% 88.01/88.21 ($false),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19868, 173, 19853, 19852, 19865])).
% 88.01/88.21 tff(19870,plain,((~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.21 tff(19871,plain,
% 88.01/88.21 (~node15(c_e_h_3, c_e, s8, s9)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19870, 19853, 19852])).
% 88.01/88.21 tff(19872,assumption,(node17(c_e_h_3, c_e, s8)), introduced(assumption)).
% 88.01/88.21 tff(19873,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19874,plain,
% 88.01/88.21 ((m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8))) <=> ((~node17(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19875,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8))))),
% 88.01/88.21 inference(monotonicity,[status(thm)],[19874])).
% 88.01/88.21 tff(19876,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 88.01/88.21 inference(transitivity,[status(thm)],[19875, 19873])).
% 88.01/88.21 tff(19877,plain,
% 88.01/88.21 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8)))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19878,plain,
% 88.01/88.21 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19877, 19876])).
% 88.01/88.21 tff(19879,plain,
% 88.01/88.21 (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19878, 245, 19872])).
% 88.01/88.21 tff(19880,plain,
% 88.01/88.21 (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19879, 19864])).
% 88.01/88.21 tff(19881,assumption,(~node15(c_e_h_3, c_e, s8, s9)), introduced(assumption)).
% 88.01/88.21 tff(19882,assumption,(node14(c_e_h_3, c_e, s8, s9)), introduced(assumption)).
% 88.01/88.21 tff(19883,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19884,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19885,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19884, 19883])).
% 88.01/88.21 tff(19886,plain,
% 88.01/88.21 ($false),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19885, 283, 19852, 19882, 19864])).
% 88.01/88.21 tff(19887,plain,((~node14(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.21 tff(19888,plain,
% 88.01/88.21 (~node14(c_e_h_3, c_e, s8, s9)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19887, 19864, 19852])).
% 88.01/88.21 tff(19889,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_e, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_e, s8, s9))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19890,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_e, s8, s9))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19891,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_e, s8, s9)),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19890, 19889])).
% 88.01/88.21 tff(19892,plain,
% 88.01/88.21 (node19(c_e_h_3, c_e, s8, s9)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19891, 141, 2636])).
% 88.01/88.21 tff(19893,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s8, s9)) | node15(c_e_h_3, c_e, s8, s9) | node14(c_e_h_3, c_e, s8, s9) | node16(c_e_h_3, c_e, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s8, s9)) | node15(c_e_h_3, c_e, s8, s9) | node14(c_e_h_3, c_e, s8, s9) | node16(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19894,plain,
% 88.01/88.21 ((node16(c_e_h_3, c_e, s8) | node14(c_e_h_3, c_e, s8, s9) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9))) <=> ((~node19(c_e_h_3, c_e, s8, s9)) | node15(c_e_h_3, c_e, s8, s9) | node14(c_e_h_3, c_e, s8, s9) | node16(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19895,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s8) | node14(c_e_h_3, c_e, s8, s9) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s8, s9)) | node15(c_e_h_3, c_e, s8, s9) | node14(c_e_h_3, c_e, s8, s9) | node16(c_e_h_3, c_e, s8)))),
% 88.01/88.21 inference(monotonicity,[status(thm)],[19894])).
% 88.01/88.21 tff(19896,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s8) | node14(c_e_h_3, c_e, s8, s9) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s8, s9)) | node15(c_e_h_3, c_e, s8, s9) | node14(c_e_h_3, c_e, s8, s9) | node16(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(transitivity,[status(thm)],[19895, 19893])).
% 88.01/88.21 tff(19897,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s8) | node14(c_e_h_3, c_e, s8, s9) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19898,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s8, s9)) | node15(c_e_h_3, c_e, s8, s9) | node14(c_e_h_3, c_e, s8, s9) | node16(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19897, 19896])).
% 88.01/88.21 tff(19899,plain,
% 88.01/88.21 (node15(c_e_h_3, c_e, s8, s9) | node14(c_e_h_3, c_e, s8, s9) | node16(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19898, 189, 19892])).
% 88.01/88.21 tff(19900,plain,
% 88.01/88.21 (node16(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19899, 19888, 19881])).
% 88.01/88.21 tff(19901,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19902,plain,
% 88.01/88.21 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19903,plain,
% 88.01/88.21 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19902, 19901])).
% 88.01/88.21 tff(19904,plain,
% 88.01/88.21 ($false),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19903, 228, 19900, 19864, 19880])).
% 88.01/88.21 tff(19905,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s8) | node15(c_e_h_3, c_e, s8, s9) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.21 tff(19906,plain,
% 88.01/88.21 (~node17(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19905, 19871, 19864, 19852])).
% 88.01/88.21 tff(19907,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_e, s8, s9) | node17(c_e_h_3, c_e, s8) | (~node19(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s8, s9) | node17(c_e_h_3, c_e, s8) | (~node19(c_e_h_3, c_e, s8, s9)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19908,plain,
% 88.01/88.21 ((node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9))) <=> (node18(c_e_h_3, c_e, s8, s9) | node17(c_e_h_3, c_e, s8) | (~node19(c_e_h_3, c_e, s8, s9)))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19909,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_e, s8, s9) | node17(c_e_h_3, c_e, s8) | (~node19(c_e_h_3, c_e, s8, s9))))),
% 88.01/88.21 inference(monotonicity,[status(thm)],[19908])).
% 88.01/88.21 tff(19910,plain,
% 88.01/88.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s8, s9) | node17(c_e_h_3, c_e, s8) | (~node19(c_e_h_3, c_e, s8, s9)))),
% 88.01/88.21 inference(transitivity,[status(thm)],[19909, 19907])).
% 88.01/88.21 tff(19911,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))),
% 88.01/88.21 inference(quant_inst,[status(thm)],[])).
% 88.01/88.21 tff(19912,plain,
% 88.01/88.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s8, s9) | node17(c_e_h_3, c_e, s8) | (~node19(c_e_h_3, c_e, s8, s9))),
% 88.01/88.21 inference(modus_ponens,[status(thm)],[19911, 19910])).
% 88.01/88.21 tff(19913,plain,
% 88.01/88.21 (node18(c_e_h_3, c_e, s8, s9) | node17(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19912, 156, 19892])).
% 88.01/88.21 tff(19914,plain,
% 88.01/88.21 ($false),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19913, 19906, 19863])).
% 88.01/88.21 tff(19915,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s8) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.21 tff(19916,plain,
% 88.01/88.21 (m_c_h_element_v_in1(c_e_h_3, c_e, s8)),
% 88.01/88.21 inference(unit_resolution,[status(thm)],[19915, 19853, 19852])).
% 88.01/88.21 tff(19917,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s8)), introduced(assumption)).
% 88.01/88.21 tff(19918,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19919,plain,
% 88.01/88.21 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8))) <=> ((~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(rewrite,[status(thm)],[])).
% 88.01/88.21 tff(19920,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 88.01/88.21 inference(monotonicity,[status(thm)],[19919])).
% 88.01/88.21 tff(19921,plain,
% 88.01/88.21 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 88.01/88.21 inference(transitivity,[status(thm)],[19920, 19918])).
% 88.01/88.22 tff(19922,plain,
% 88.01/88.22 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19923,plain,
% 88.01/88.22 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19922, 19921])).
% 88.01/88.22 tff(19924,plain,
% 88.01/88.22 ((~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8))),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19923, 209, 19917])).
% 88.01/88.22 tff(19925,plain,
% 88.01/88.22 (~node17(c_e_h_3, c_e, s8)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19924, 19916])).
% 88.01/88.22 tff(19926,plain,
% 88.01/88.22 ($false),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19913, 19925, 19863])).
% 88.01/88.22 tff(19927,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.22 tff(19928,plain,
% 88.01/88.22 (~m_c_h_element_v_out(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19927, 19851, 19846])).
% 88.01/88.22 tff(19929,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s9)), introduced(assumption)).
% 88.01/88.22 tff(19930,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s9)), introduced(assumption)).
% 88.01/88.22 tff(19931,assumption,(node15(c_e_h_3, c_e, s9, s10)), introduced(assumption)).
% 88.01/88.22 tff(19932,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19933,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19934,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19933, 19932])).
% 88.01/88.22 tff(19935,plain,
% 88.01/88.22 ($false),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19934, 173, 19930, 19243, 19931])).
% 88.01/88.22 tff(19936,plain,((~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.22 tff(19937,plain,
% 88.01/88.22 (~node15(c_e_h_3, c_e, s9, s10)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19936, 19930, 19243])).
% 88.01/88.22 tff(19938,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s9)), introduced(assumption)).
% 88.01/88.22 tff(19939,assumption,(~node15(c_e_h_3, c_e, s9, s10)), introduced(assumption)).
% 88.01/88.22 tff(19940,plain,
% 88.01/88.22 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19941,plain,
% 88.01/88.22 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19942,plain,
% 88.01/88.22 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19941, 19940])).
% 88.01/88.22 tff(19943,plain,
% 88.01/88.22 ((~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19942, 228, 19929])).
% 88.01/88.22 tff(19944,plain,
% 88.01/88.22 (~node16(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19943, 19938])).
% 88.01/88.22 tff(19945,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_3, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_3, c_e, s9, s10))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19946,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_3, c_e, s9, s10))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19947,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_3, c_e, s9, s10)),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19946, 19945])).
% 88.01/88.22 tff(19948,plain,
% 88.01/88.22 (node19(c_e_h_3, c_e, s9, s10)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19947, 141, 3175])).
% 88.01/88.22 tff(19949,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s9) | node15(c_e_h_3, c_e, s9, s10) | node14(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s9) | node15(c_e_h_3, c_e, s9, s10) | node14(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19950,plain,
% 88.01/88.22 ((node16(c_e_h_3, c_e, s9) | node14(c_e_h_3, c_e, s9, s10) | node15(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10))) <=> (node16(c_e_h_3, c_e, s9) | node15(c_e_h_3, c_e, s9, s10) | node14(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19951,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s9) | node14(c_e_h_3, c_e, s9, s10) | node15(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s9) | node15(c_e_h_3, c_e, s9, s10) | node14(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10))))),
% 88.01/88.22 inference(monotonicity,[status(thm)],[19950])).
% 88.01/88.22 tff(19952,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s9) | node14(c_e_h_3, c_e, s9, s10) | node15(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s9) | node15(c_e_h_3, c_e, s9, s10) | node14(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(transitivity,[status(thm)],[19951, 19949])).
% 88.01/88.22 tff(19953,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s9) | node14(c_e_h_3, c_e, s9, s10) | node15(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19954,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s9) | node15(c_e_h_3, c_e, s9, s10) | node14(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10))),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19953, 19952])).
% 88.01/88.22 tff(19955,plain,
% 88.01/88.22 (node16(c_e_h_3, c_e, s9) | node15(c_e_h_3, c_e, s9, s10) | node14(c_e_h_3, c_e, s9, s10)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19954, 189, 19948])).
% 88.01/88.22 tff(19956,plain,
% 88.01/88.22 (node14(c_e_h_3, c_e, s9, s10)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19955, 19944, 19939])).
% 88.01/88.22 tff(19957,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node14(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node14(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19958,plain,
% 88.01/88.22 (((~node14(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node14(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19959,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node14(c_e_h_3, c_e, s9, s10))))),
% 88.01/88.22 inference(monotonicity,[status(thm)],[19958])).
% 88.01/88.22 tff(19960,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node14(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(transitivity,[status(thm)],[19959, 19957])).
% 88.01/88.22 tff(19961,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19962,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node14(c_e_h_3, c_e, s9, s10))),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19961, 19960])).
% 88.01/88.22 tff(19963,plain,
% 88.01/88.22 ($false),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19962, 283, 19243, 19956, 19938])).
% 88.01/88.22 tff(19964,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | node15(c_e_h_3, c_e, s9, s10) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.22 tff(19965,plain,
% 88.01/88.22 (m_c_h_element_v_in1(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19964, 19937, 19243, 19929])).
% 88.01/88.22 tff(19966,plain,
% 88.01/88.22 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19967,plain,
% 88.01/88.22 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9) | (~node17(c_e_h_3, c_e, s9))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19968,plain,
% 88.01/88.22 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9) | (~node17(c_e_h_3, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)))),
% 88.01/88.22 inference(monotonicity,[status(thm)],[19967])).
% 88.01/88.22 tff(19969,plain,
% 88.01/88.22 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9) | (~node17(c_e_h_3, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 88.01/88.22 inference(transitivity,[status(thm)],[19968, 19966])).
% 88.01/88.22 tff(19970,plain,
% 88.01/88.22 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9) | (~node17(c_e_h_3, c_e, s9)))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19971,plain,
% 88.01/88.22 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19970, 19969])).
% 88.01/88.22 tff(19972,plain,
% 88.01/88.22 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9))),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19971, 209, 19929])).
% 88.01/88.22 tff(19973,plain,
% 88.01/88.22 (~node17(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19972, 19965])).
% 88.01/88.22 tff(19974,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19975,plain,
% 88.01/88.22 ((node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10))) <=> (node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19976,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(monotonicity,[status(thm)],[19975])).
% 88.01/88.22 tff(19977,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10))),
% 88.01/88.22 inference(transitivity,[status(thm)],[19976, 19974])).
% 88.01/88.22 tff(19978,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19979,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10)),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19978, 19977])).
% 88.01/88.22 tff(19980,plain,
% 88.01/88.22 (node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19979, 156, 19948])).
% 88.01/88.22 tff(19981,plain,
% 88.01/88.22 (node18(c_e_h_3, c_e, s9, s10)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19980, 19973])).
% 88.01/88.22 tff(19982,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19983,plain,
% 88.01/88.22 (((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~node18(c_e_h_3, c_e, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19984,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~node18(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10))))),
% 88.01/88.22 inference(monotonicity,[status(thm)],[19983])).
% 88.01/88.22 tff(19985,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~node18(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(transitivity,[status(thm)],[19984, 19982])).
% 88.01/88.22 tff(19986,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~node18(c_e_h_3, c_e, s9, s10)))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19987,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10))),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19986, 19985])).
% 88.01/88.22 tff(19988,plain,
% 88.01/88.22 ($false),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19987, 124, 19930, 19243, 19981])).
% 88.01/88.22 tff(19989,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.22 tff(19990,plain,
% 88.01/88.22 ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19989, 19928])).
% 88.01/88.22 tff(19991,plain,
% 88.01/88.22 (m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19990, 19243])).
% 88.01/88.22 tff(19992,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s9)), introduced(assumption)).
% 88.01/88.22 tff(19993,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s9)), introduced(assumption)).
% 88.01/88.22 tff(19994,plain,
% 88.01/88.22 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(19995,plain,
% 88.01/88.22 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(19996,plain,
% 88.01/88.22 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[19995, 19994])).
% 88.01/88.22 tff(19997,plain,
% 88.01/88.22 ($false),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19996, 365, 19993, 19992])).
% 88.01/88.22 tff(19998,plain,((~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.22 tff(19999,plain,
% 88.01/88.22 (m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[19998, 19991])).
% 88.01/88.22 tff(20000,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s8)), introduced(assumption)).
% 88.01/88.22 tff(20001,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s9)), introduced(assumption)).
% 88.01/88.22 tff(20002,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(20003,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 88.01/88.22 inference(quant_inst,[status(thm)],[])).
% 88.01/88.22 tff(20004,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 88.01/88.22 inference(modus_ponens,[status(thm)],[20003, 20002])).
% 88.01/88.22 tff(20005,plain,
% 88.01/88.22 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[20004, 107])).
% 88.01/88.22 tff(20006,plain,
% 88.01/88.22 (~node22(c_e_h_3, c_i, s8, s9)),
% 88.01/88.22 inference(unit_resolution,[status(thm)],[20005, 20001, 20000])).
% 88.01/88.22 tff(20007,assumption,(~node20(c_e_h_3, c_i, s8)), introduced(assumption)).
% 88.01/88.22 tff(20008,plain,
% 88.01/88.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9)))),
% 88.01/88.22 inference(rewrite,[status(thm)],[])).
% 88.01/88.22 tff(20009,plain,
% 88.01/88.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9)))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20010,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9))),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20009, 20008])).
% 88.01/88.23 tff(20011,plain,
% 88.01/88.23 (node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9))),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20010, 51])).
% 88.01/88.23 tff(20012,plain,
% 88.01/88.23 (~node21(c_e_h_3, c_i, s8, s9)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20011, 20001, 20007])).
% 88.01/88.23 tff(20013,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20014,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20015,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20014, 20013])).
% 88.01/88.23 tff(20016,plain,
% 88.01/88.23 ($false),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20015, 81, 2636, 20012, 20006])).
% 88.01/88.23 tff(20017,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | node20(c_e_h_3, c_i, s8) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.23 tff(20018,plain,
% 88.01/88.23 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | node20(c_e_h_3, c_i, s8)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20017, 19847])).
% 88.01/88.23 tff(20019,plain,
% 88.01/88.23 (node20(c_e_h_3, c_i, s8)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20018, 19999])).
% 88.01/88.23 tff(20020,plain,
% 88.01/88.23 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s8))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20021,plain,
% 88.01/88.23 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s8))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20022,plain,
% 88.01/88.23 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s8)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20021, 20020])).
% 88.01/88.23 tff(20023,plain,
% 88.01/88.23 (m_and_h_gate_v_in1(c_e_h_3, c_i, s8)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20022, 37, 20019])).
% 88.01/88.23 tff(20024,plain,
% 88.01/88.23 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20025,plain,
% 88.01/88.23 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20026,plain,
% 88.01/88.23 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20025, 20024])).
% 88.01/88.23 tff(20027,plain,
% 88.01/88.23 (m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20026, 23, 20023])).
% 88.01/88.23 tff(20028,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_q, s5)), introduced(assumption)).
% 88.01/88.23 tff(20029,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s4)), introduced(assumption)).
% 88.01/88.23 tff(20030,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s5)), introduced(assumption)).
% 88.01/88.23 tff(20031,assumption,(node18(c_e_h_2, c_f, s4, s5)), introduced(assumption)).
% 88.01/88.23 tff(20032,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node18(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node18(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20033,plain,
% 88.01/88.23 (((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node18(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20034,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node18(c_e_h_2, c_f, s4, s5))))),
% 88.01/88.23 inference(monotonicity,[status(thm)],[20033])).
% 88.01/88.23 tff(20035,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node18(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(transitivity,[status(thm)],[20034, 20032])).
% 88.01/88.23 tff(20036,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20037,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node18(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20036, 20035])).
% 88.01/88.23 tff(20038,plain,
% 88.01/88.23 ($false),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20037, 124, 20029, 20030, 20031])).
% 88.01/88.23 tff(20039,plain,((~node18(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.23 tff(20040,plain,
% 88.01/88.23 (~node18(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20039, 20030, 20029])).
% 88.01/88.23 tff(20041,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20042,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20043,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20042, 20041])).
% 88.01/88.23 tff(20044,plain,
% 88.01/88.23 (node19(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20043, 141, 1432])).
% 88.01/88.23 tff(20045,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s4) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s4) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20046,plain,
% 88.01/88.23 ((node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5))) <=> (node17(c_e_h_2, c_f, s4) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20047,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s4) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(monotonicity,[status(thm)],[20046])).
% 88.01/88.23 tff(20048,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s4) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(transitivity,[status(thm)],[20047, 20045])).
% 88.01/88.23 tff(20049,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20050,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s4) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20049, 20048])).
% 88.01/88.23 tff(20051,plain,
% 88.01/88.23 (node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20050, 156, 20044])).
% 88.01/88.23 tff(20052,plain,
% 88.01/88.23 (node17(c_e_h_2, c_f, s4)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20051, 20040])).
% 88.01/88.23 tff(20053,plain,
% 88.01/88.23 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20054,plain,
% 88.01/88.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20055,plain,
% 88.01/88.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20054, 20053])).
% 88.01/88.23 tff(20056,plain,
% 88.01/88.23 (~m_c_h_element_v_in2(c_e_h_2, c_f, s4)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20055, 2218, 1777])).
% 88.01/88.23 tff(20057,plain,
% 88.01/88.23 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | (~node17(c_e_h_2, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | (~node17(c_e_h_2, c_f, s4)))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20058,plain,
% 88.01/88.23 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~node17(c_e_h_2, c_f, s4))) <=> (m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | (~node17(c_e_h_2, c_f, s4)))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20059,plain,
% 88.01/88.23 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~node17(c_e_h_2, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | (~node17(c_e_h_2, c_f, s4))))),
% 88.01/88.23 inference(monotonicity,[status(thm)],[20058])).
% 88.01/88.23 tff(20060,plain,
% 88.01/88.23 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~node17(c_e_h_2, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | (~node17(c_e_h_2, c_f, s4)))),
% 88.01/88.23 inference(transitivity,[status(thm)],[20059, 20057])).
% 88.01/88.23 tff(20061,plain,
% 88.01/88.23 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~node17(c_e_h_2, c_f, s4)))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20062,plain,
% 88.01/88.23 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | (~node17(c_e_h_2, c_f, s4))),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20061, 20060])).
% 88.01/88.23 tff(20063,plain,
% 88.01/88.23 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | (~node17(c_e_h_2, c_f, s4))),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20062, 209, 20056])).
% 88.01/88.23 tff(20064,plain,
% 88.01/88.23 (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20063, 20052])).
% 88.01/88.23 tff(20065,plain,
% 88.01/88.23 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s4))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20066,plain,
% 88.01/88.23 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s4))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20067,plain,
% 88.01/88.23 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s4)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20066, 20065])).
% 88.01/88.23 tff(20068,plain,
% 88.01/88.23 ((~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20067, 228, 20056])).
% 88.01/88.23 tff(20069,plain,
% 88.01/88.23 (~node16(c_e_h_2, c_f, s4)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20068, 20064])).
% 88.01/88.23 tff(20070,assumption,(node15(c_e_h_2, c_f, s4, s5)), introduced(assumption)).
% 88.01/88.23 tff(20071,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20072,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20073,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20072, 20071])).
% 88.01/88.23 tff(20074,plain,
% 88.01/88.23 ($false),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20073, 173, 20029, 20030, 20070])).
% 88.01/88.23 tff(20075,plain,((~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.23 tff(20076,plain,
% 88.01/88.23 (~node15(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20075, 20030, 20029])).
% 88.01/88.23 tff(20077,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s4, s5)) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | node14(c_e_h_2, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s4, s5)) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | node14(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20078,plain,
% 88.01/88.23 ((node16(c_e_h_2, c_f, s4) | node14(c_e_h_2, c_f, s4, s5) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5))) <=> ((~node19(c_e_h_2, c_f, s4, s5)) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | node14(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20079,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s4) | node14(c_e_h_2, c_f, s4, s5) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s4, s5)) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | node14(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(monotonicity,[status(thm)],[20078])).
% 88.01/88.23 tff(20080,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s4) | node14(c_e_h_2, c_f, s4, s5) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s4, s5)) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | node14(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(transitivity,[status(thm)],[20079, 20077])).
% 88.01/88.23 tff(20081,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s4) | node14(c_e_h_2, c_f, s4, s5) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20082,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s4, s5)) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | node14(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20081, 20080])).
% 88.01/88.23 tff(20083,plain,
% 88.01/88.23 (node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | node14(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20082, 189, 20044])).
% 88.01/88.23 tff(20084,plain,
% 88.01/88.23 (node14(c_e_h_2, c_f, s4, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20083, 20076, 20069])).
% 88.01/88.23 tff(20085,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node14(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node14(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20086,plain,
% 88.01/88.23 (((~node14(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node14(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20087,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node14(c_e_h_2, c_f, s4, s5))))),
% 88.01/88.23 inference(monotonicity,[status(thm)],[20086])).
% 88.01/88.23 tff(20088,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node14(c_e_h_2, c_f, s4, s5)))),
% 88.01/88.23 inference(transitivity,[status(thm)],[20087, 20085])).
% 88.01/88.23 tff(20089,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20090,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node14(c_e_h_2, c_f, s4, s5))),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20089, 20088])).
% 88.01/88.23 tff(20091,plain,
% 88.01/88.23 ($false),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20090, 283, 20030, 20064, 20084])).
% 88.01/88.23 tff(20092,plain,((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.23 tff(20093,plain,
% 88.01/88.23 (~m_c_h_element_v_out(c_e_h_2, c_f, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20092, 18052])).
% 88.01/88.23 tff(20094,plain,
% 88.01/88.23 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20095,plain,
% 88.01/88.23 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20096,plain,
% 88.01/88.23 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s5)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20095, 20094])).
% 88.01/88.23 tff(20097,plain,
% 88.01/88.23 ($false),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20096, 1666, 20093, 20028])).
% 88.01/88.23 tff(20098,plain,(~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.23 tff(20099,plain,
% 88.01/88.23 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s5))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20100,plain,
% 88.01/88.23 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s5))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20101,plain,
% 88.01/88.23 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s5)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20100, 20099])).
% 88.01/88.23 tff(20102,plain,
% 88.01/88.23 (~node20(c_e_h_2, c_q, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20101, 37, 20098])).
% 88.01/88.23 tff(20103,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s5)), introduced(assumption)).
% 88.01/88.23 tff(20104,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s6)), introduced(assumption)).
% 88.01/88.23 tff(20105,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20106,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 88.01/88.23 inference(quant_inst,[status(thm)],[])).
% 88.01/88.23 tff(20107,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 88.01/88.23 inference(modus_ponens,[status(thm)],[20106, 20105])).
% 88.01/88.23 tff(20108,plain,
% 88.01/88.23 ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20107, 107])).
% 88.01/88.23 tff(20109,plain,
% 88.01/88.23 (~node22(c_e_h_2, c_q, s5, s6)),
% 88.01/88.23 inference(unit_resolution,[status(thm)],[20108, 20104, 20103])).
% 88.01/88.23 tff(20110,plain,
% 88.01/88.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6))),
% 88.01/88.23 inference(rewrite,[status(thm)],[])).
% 88.01/88.23 tff(20111,plain,
% 88.01/88.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20112,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6)),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20111, 20110])).
% 88.01/88.24 tff(20113,plain,
% 88.01/88.24 (node21(c_e_h_2, c_q, s5, s6)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20112, 81, 1499, 20109])).
% 88.01/88.24 tff(20114,assumption,(~node20(c_e_h_2, c_q, s5)), introduced(assumption)).
% 88.01/88.24 tff(20115,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | node20(c_e_h_2, c_q, s5) | (~node21(c_e_h_2, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | node20(c_e_h_2, c_q, s5) | (~node21(c_e_h_2, c_q, s5, s6)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20116,plain,
% 88.01/88.24 ((node20(c_e_h_2, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node21(c_e_h_2, c_q, s5, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | node20(c_e_h_2, c_q, s5) | (~node21(c_e_h_2, c_q, s5, s6)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20117,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node21(c_e_h_2, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | node20(c_e_h_2, c_q, s5) | (~node21(c_e_h_2, c_q, s5, s6))))),
% 88.01/88.24 inference(monotonicity,[status(thm)],[20116])).
% 88.01/88.24 tff(20118,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node21(c_e_h_2, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | node20(c_e_h_2, c_q, s5) | (~node21(c_e_h_2, c_q, s5, s6)))),
% 88.01/88.24 inference(transitivity,[status(thm)],[20117, 20115])).
% 88.01/88.24 tff(20119,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node21(c_e_h_2, c_q, s5, s6)))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20120,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | node20(c_e_h_2, c_q, s5) | (~node21(c_e_h_2, c_q, s5, s6))),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20119, 20118])).
% 88.01/88.24 tff(20121,plain,
% 88.01/88.24 ($false),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20120, 51, 20104, 20114, 20113])).
% 88.01/88.24 tff(20122,plain,((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | node20(c_e_h_2, c_q, s5) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.24 tff(20123,plain,
% 88.01/88.24 ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20122, 20102])).
% 88.01/88.24 tff(20124,plain,
% 88.01/88.24 (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20123, 18081])).
% 88.01/88.24 tff(20125,plain,
% 88.01/88.24 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s6))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20126,plain,
% 88.01/88.24 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s6))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20127,plain,
% 88.01/88.24 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s6)),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20126, 20125])).
% 88.01/88.24 tff(20128,plain,
% 88.01/88.24 (node3(c_e_h_2, c_e_h_3, s6)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20127, 7448, 814])).
% 88.01/88.24 tff(20129,plain,
% 88.01/88.24 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s6)) | (~node3(c_e_h_2, c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s6)) | (~node3(c_e_h_2, c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20130,plain,
% 88.01/88.24 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s6)) | (~node3(c_e_h_2, c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20131,plain,
% 88.01/88.24 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s6)) | (~node3(c_e_h_2, c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6)),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20130, 20129])).
% 88.01/88.24 tff(20132,plain,
% 88.01/88.24 ((~m_cell_v_ack(c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20131, 836, 20128])).
% 88.01/88.24 tff(20133,plain,
% 88.01/88.24 (~m_cell_v_ack(c_e_h_3, s6)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20132, 20124])).
% 88.01/88.24 tff(20134,plain,
% 88.01/88.24 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)) | m_cell_v_ack(c_e_h_3, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)) | m_cell_v_ack(c_e_h_3, s6))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20135,plain,
% 88.01/88.24 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)) | m_cell_v_ack(c_e_h_3, s6))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20136,plain,
% 88.01/88.24 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)) | m_cell_v_ack(c_e_h_3, s6)),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20135, 20134])).
% 88.01/88.24 tff(20137,plain,
% 88.01/88.24 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20136, 848, 20133])).
% 88.01/88.24 tff(20138,plain,
% 88.01/88.24 (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[18127, 18100, 18099, 18098])).
% 88.01/88.24 tff(20139,plain,
% 88.01/88.24 (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[18131, 309, 20138])).
% 88.01/88.24 tff(20140,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s8)), introduced(assumption)).
% 88.01/88.24 tff(20141,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)), introduced(assumption)).
% 88.01/88.24 tff(20142,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)), introduced(assumption)).
% 88.01/88.24 tff(20143,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s7)), introduced(assumption)).
% 88.01/88.24 tff(20144,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20145,plain,
% 88.01/88.24 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7))) <=> (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20146,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7))))),
% 88.01/88.24 inference(monotonicity,[status(thm)],[20145])).
% 88.01/88.24 tff(20147,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)))),
% 88.01/88.24 inference(transitivity,[status(thm)],[20146, 20144])).
% 88.01/88.24 tff(20148,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20149,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7))),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20148, 20147])).
% 88.01/88.24 tff(20150,plain,
% 88.01/88.24 (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7))),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20149, 862])).
% 88.01/88.24 tff(20151,plain,
% 88.01/88.24 (~node5(c_e_h_3, c_j, s6, s7)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20150, 20143, 20142, 20141])).
% 88.01/88.24 tff(20152,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s6)), introduced(assumption)).
% 88.01/88.24 tff(20153,assumption,(node6(c_e_h_3, c_j, s6, s7)), introduced(assumption)).
% 88.01/88.24 tff(20154,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s6, s7)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20155,plain,
% 88.01/88.24 (((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s6, s7)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20156,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s6, s7))))),
% 88.01/88.24 inference(monotonicity,[status(thm)],[20155])).
% 88.01/88.24 tff(20157,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s6, s7)))),
% 88.01/88.24 inference(transitivity,[status(thm)],[20156, 20154])).
% 88.01/88.24 tff(20158,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20159,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s6, s7))),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20158, 20157])).
% 88.01/88.24 tff(20160,plain,
% 88.01/88.24 ($false),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20159, 899, 20152, 20143, 20153])).
% 88.01/88.24 tff(20161,plain,((~node6(c_e_h_3, c_j, s6, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.24 tff(20162,plain,
% 88.01/88.24 (~node6(c_e_h_3, c_j, s6, s7)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20161, 20143, 20152])).
% 88.01/88.24 tff(20163,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_3, c_j, s6, s7) | node6(c_e_h_3, c_j, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_3, c_j, s6, s7) | node6(c_e_h_3, c_j, s6, s7))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20164,plain,
% 88.01/88.24 ((node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7) | (~trans(s6, s7))) <=> ((~trans(s6, s7)) | node5(c_e_h_3, c_j, s6, s7) | node6(c_e_h_3, c_j, s6, s7))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20165,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_3, c_j, s6, s7) | node6(c_e_h_3, c_j, s6, s7)))),
% 88.01/88.24 inference(monotonicity,[status(thm)],[20164])).
% 88.01/88.24 tff(20166,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_3, c_j, s6, s7) | node6(c_e_h_3, c_j, s6, s7))),
% 88.01/88.24 inference(transitivity,[status(thm)],[20165, 20163])).
% 88.01/88.24 tff(20167,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7) | (~trans(s6, s7)))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20168,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_3, c_j, s6, s7) | node6(c_e_h_3, c_j, s6, s7)),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20167, 20166])).
% 88.01/88.24 tff(20169,plain,
% 88.01/88.24 (node5(c_e_h_3, c_j, s6, s7) | node6(c_e_h_3, c_j, s6, s7)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20168, 881, 1552])).
% 88.01/88.24 tff(20170,plain,
% 88.01/88.24 ($false),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20169, 20162, 20151])).
% 88.01/88.24 tff(20171,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.24 tff(20172,plain,
% 88.01/88.24 (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20171, 20138, 20142, 20141])).
% 88.01/88.24 tff(20173,plain,
% 88.01/88.24 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20174,plain,
% 88.01/88.24 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20175,plain,
% 88.01/88.24 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7)),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20174, 20173])).
% 88.01/88.24 tff(20176,plain,
% 88.01/88.24 (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20175, 309, 20172])).
% 88.01/88.24 tff(20177,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s7)), introduced(assumption)).
% 88.01/88.24 tff(20178,assumption,(node18(c_e_h_3, c_h, s7, s8)), introduced(assumption)).
% 88.01/88.24 tff(20179,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20180,plain,
% 88.01/88.24 (((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~node18(c_e_h_3, c_h, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20181,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~node18(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8))))),
% 88.01/88.24 inference(monotonicity,[status(thm)],[20180])).
% 88.01/88.24 tff(20182,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~node18(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.24 inference(transitivity,[status(thm)],[20181, 20179])).
% 88.01/88.24 tff(20183,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~node18(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20184,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8))),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20183, 20182])).
% 88.01/88.24 tff(20185,plain,
% 88.01/88.24 ($false),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20184, 124, 20177, 20178, 20140])).
% 88.01/88.24 tff(20186,plain,((~node18(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.24 tff(20187,plain,
% 88.01/88.24 (~node18(c_e_h_3, c_h, s7, s8)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20186, 20140, 20177])).
% 88.01/88.24 tff(20188,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_h, s7, s8))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20189,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_h, s7, s8))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20190,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_h, s7, s8)),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20189, 20188])).
% 88.01/88.24 tff(20191,plain,
% 88.01/88.24 (node19(c_e_h_3, c_h, s7, s8)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20190, 141, 2152])).
% 88.01/88.24 tff(20192,plain,
% 88.01/88.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20193,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.24 inference(quant_inst,[status(thm)],[])).
% 88.01/88.24 tff(20194,plain,
% 88.01/88.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8))),
% 88.01/88.24 inference(modus_ponens,[status(thm)],[20193, 20192])).
% 88.01/88.24 tff(20195,plain,
% 88.01/88.24 (node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20194, 156, 20191])).
% 88.01/88.24 tff(20196,plain,
% 88.01/88.24 (node17(c_e_h_3, c_h, s7)),
% 88.01/88.24 inference(unit_resolution,[status(thm)],[20195, 20187])).
% 88.01/88.24 tff(20197,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s7)), introduced(assumption)).
% 88.01/88.24 tff(20198,plain,
% 88.01/88.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20199,plain,
% 88.01/88.24 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)))),
% 88.01/88.24 inference(rewrite,[status(thm)],[])).
% 88.01/88.24 tff(20200,plain,
% 88.01/88.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7))))),
% 88.01/88.25 inference(monotonicity,[status(thm)],[20199])).
% 88.01/88.25 tff(20201,plain,
% 88.01/88.25 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)))),
% 88.01/88.25 inference(transitivity,[status(thm)],[20200, 20198])).
% 88.01/88.25 tff(20202,plain,
% 88.01/88.25 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20203,plain,
% 88.01/88.25 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7))),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20202, 20201])).
% 88.01/88.25 tff(20204,plain,
% 88.01/88.25 ((~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7))),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20203, 209, 20197])).
% 88.01/88.25 tff(20205,plain,
% 88.01/88.25 (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20204, 20196])).
% 88.01/88.25 tff(20206,plain,
% 88.01/88.25 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20207,plain,
% 88.01/88.25 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20208,plain,
% 88.01/88.25 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20207, 20206])).
% 88.01/88.25 tff(20209,plain,
% 88.01/88.25 ((~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20208, 228, 20197])).
% 88.01/88.25 tff(20210,plain,
% 88.01/88.25 (~node16(c_e_h_3, c_h, s7)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20209, 20205])).
% 88.01/88.25 tff(20211,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s7)), introduced(assumption)).
% 88.01/88.25 tff(20212,assumption,(node14(c_e_h_3, c_h, s7, s8)), introduced(assumption)).
% 88.01/88.25 tff(20213,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20214,plain,
% 88.01/88.25 (((~node14(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20215,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8))))),
% 88.01/88.25 inference(monotonicity,[status(thm)],[20214])).
% 88.01/88.25 tff(20216,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.25 inference(transitivity,[status(thm)],[20215, 20213])).
% 88.01/88.25 tff(20217,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20218,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8))),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20217, 20216])).
% 88.01/88.25 tff(20219,plain,
% 88.01/88.25 ($false),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20218, 283, 20212, 20140, 20211])).
% 88.01/88.25 tff(20220,plain,((~node14(c_e_h_3, c_h, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.25 tff(20221,plain,
% 88.01/88.25 (~node14(c_e_h_3, c_h, s7, s8)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20220, 20140, 20205])).
% 88.01/88.25 tff(20222,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_h, s7, s8) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_h, s7, s8) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20223,plain,
% 88.01/88.25 ((node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8))) <=> (node15(c_e_h_3, c_h, s7, s8) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20224,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_h, s7, s8) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8))))),
% 88.01/88.25 inference(monotonicity,[status(thm)],[20223])).
% 88.01/88.25 tff(20225,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_h, s7, s8) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.25 inference(transitivity,[status(thm)],[20224, 20222])).
% 88.01/88.25 tff(20226,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20227,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_h, s7, s8) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8))),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20226, 20225])).
% 88.01/88.25 tff(20228,plain,
% 88.01/88.25 (node15(c_e_h_3, c_h, s7, s8) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20227, 189, 20191])).
% 88.01/88.25 tff(20229,plain,
% 88.01/88.25 (node15(c_e_h_3, c_h, s7, s8)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20228, 20221, 20210])).
% 88.01/88.25 tff(20230,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20231,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20232,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20231, 20230])).
% 88.01/88.25 tff(20233,plain,
% 88.01/88.25 ($false),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20232, 173, 20177, 20229, 20140])).
% 88.01/88.25 tff(20234,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.25 tff(20235,plain,
% 88.01/88.25 (m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20234, 20176, 20140])).
% 88.01/88.25 tff(20236,plain,
% 88.01/88.25 (m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[18219, 20235, 20139])).
% 88.01/88.25 tff(20237,plain,
% 88.01/88.25 (m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[16965, 20236, 16889])).
% 88.01/88.25 tff(20238,plain,
% 88.01/88.25 ($false),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[16887, 309, 18100, 20237])).
% 88.01/88.25 tff(20239,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.25 tff(20240,plain,
% 88.01/88.25 ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20239, 17978, 20137, 16884, 16250, 18097])).
% 88.01/88.25 tff(20241,plain,
% 88.01/88.25 (m_or_h_gate_v_in1(c_e_h_3, c_j, s6)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20240, 20027])).
% 88.01/88.25 tff(20242,plain,
% 88.01/88.25 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20243,plain,
% 88.01/88.25 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20244,plain,
% 88.01/88.25 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20243, 20242])).
% 88.01/88.25 tff(20245,plain,
% 88.01/88.25 (m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20244, 801, 20241])).
% 88.01/88.25 tff(20246,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s5)), introduced(assumption)).
% 88.01/88.25 tff(20247,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s6)), introduced(assumption)).
% 88.01/88.25 tff(20248,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20249,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20250,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20249, 20248])).
% 88.01/88.25 tff(20251,plain,
% 88.01/88.25 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20250, 107])).
% 88.01/88.25 tff(20252,plain,
% 88.01/88.25 (~node22(c_e_h_3, c_l, s5, s6)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20251, 20247, 20246])).
% 88.01/88.25 tff(20253,assumption,(~node20(c_e_h_3, c_l, s5)), introduced(assumption)).
% 88.01/88.25 tff(20254,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6)))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20255,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6)))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20256,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6))),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20255, 20254])).
% 88.01/88.25 tff(20257,plain,
% 88.01/88.25 (node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6))),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20256, 51])).
% 88.01/88.25 tff(20258,plain,
% 88.01/88.25 (~node21(c_e_h_3, c_l, s5, s6)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20257, 20247, 20253])).
% 88.01/88.25 tff(20259,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20260,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20261,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20260, 20259])).
% 88.01/88.25 tff(20262,plain,
% 88.01/88.25 ($false),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20261, 81, 1499, 20258, 20252])).
% 88.01/88.25 tff(20263,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5) | node20(c_e_h_3, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.25 tff(20264,plain,
% 88.01/88.25 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | node20(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20263, 17974])).
% 88.01/88.25 tff(20265,plain,
% 88.01/88.25 (node20(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20264, 20245])).
% 88.01/88.25 tff(20266,plain,
% 88.01/88.25 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20267,plain,
% 88.01/88.25 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20268,plain,
% 88.01/88.25 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20267, 20266])).
% 88.01/88.25 tff(20269,plain,
% 88.01/88.25 (m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20268, 37, 20265])).
% 88.01/88.25 tff(20270,plain,
% 88.01/88.25 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20271,plain,
% 88.01/88.25 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20272,plain,
% 88.01/88.25 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20271, 20270])).
% 88.01/88.25 tff(20273,plain,
% 88.01/88.25 (m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20272, 10554, 20269])).
% 88.01/88.25 tff(20274,plain,
% 88.01/88.25 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[17943, 17938])).
% 88.01/88.25 tff(20275,plain,
% 88.01/88.25 (~node20(c_e_h_3, c_l, s4)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[17951, 20274])).
% 88.01/88.25 tff(20276,plain,
% 88.01/88.25 (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[17972, 20275, 17962])).
% 88.01/88.25 tff(20277,plain,
% 88.01/88.25 (node20(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20263, 20276, 20247])).
% 88.01/88.25 tff(20278,plain,
% 88.01/88.25 (m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20268, 37, 20277])).
% 88.01/88.25 tff(20279,assumption,(~node20(c_e_h_3, c_k, s4)), introduced(assumption)).
% 88.01/88.25 tff(20280,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s5)), introduced(assumption)).
% 88.01/88.25 tff(20281,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s4) | (~node21(c_e_h_3, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s4) | (~node21(c_e_h_3, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20282,plain,
% 88.01/88.25 ((node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node21(c_e_h_3, c_k, s4, s5))) <=> (node20(c_e_h_3, c_k, s4) | (~node21(c_e_h_3, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20283,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node21(c_e_h_3, c_k, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s4) | (~node21(c_e_h_3, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5))))),
% 88.01/88.25 inference(monotonicity,[status(thm)],[20282])).
% 88.01/88.25 tff(20284,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node21(c_e_h_3, c_k, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s4) | (~node21(c_e_h_3, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))),
% 88.01/88.25 inference(transitivity,[status(thm)],[20283, 20281])).
% 88.01/88.25 tff(20285,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node21(c_e_h_3, c_k, s4, s5)))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20286,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s4) | (~node21(c_e_h_3, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20285, 20284])).
% 88.01/88.25 tff(20287,plain,
% 88.01/88.25 (node20(c_e_h_3, c_k, s4) | (~node21(c_e_h_3, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20286, 51])).
% 88.01/88.25 tff(20288,plain,
% 88.01/88.25 (~node21(c_e_h_3, c_k, s4, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20287, 20280, 20279])).
% 88.01/88.25 tff(20289,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20290,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20291,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20290, 20289])).
% 88.01/88.25 tff(20292,plain,
% 88.01/88.25 (node22(c_e_h_3, c_k, s4, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20291, 81, 1432, 20288])).
% 88.01/88.25 tff(20293,plain,
% 88.01/88.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20294,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20295,plain,
% 88.01/88.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20294, 20293])).
% 88.01/88.25 tff(20296,plain,
% 88.01/88.25 ($false),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20295, 107, 17938, 20280, 20292])).
% 88.01/88.25 tff(20297,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.25 tff(20298,plain,
% 88.01/88.25 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20297, 17938, 20279])).
% 88.01/88.25 tff(20299,plain,
% 88.01/88.25 ($false),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20272, 10554, 20298, 20278])).
% 88.01/88.25 tff(20300,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.25 tff(20301,plain,
% 88.01/88.25 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4) | node20(c_e_h_3, c_k, s4)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20300, 17936])).
% 88.01/88.25 tff(20302,plain,
% 88.01/88.25 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | node20(c_e_h_3, c_k, s4)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20301, 16734])).
% 88.01/88.25 tff(20303,plain,
% 88.01/88.25 (node20(c_e_h_3, c_k, s4)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20302, 20245])).
% 88.01/88.25 tff(20304,plain,
% 88.01/88.25 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20305,plain,
% 88.01/88.25 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20306,plain,
% 88.01/88.25 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 88.01/88.25 inference(modus_ponens,[status(thm)],[20305, 20304])).
% 88.01/88.25 tff(20307,plain,
% 88.01/88.25 (m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 88.01/88.25 inference(unit_resolution,[status(thm)],[20306, 37, 20303])).
% 88.01/88.25 tff(20308,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s4)), introduced(assumption)).
% 88.01/88.25 tff(20309,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s4)), introduced(assumption)).
% 88.01/88.25 tff(20310,plain,
% 88.01/88.25 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))),
% 88.01/88.25 inference(rewrite,[status(thm)],[])).
% 88.01/88.25 tff(20311,plain,
% 88.01/88.25 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))),
% 88.01/88.25 inference(quant_inst,[status(thm)],[])).
% 88.01/88.25 tff(20312,plain,
% 88.01/88.25 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20311, 20310])).
% 88.01/88.26 tff(20313,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20312, 13114, 20309, 20308])).
% 88.01/88.26 tff(20314,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20315,plain,
% 88.01/88.26 (m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20314, 20307])).
% 88.01/88.26 tff(20316,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s4)), introduced(assumption)).
% 88.01/88.26 tff(20317,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s5)), introduced(assumption)).
% 88.01/88.26 tff(20318,assumption,(node6(c_e_h_3, c_g, s4, s5)), introduced(assumption)).
% 88.01/88.26 tff(20319,plain,
% 88.01/88.26 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X))) <=> (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X))))),
% 88.01/88.26 inference(bind,[status(th)],[])).
% 88.01/88.26 tff(20320,plain,
% 88.01/88.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 88.01/88.26 inference(quant_intro,[status(thm)],[20319])).
% 88.01/88.26 tff(20321,plain,
% 88.01/88.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20322,plain,
% 88.01/88.26 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) <=> (m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X)))), (((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))) <=> ((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))))), rewrite(((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))) <=> (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))), (((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))) <=> (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))))),
% 88.01/88.26 inference(bind,[status(th)],[])).
% 88.01/88.26 tff(20323,plain,
% 88.01/88.26 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 88.01/88.26 inference(quant_intro,[status(thm)],[20322])).
% 88.01/88.26 tff(20324,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_or_h_gate_6')).
% 88.01/88.26 tff(20325,plain,
% 88.01/88.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20324, 20323])).
% 88.01/88.26 tff(20326,plain,
% 88.01/88.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20325, 20321])).
% 88.01/88.26 tff(20327,plain,(
% 88.01/88.26 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 88.01/88.26 inference(skolemize,[status(sab)],[20326])).
% 88.01/88.26 tff(20328,plain,
% 88.01/88.26 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20327, 20320])).
% 88.01/88.26 tff(20329,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20330,plain,
% 88.01/88.26 ((m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4))) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20331,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5))))),
% 88.01/88.26 inference(monotonicity,[status(thm)],[20330])).
% 88.01/88.26 tff(20332,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 88.01/88.26 inference(transitivity,[status(thm)],[20331, 20329])).
% 88.01/88.26 tff(20333,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20334,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20333, 20332])).
% 88.01/88.26 tff(20335,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20334, 20328, 20316, 20318, 20317])).
% 88.01/88.26 tff(20336,plain,((~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20337,plain,
% 88.01/88.26 (~node6(c_e_h_3, c_g, s4, s5)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20336, 20317, 20316])).
% 88.01/88.26 tff(20338,plain,
% 88.01/88.26 (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[17908, 16672])).
% 88.01/88.26 tff(20339,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)), introduced(assumption)).
% 88.01/88.26 tff(20340,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s2)), introduced(assumption)).
% 88.01/88.26 tff(20341,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s1)), introduced(assumption)).
% 88.01/88.26 tff(20342,assumption,(node22(c_e_h_1, c_p, s0, s1)), introduced(assumption)).
% 88.01/88.26 tff(20343,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node22(c_e_h_1, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node22(c_e_h_1, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20344,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node22(c_e_h_1, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20345,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node22(c_e_h_1, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20344, 20343])).
% 88.01/88.26 tff(20346,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20345, 107, 20342, 17792, 20341])).
% 88.01/88.26 tff(20347,plain,((~node22(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20348,plain,
% 88.01/88.26 (~node22(c_e_h_1, c_p, s0, s1)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20347, 20341])).
% 88.01/88.26 tff(20349,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s0)), introduced(assumption)).
% 88.01/88.26 tff(20350,plain,
% 88.01/88.26 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s0))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20351,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20350, 94, 20349])).
% 88.01/88.26 tff(20352,plain,(~m_and_h_gate_v_out(c_e_h_1, c_k, s0)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20353,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_p, s0)), introduced(assumption)).
% 88.01/88.26 tff(20354,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s0)), introduced(assumption)).
% 88.01/88.26 tff(20355,plain,
% 88.01/88.26 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X)))),
% 88.01/88.26 inference(bind,[status(th)],[])).
% 88.01/88.26 tff(20356,plain,
% 88.01/88.26 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 88.01/88.26 inference(quant_intro,[status(thm)],[20355])).
% 88.01/88.26 tff(20357,plain,
% 88.01/88.26 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20358,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_64')).
% 88.01/88.26 tff(20359,plain,
% 88.01/88.26 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20358, 20357])).
% 88.01/88.26 tff(20360,plain,(
% 88.01/88.26 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 88.01/88.26 inference(skolemize,[status(sab)],[20359])).
% 88.01/88.26 tff(20361,plain,
% 88.01/88.26 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20360, 20356])).
% 88.01/88.26 tff(20362,plain,
% 88.01/88.26 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20363,plain,
% 88.01/88.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20364,plain,
% 88.01/88.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20363, 20362])).
% 88.01/88.26 tff(20365,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20364, 20361, 20354, 20353])).
% 88.01/88.26 tff(20366,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20367,plain,
% 88.01/88.26 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20366, 20352])).
% 88.01/88.26 tff(20368,plain,
% 88.01/88.26 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s0))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20369,plain,
% 88.01/88.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s0))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20370,plain,
% 88.01/88.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s0)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20369, 20368])).
% 88.01/88.26 tff(20371,plain,
% 88.01/88.26 (~node20(c_e_h_1, c_p, s0)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20370, 37, 20367])).
% 88.01/88.26 tff(20372,assumption,(~node20(c_e_h_1, c_p, s0)), introduced(assumption)).
% 88.01/88.26 tff(20373,assumption,(node21(c_e_h_1, c_p, s0, s1)), introduced(assumption)).
% 88.01/88.26 tff(20374,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20375,plain,
% 88.01/88.26 ((node20(c_e_h_1, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node21(c_e_h_1, c_p, s0, s1))) <=> (node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20376,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node21(c_e_h_1, c_p, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1))))),
% 88.01/88.26 inference(monotonicity,[status(thm)],[20375])).
% 88.01/88.26 tff(20377,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node21(c_e_h_1, c_p, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)))),
% 88.01/88.26 inference(transitivity,[status(thm)],[20376, 20374])).
% 88.01/88.26 tff(20378,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node21(c_e_h_1, c_p, s0, s1)))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20379,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20378, 20377])).
% 88.01/88.26 tff(20380,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20379, 51, 20373, 20341, 20372])).
% 88.01/88.26 tff(20381,plain,((~node21(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | node20(c_e_h_1, c_p, s0)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20382,plain,
% 88.01/88.26 ((~node21(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1))),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20381, 20371])).
% 88.01/88.26 tff(20383,plain,
% 88.01/88.26 (~node21(c_e_h_1, c_p, s0, s1)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20382, 20341])).
% 88.01/88.26 tff(20384,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20385,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20386,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20385, 20384])).
% 88.01/88.26 tff(20387,plain,
% 88.01/88.26 (node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20386, 81, 71])).
% 88.01/88.26 tff(20388,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20387, 20383, 20348])).
% 88.01/88.26 tff(20389,plain,(~m_and_h_gate_v_out(c_e_h_1, c_p, s1)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20390,plain,
% 88.01/88.26 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20391,plain,
% 88.01/88.26 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20392,plain,
% 88.01/88.26 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20391, 20390])).
% 88.01/88.26 tff(20393,plain,
% 88.01/88.26 (~m_cell_v_req(c_e_h_1, s1)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20392, 17799, 20389])).
% 88.01/88.26 tff(20394,plain,
% 88.01/88.26 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s1))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20395,plain,
% 88.01/88.26 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s1))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20396,plain,
% 88.01/88.26 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s1)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20395, 20394])).
% 88.01/88.26 tff(20397,plain,
% 88.01/88.26 (node1(c_e_h_3, c_e_h_1, s1)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20396, 3860, 17810])).
% 88.01/88.26 tff(20398,plain,
% 88.01/88.26 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_1, s1) | (~node1(c_e_h_3, c_e_h_1, s1)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s1) | (~node1(c_e_h_3, c_e_h_1, s1)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20399,plain,
% 88.01/88.26 (((~node1(c_e_h_3, c_e_h_1, s1)) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1))) <=> (m_cell_v_req(c_e_h_1, s1) | (~node1(c_e_h_3, c_e_h_1, s1)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20400,plain,
% 88.01/88.26 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s1)) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_1, s1) | (~node1(c_e_h_3, c_e_h_1, s1)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1))))),
% 88.01/88.26 inference(monotonicity,[status(thm)],[20399])).
% 88.01/88.26 tff(20401,plain,
% 88.01/88.26 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s1)) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s1) | (~node1(c_e_h_3, c_e_h_1, s1)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))),
% 88.01/88.26 inference(transitivity,[status(thm)],[20400, 20398])).
% 88.01/88.26 tff(20402,plain,
% 88.01/88.26 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s1)) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20403,plain,
% 88.01/88.26 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s1) | (~node1(c_e_h_3, c_e_h_1, s1)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20402, 20401])).
% 88.01/88.26 tff(20404,plain,
% 88.01/88.26 (m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1))),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20403, 17824, 20397])).
% 88.01/88.26 tff(20405,plain,
% 88.01/88.26 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20404, 20393])).
% 88.01/88.26 tff(20406,assumption,(node13(c_e_h_3, c_b, s1, s2)), introduced(assumption)).
% 88.01/88.26 tff(20407,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20408,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20409,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20408, 20407])).
% 88.01/88.26 tff(20410,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20409, 17691, 20406, 17853, 20340])).
% 88.01/88.26 tff(20411,plain,((~node13(c_e_h_3, c_b, s1, s2)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20412,plain,
% 88.01/88.26 (~node13(c_e_h_3, c_b, s1, s2)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20411, 20340])).
% 88.01/88.26 tff(20413,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20414,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20415,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2)),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20414, 20413])).
% 88.01/88.26 tff(20416,plain,
% 88.01/88.26 (node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20415, 17707, 344])).
% 88.01/88.26 tff(20417,plain,
% 88.01/88.26 (node12(c_e_h_3, c_b, s1, s2)),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20416, 20412])).
% 88.01/88.26 tff(20418,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~node12(c_e_h_3, c_b, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~node12(c_e_h_3, c_b, s1, s2)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20419,plain,
% 88.01/88.26 (((~node12(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~node12(c_e_h_3, c_b, s1, s2)))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20420,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~node12(c_e_h_3, c_b, s1, s2))))),
% 88.01/88.26 inference(monotonicity,[status(thm)],[20419])).
% 88.01/88.26 tff(20421,plain,
% 88.01/88.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~node12(c_e_h_3, c_b, s1, s2)))),
% 88.01/88.26 inference(transitivity,[status(thm)],[20420, 20418])).
% 88.01/88.26 tff(20422,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)))),
% 88.01/88.26 inference(quant_inst,[status(thm)],[])).
% 88.01/88.26 tff(20423,plain,
% 88.01/88.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~node12(c_e_h_3, c_b, s1, s2))),
% 88.01/88.26 inference(modus_ponens,[status(thm)],[20422, 20421])).
% 88.01/88.26 tff(20424,plain,
% 88.01/88.26 ($false),
% 88.01/88.26 inference(unit_resolution,[status(thm)],[20423, 17742, 20417, 20405, 20340])).
% 88.01/88.26 tff(20425,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.26 tff(20426,plain,
% 88.01/88.26 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))),
% 88.01/88.26 inference(rewrite,[status(thm)],[])).
% 88.01/88.26 tff(20427,plain,
% 88.01/88.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))),
% 88.01/88.27 inference(quant_inst,[status(thm)],[])).
% 88.01/88.27 tff(20428,plain,
% 88.01/88.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2)),
% 88.01/88.27 inference(modus_ponens,[status(thm)],[20427, 20426])).
% 88.01/88.27 tff(20429,plain,
% 88.01/88.27 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20428, 7744, 20425])).
% 88.01/88.27 tff(20430,plain,
% 88.01/88.27 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s2))),
% 88.01/88.27 inference(rewrite,[status(thm)],[])).
% 88.01/88.27 tff(20431,plain,
% 88.01/88.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s2))),
% 88.01/88.27 inference(quant_inst,[status(thm)],[])).
% 88.01/88.27 tff(20432,plain,
% 88.01/88.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s2)),
% 88.01/88.27 inference(modus_ponens,[status(thm)],[20431, 20430])).
% 88.01/88.27 tff(20433,plain,
% 88.01/88.27 (~node20(c_e_h_3, c_d, s2)),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20432, 37, 20429])).
% 88.01/88.27 tff(20434,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s3)), introduced(assumption)).
% 88.01/88.27 tff(20435,assumption,(node22(c_e_h_3, c_d, s2, s3)), introduced(assumption)).
% 88.01/88.27 tff(20436,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node22(c_e_h_3, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node22(c_e_h_3, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 88.01/88.27 inference(rewrite,[status(thm)],[])).
% 88.01/88.27 tff(20437,plain,
% 88.01/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node22(c_e_h_3, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 88.01/88.27 inference(quant_inst,[status(thm)],[])).
% 88.01/88.27 tff(20438,plain,
% 88.01/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node22(c_e_h_3, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2)),
% 88.01/88.27 inference(modus_ponens,[status(thm)],[20437, 20436])).
% 88.01/88.27 tff(20439,plain,
% 88.01/88.27 ($false),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20438, 107, 20434, 20435, 17876])).
% 88.01/88.27 tff(20440,plain,((~node22(c_e_h_3, c_d, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3))), inference(lemma,lemma(discharge,[]))).
% 88.01/88.27 tff(20441,plain,
% 88.01/88.27 (~node22(c_e_h_3, c_d, s2, s3)),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20440, 20434])).
% 88.01/88.27 tff(20442,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3))),
% 88.01/88.27 inference(rewrite,[status(thm)],[])).
% 88.01/88.27 tff(20443,plain,
% 88.01/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3))),
% 88.01/88.27 inference(quant_inst,[status(thm)],[])).
% 88.01/88.27 tff(20444,plain,
% 88.01/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3)),
% 88.01/88.27 inference(modus_ponens,[status(thm)],[20443, 20442])).
% 88.01/88.27 tff(20445,plain,
% 88.01/88.27 (node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3)),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20444, 81, 582])).
% 88.01/88.27 tff(20446,plain,
% 88.01/88.27 (node21(c_e_h_3, c_d, s2, s3)),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20445, 20441])).
% 88.01/88.27 tff(20447,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3)))),
% 88.01/88.27 inference(rewrite,[status(thm)],[])).
% 88.01/88.27 tff(20448,plain,
% 88.01/88.27 ((node20(c_e_h_3, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node21(c_e_h_3, c_d, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3)))),
% 88.01/88.27 inference(rewrite,[status(thm)],[])).
% 88.01/88.27 tff(20449,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node21(c_e_h_3, c_d, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3))))),
% 88.01/88.27 inference(monotonicity,[status(thm)],[20448])).
% 88.01/88.27 tff(20450,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node21(c_e_h_3, c_d, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3)))),
% 88.01/88.27 inference(transitivity,[status(thm)],[20449, 20447])).
% 88.01/88.27 tff(20451,plain,
% 88.01/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node21(c_e_h_3, c_d, s2, s3)))),
% 88.01/88.27 inference(quant_inst,[status(thm)],[])).
% 88.01/88.27 tff(20452,plain,
% 88.01/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3))),
% 88.01/88.27 inference(modus_ponens,[status(thm)],[20451, 20450])).
% 88.01/88.27 tff(20453,plain,
% 88.01/88.27 ($false),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20452, 51, 20434, 20446, 20433])).
% 88.01/88.27 tff(20454,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.27 tff(20455,plain,
% 88.01/88.27 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))),
% 88.01/88.27 inference(rewrite,[status(thm)],[])).
% 88.01/88.27 tff(20456,plain,
% 88.01/88.27 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))),
% 88.01/88.27 inference(quant_inst,[status(thm)],[])).
% 88.01/88.27 tff(20457,plain,
% 88.01/88.27 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)),
% 88.01/88.27 inference(modus_ponens,[status(thm)],[20456, 20455])).
% 88.01/88.27 tff(20458,plain,
% 88.01/88.27 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20457, 15952, 20454])).
% 88.01/88.27 tff(20459,assumption,(node5(c_e_h_3, c_g, s3, s4)), introduced(assumption)).
% 88.01/88.27 tff(20460,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node5(c_e_h_3, c_g, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node5(c_e_h_3, c_g, s3, s4)))),
% 88.01/88.27 inference(rewrite,[status(thm)],[])).
% 88.01/88.27 tff(20461,plain,
% 88.01/88.27 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4))) <=> (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node5(c_e_h_3, c_g, s3, s4)))),
% 88.01/88.27 inference(rewrite,[status(thm)],[])).
% 88.01/88.27 tff(20462,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node5(c_e_h_3, c_g, s3, s4))))),
% 88.01/88.27 inference(monotonicity,[status(thm)],[20461])).
% 88.01/88.27 tff(20463,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node5(c_e_h_3, c_g, s3, s4)))),
% 88.01/88.27 inference(transitivity,[status(thm)],[20462, 20460])).
% 88.01/88.27 tff(20464,plain,
% 88.01/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))),
% 88.01/88.27 inference(quant_inst,[status(thm)],[])).
% 88.01/88.27 tff(20465,plain,
% 88.01/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node5(c_e_h_3, c_g, s3, s4))),
% 88.01/88.27 inference(modus_ponens,[status(thm)],[20464, 20463])).
% 88.01/88.27 tff(20466,plain,
% 88.01/88.27 ($false),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20465, 862, 20316, 20459, 20458, 20339])).
% 88.01/88.27 tff(20467,plain,((~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 88.01/88.27 tff(20468,plain,
% 88.01/88.27 (~node5(c_e_h_3, c_g, s3, s4)),
% 88.01/88.27 inference(unit_resolution,[status(thm)],[20467, 20316, 20339])).
% 88.01/88.27 tff(20469,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s3)), introduced(assumption)).
% 88.01/88.27 tff(20470,assumption,(node6(c_e_h_3, c_g, s3, s4)), introduced(assumption)).
% 88.01/88.27 tff(20471,plain,
% 88.01/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s3, s4)))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20472,plain,
% 88.09/88.27 (((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s3, s4)))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20473,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s3, s4))))),
% 88.09/88.27 inference(monotonicity,[status(thm)],[20472])).
% 88.09/88.27 tff(20474,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s3, s4)))),
% 88.09/88.27 inference(transitivity,[status(thm)],[20473, 20471])).
% 88.09/88.27 tff(20475,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))),
% 88.09/88.27 inference(quant_inst,[status(thm)],[])).
% 88.09/88.27 tff(20476,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s3, s4))),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20475, 20474])).
% 88.09/88.27 tff(20477,plain,
% 88.09/88.27 ($false),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20476, 899, 20469, 20316, 20470])).
% 88.09/88.27 tff(20478,plain,((~node6(c_e_h_3, c_g, s3, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4))), inference(lemma,lemma(discharge,[]))).
% 88.09/88.27 tff(20479,plain,
% 88.09/88.27 (~node6(c_e_h_3, c_g, s3, s4)),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20478, 20316, 20469])).
% 88.09/88.27 tff(20480,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20481,plain,
% 88.09/88.27 ((node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20482,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4)))),
% 88.09/88.27 inference(monotonicity,[status(thm)],[20481])).
% 88.09/88.27 tff(20483,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4))),
% 88.09/88.27 inference(transitivity,[status(thm)],[20482, 20480])).
% 88.09/88.27 tff(20484,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4) | (~trans(s3, s4)))),
% 88.09/88.27 inference(quant_inst,[status(thm)],[])).
% 88.09/88.27 tff(20485,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4)),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20484, 20483])).
% 88.09/88.27 tff(20486,plain,
% 88.09/88.27 (node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4)),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20485, 881, 679])).
% 88.09/88.27 tff(20487,plain,
% 88.09/88.27 ($false),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20486, 20479, 20468])).
% 88.09/88.27 tff(20488,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.27 tff(20489,plain,
% 88.09/88.27 ((~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20488, 20338])).
% 88.09/88.27 tff(20490,plain,
% 88.09/88.27 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20489, 20316])).
% 88.09/88.27 tff(20491,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s3)), introduced(assumption)).
% 88.09/88.27 tff(20492,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s3)), introduced(assumption)).
% 88.09/88.27 tff(20493,plain,
% 88.09/88.27 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20494,plain,
% 88.09/88.27 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))),
% 88.09/88.27 inference(quant_inst,[status(thm)],[])).
% 88.09/88.27 tff(20495,plain,
% 88.09/88.27 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20494, 20493])).
% 88.09/88.27 tff(20496,plain,
% 88.09/88.27 ($false),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20495, 15941, 20492, 20491])).
% 88.09/88.27 tff(20497,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.27 tff(20498,plain,
% 88.09/88.27 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20497, 20490])).
% 88.09/88.27 tff(20499,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s3)), introduced(assumption)).
% 88.09/88.27 tff(20500,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s4)), introduced(assumption)).
% 88.09/88.27 tff(20501,assumption,(node22(c_e_h_3, c_c, s3, s4)), introduced(assumption)).
% 88.09/88.27 tff(20502,plain,
% 88.09/88.27 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X))) <=> (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X))))),
% 88.09/88.27 inference(bind,[status(th)],[])).
% 88.09/88.27 tff(20503,plain,
% 88.09/88.27 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 88.09/88.27 inference(quant_intro,[status(thm)],[20502])).
% 88.09/88.27 tff(20504,plain,
% 88.09/88.27 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20505,plain,
% 88.09/88.27 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) <=> (m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X)))), (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))) <=> ((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))))), rewrite(((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))) <=> (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))), (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))) <=> (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))))),
% 88.09/88.27 inference(bind,[status(th)],[])).
% 88.09/88.27 tff(20506,plain,
% 88.09/88.27 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 88.09/88.27 inference(quant_intro,[status(thm)],[20505])).
% 88.09/88.27 tff(20507,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_6')).
% 88.09/88.27 tff(20508,plain,
% 88.09/88.27 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20507, 20506])).
% 88.09/88.27 tff(20509,plain,
% 88.09/88.27 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20508, 20504])).
% 88.09/88.27 tff(20510,plain,(
% 88.09/88.27 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 88.09/88.27 inference(skolemize,[status(sab)],[20509])).
% 88.09/88.27 tff(20511,plain,
% 88.09/88.27 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20510, 20503])).
% 88.09/88.27 tff(20512,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20513,plain,
% 88.09/88.27 ((m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20514,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4))))),
% 88.09/88.27 inference(monotonicity,[status(thm)],[20513])).
% 88.09/88.27 tff(20515,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)))),
% 88.09/88.27 inference(transitivity,[status(thm)],[20514, 20512])).
% 88.09/88.27 tff(20516,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)))),
% 88.09/88.27 inference(quant_inst,[status(thm)],[])).
% 88.09/88.27 tff(20517,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4))),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20516, 20515])).
% 88.09/88.27 tff(20518,plain,
% 88.09/88.27 ($false),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20517, 20511, 20499, 20500, 20501])).
% 88.09/88.27 tff(20519,plain,((~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.27 tff(20520,plain,
% 88.09/88.27 (~node22(c_e_h_3, c_c, s3, s4)),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20519, 20500, 20499])).
% 88.09/88.27 tff(20521,assumption,(node22(c_e_h_3, c_c, s2, s3)), introduced(assumption)).
% 88.09/88.27 tff(20522,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node22(c_e_h_3, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node22(c_e_h_3, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20523,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node22(c_e_h_3, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 88.09/88.27 inference(quant_inst,[status(thm)],[])).
% 88.09/88.27 tff(20524,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node22(c_e_h_3, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2)),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20523, 20522])).
% 88.09/88.27 tff(20525,plain,
% 88.09/88.27 ($false),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20524, 107, 20521, 20499, 17771])).
% 88.09/88.27 tff(20526,plain,((~node22(c_e_h_3, c_c, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.27 tff(20527,plain,
% 88.09/88.27 (~node22(c_e_h_3, c_c, s2, s3)),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20526, 20499, 17771])).
% 88.09/88.27 tff(20528,plain,
% 88.09/88.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3))),
% 88.09/88.27 inference(rewrite,[status(thm)],[])).
% 88.09/88.27 tff(20529,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3))),
% 88.09/88.27 inference(quant_inst,[status(thm)],[])).
% 88.09/88.27 tff(20530,plain,
% 88.09/88.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3)),
% 88.09/88.27 inference(modus_ponens,[status(thm)],[20529, 20528])).
% 88.09/88.27 tff(20531,plain,
% 88.09/88.27 (node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3)),
% 88.09/88.27 inference(unit_resolution,[status(thm)],[20530, 81, 582])).
% 88.09/88.27 tff(20532,plain,
% 88.09/88.27 (node21(c_e_h_3, c_c, s2, s3)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20531, 20527])).
% 88.09/88.28 tff(20533,assumption,(~node20(c_e_h_3, c_c, s2)), introduced(assumption)).
% 88.09/88.28 tff(20534,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3)))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20535,plain,
% 88.09/88.28 ((node20(c_e_h_3, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3)))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20536,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3))))),
% 88.09/88.28 inference(monotonicity,[status(thm)],[20535])).
% 88.09/88.28 tff(20537,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3)))),
% 88.09/88.28 inference(transitivity,[status(thm)],[20536, 20534])).
% 88.09/88.28 tff(20538,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s2, s3)))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20539,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20538, 20537])).
% 88.09/88.28 tff(20540,plain,
% 88.09/88.28 ($false),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20539, 51, 20533, 20532, 20499])).
% 88.09/88.28 tff(20541,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | m_and_h_gate_v_out(c_e_h_3, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.28 tff(20542,plain,
% 88.09/88.28 ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20541, 17770])).
% 88.09/88.28 tff(20543,plain,
% 88.09/88.28 (node20(c_e_h_3, c_c, s2)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20542, 20499])).
% 88.09/88.28 tff(20544,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)), introduced(assumption)).
% 88.09/88.28 tff(20545,assumption,(node20(c_e_h_3, c_c, s2)), introduced(assumption)).
% 88.09/88.28 tff(20546,plain,
% 88.09/88.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20547,plain,
% 88.09/88.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20548,plain,
% 88.09/88.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20547, 20546])).
% 88.09/88.28 tff(20549,plain,
% 88.09/88.28 ($false),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20548, 37, 20545, 20544])).
% 88.09/88.28 tff(20550,plain,((~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.28 tff(20551,plain,
% 88.09/88.28 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20550, 20543])).
% 88.09/88.28 tff(20552,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s2)), introduced(assumption)).
% 88.09/88.28 tff(20553,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)), introduced(assumption)).
% 88.09/88.28 tff(20554,plain,
% 88.09/88.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20555,plain,
% 88.09/88.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20556,plain,
% 88.09/88.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20555, 20554])).
% 88.09/88.28 tff(20557,plain,
% 88.09/88.28 ($false),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20556, 477, 20553, 20552])).
% 88.09/88.28 tff(20558,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.28 tff(20559,plain,
% 88.09/88.28 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20558, 20551])).
% 88.09/88.28 tff(20560,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s2)), introduced(assumption)).
% 88.09/88.28 tff(20561,assumption,(node13(c_e_h_3, c_a, s1, s2)), introduced(assumption)).
% 88.09/88.28 tff(20562,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20563,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20564,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20563, 20562])).
% 88.09/88.28 tff(20565,plain,
% 88.09/88.28 ($false),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20564, 17691, 17750, 20560, 20561])).
% 88.09/88.28 tff(20566,plain,((~node13(c_e_h_3, c_a, s1, s2)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2))), inference(lemma,lemma(discharge,[]))).
% 88.09/88.28 tff(20567,plain,
% 88.09/88.28 (~node13(c_e_h_3, c_a, s1, s2)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20566, 20560])).
% 88.09/88.28 tff(20568,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20569,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20570,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20569, 20568])).
% 88.09/88.28 tff(20571,plain,
% 88.09/88.28 (node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20570, 17707, 344])).
% 88.09/88.28 tff(20572,plain,
% 88.09/88.28 (node12(c_e_h_3, c_a, s1, s2)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20571, 20567])).
% 88.09/88.28 tff(20573,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2)))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20574,plain,
% 88.09/88.28 (((~node12(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2)))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20575,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2))))),
% 88.09/88.28 inference(monotonicity,[status(thm)],[20574])).
% 88.09/88.28 tff(20576,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2)))),
% 88.09/88.28 inference(transitivity,[status(thm)],[20575, 20573])).
% 88.09/88.28 tff(20577,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20578,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20577, 20576])).
% 88.09/88.28 tff(20579,plain,
% 88.09/88.28 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20578, 17742, 20560, 20572])).
% 88.09/88.28 tff(20580,plain,
% 88.09/88.28 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)) | m_user_v_req(c_e_h_3, c_u, s1))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)) | m_user_v_req(c_e_h_3, c_u, s1))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20581,plain,
% 88.09/88.28 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)) | m_user_v_req(c_e_h_3, c_u, s1))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20582,plain,
% 88.09/88.28 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)) | m_user_v_req(c_e_h_3, c_u, s1)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20581, 20580])).
% 88.09/88.28 tff(20583,plain,
% 88.09/88.28 (m_user_v_req(c_e_h_3, c_u, s1)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20582, 17728, 20579])).
% 88.09/88.28 tff(20584,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s1)), introduced(assumption)).
% 88.09/88.28 tff(20585,assumption,(node21(c_e_h_3, c_r, s0, s1)), introduced(assumption)).
% 88.09/88.28 tff(20586,plain,
% 88.09/88.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20587,plain,
% 88.09/88.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20588,plain,
% 88.09/88.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20587, 20586])).
% 88.09/88.28 tff(20589,plain,
% 88.09/88.28 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20588, 1884, 19287])).
% 88.09/88.28 tff(20590,plain,
% 88.09/88.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20591,plain,
% 88.09/88.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20592,plain,
% 88.09/88.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20591, 20590])).
% 88.09/88.28 tff(20593,plain,
% 88.09/88.28 (~node20(c_e_h_3, c_r, s0)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20592, 37, 20589])).
% 88.09/88.28 tff(20594,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | node20(c_e_h_3, c_r, s0) | (~node21(c_e_h_3, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | node20(c_e_h_3, c_r, s0) | (~node21(c_e_h_3, c_r, s0, s1)))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20595,plain,
% 88.09/88.28 ((node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | node20(c_e_h_3, c_r, s0) | (~node21(c_e_h_3, c_r, s0, s1)))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20596,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | node20(c_e_h_3, c_r, s0) | (~node21(c_e_h_3, c_r, s0, s1))))),
% 88.09/88.28 inference(monotonicity,[status(thm)],[20595])).
% 88.09/88.28 tff(20597,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | node20(c_e_h_3, c_r, s0) | (~node21(c_e_h_3, c_r, s0, s1)))),
% 88.09/88.28 inference(transitivity,[status(thm)],[20596, 20594])).
% 88.09/88.28 tff(20598,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20599,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | node20(c_e_h_3, c_r, s0) | (~node21(c_e_h_3, c_r, s0, s1))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20598, 20597])).
% 88.09/88.28 tff(20600,plain,
% 88.09/88.28 ($false),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20599, 51, 20584, 20593, 20585])).
% 88.09/88.28 tff(20601,plain,((~node21(c_e_h_3, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1))), inference(lemma,lemma(discharge,[]))).
% 88.09/88.28 tff(20602,plain,
% 88.09/88.28 (~node21(c_e_h_3, c_r, s0, s1)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20601, 20584])).
% 88.09/88.28 tff(20603,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20604,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20605,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20604, 20603])).
% 88.09/88.28 tff(20606,plain,
% 88.09/88.28 (node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20605, 81, 71])).
% 88.09/88.28 tff(20607,plain,
% 88.09/88.28 (node22(c_e_h_3, c_r, s0, s1)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20606, 20602])).
% 88.09/88.28 tff(20608,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s0)), introduced(assumption)).
% 88.09/88.28 tff(20609,plain,
% 88.09/88.28 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20610,plain,
% 88.09/88.28 ($false),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20609, 94, 20608])).
% 88.09/88.28 tff(20611,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.28 tff(20612,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20613,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20614,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20613, 20612])).
% 88.09/88.28 tff(20615,plain,
% 88.09/88.28 ($false),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20614, 107, 20611, 20584, 20607])).
% 88.09/88.28 tff(20616,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.28 tff(20617,plain,
% 88.09/88.28 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20618,plain,
% 88.09/88.28 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20619,plain,
% 88.09/88.28 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20618, 20617])).
% 88.09/88.28 tff(20620,plain,
% 88.09/88.28 (~m_user_v_ack(c_e_h_3, c_u, s1)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20619, 4481, 20616])).
% 88.09/88.28 tff(20621,assumption,(~m_user_v_req(c_e_h_3, c_u, s2)), introduced(assumption)).
% 88.09/88.28 tff(20622,assumption,(~m_user_v_ack(c_e_h_3, c_u, s1)), introduced(assumption)).
% 88.09/88.28 tff(20623,assumption,(node7(c_e_h_3, c_u, s1, s2)), introduced(assumption)).
% 88.09/88.28 tff(20624,plain,
% 88.09/88.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) <=> ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)))),
% 88.09/88.28 inference(bind,[status(th)],[])).
% 88.09/88.28 tff(20625,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 88.09/88.28 inference(quant_intro,[status(thm)],[20624])).
% 88.09/88.28 tff(20626,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20627,plain,
% 88.09/88.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) <=> (m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))), (((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) | (~node7(I0, I1, X, Y))) <=> ((m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) | (~node7(I0, I1, X, Y))))), rewrite(((m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) | (~node7(I0, I1, X, Y))) <=> ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))), (((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) | (~node7(I0, I1, X, Y))) <=> ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))))),
% 88.09/88.28 inference(bind,[status(th)],[])).
% 88.09/88.28 tff(20628,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) | (~node7(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 88.09/88.28 inference(quant_intro,[status(thm)],[20627])).
% 88.09/88.28 tff(20629,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) | (~node7(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_user_2')).
% 88.09/88.28 tff(20630,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20629, 20628])).
% 88.09/88.28 tff(20631,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20630, 20626])).
% 88.09/88.28 tff(20632,plain,(
% 88.09/88.28 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 88.09/88.28 inference(skolemize,[status(sab)],[20631])).
% 88.09/88.28 tff(20633,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20632, 20625])).
% 88.09/88.28 tff(20634,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20635,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2))),
% 88.09/88.28 inference(quant_inst,[status(thm)],[])).
% 88.09/88.28 tff(20636,plain,
% 88.09/88.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2)),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20635, 20634])).
% 88.09/88.28 tff(20637,plain,
% 88.09/88.28 ($false),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20636, 20633, 20622, 20623, 20621])).
% 88.09/88.28 tff(20638,plain,((~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.28 tff(20639,plain,
% 88.09/88.28 (~node7(c_e_h_3, c_u, s1, s2)),
% 88.09/88.28 inference(unit_resolution,[status(thm)],[20638, 20621, 20622])).
% 88.09/88.28 tff(20640,plain,
% 88.09/88.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)))),
% 88.09/88.28 inference(bind,[status(th)],[])).
% 88.09/88.28 tff(20641,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 88.09/88.28 inference(quant_intro,[status(thm)],[20640])).
% 88.09/88.28 tff(20642,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 88.09/88.28 inference(rewrite,[status(thm)],[])).
% 88.09/88.28 tff(20643,plain,
% 88.09/88.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) | (~trans(X, Y))) <=> ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)))),
% 88.09/88.28 inference(bind,[status(th)],[])).
% 88.09/88.28 tff(20644,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 88.09/88.28 inference(quant_intro,[status(thm)],[20643])).
% 88.09/88.28 tff(20645,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_user_6')).
% 88.09/88.28 tff(20646,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20645, 20644])).
% 88.09/88.28 tff(20647,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20646, 20642])).
% 88.09/88.28 tff(20648,plain,(
% 88.09/88.28 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 88.09/88.28 inference(skolemize,[status(sab)],[20647])).
% 88.09/88.28 tff(20649,plain,
% 88.09/88.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 88.09/88.28 inference(modus_ponens,[status(thm)],[20648, 20641])).
% 88.09/88.28 tff(20650,plain,
% 88.09/88.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s1, s2)) | node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s1, s2)) | node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20651,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s1, s2)) | node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2))),
% 88.09/88.29 inference(quant_inst,[status(thm)],[])).
% 88.09/88.29 tff(20652,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s1, s2)) | node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2)),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20651, 20650])).
% 88.09/88.29 tff(20653,plain,
% 88.09/88.29 (node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20652, 20649, 344])).
% 88.09/88.29 tff(20654,plain,
% 88.09/88.29 (node8(c_e_h_3, c_u, s1, s2)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20653, 20639])).
% 88.09/88.29 tff(20655,assumption,(m_user_v_req(c_e_h_3, c_u, s1)), introduced(assumption)).
% 88.09/88.29 tff(20656,plain,
% 88.09/88.29 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X))) <=> (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X))))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20657,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20656])).
% 88.09/88.29 tff(20658,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20659,plain,
% 88.09/88.29 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) <=> (m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X)))), (((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))) <=> ((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))))), rewrite(((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))) <=> (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))), (((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))) <=> (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20660,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20659])).
% 88.09/88.29 tff(20661,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_user_4')).
% 88.09/88.29 tff(20662,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20661, 20660])).
% 88.09/88.29 tff(20663,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20662, 20658])).
% 88.09/88.29 tff(20664,plain,(
% 88.09/88.29 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 88.09/88.29 inference(skolemize,[status(sab)],[20663])).
% 88.09/88.29 tff(20665,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20664, 20657])).
% 88.09/88.29 tff(20666,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20667,plain,
% 88.09/88.29 ((m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1))) <=> ((~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20668,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2))))),
% 88.09/88.29 inference(monotonicity,[status(thm)],[20667])).
% 88.09/88.29 tff(20669,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)))),
% 88.09/88.29 inference(transitivity,[status(thm)],[20668, 20666])).
% 88.09/88.29 tff(20670,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)))),
% 88.09/88.29 inference(quant_inst,[status(thm)],[])).
% 88.09/88.29 tff(20671,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20670, 20669])).
% 88.09/88.29 tff(20672,plain,
% 88.09/88.29 ($false),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20671, 20665, 20655, 20654, 20621])).
% 88.09/88.29 tff(20673,plain,(m_user_v_req(c_e_h_3, c_u, s2) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_ack(c_e_h_3, c_u, s1)), inference(lemma,lemma(discharge,[]))).
% 88.09/88.29 tff(20674,plain,
% 88.09/88.29 (m_user_v_req(c_e_h_3, c_u, s2) | (~m_user_v_req(c_e_h_3, c_u, s1))),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20673, 20620])).
% 88.09/88.29 tff(20675,plain,
% 88.09/88.29 (m_user_v_req(c_e_h_3, c_u, s2)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20674, 20583])).
% 88.09/88.29 tff(20676,plain,
% 88.09/88.29 (^[I0: $i, X: $i] : refl(((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)) <=> ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20677,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20676])).
% 88.09/88.29 tff(20678,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20679,plain,
% 88.09/88.29 (^[I0: $i, X: $i] : rewrite((m_mutex_h_half_v_inp(I0, c_a, X) | (~m_user_v_req(I0, c_u, X))) <=> ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20680,plain,
% 88.09/88.29 (![I0: $i, X: $i] : (m_mutex_h_half_v_inp(I0, c_a, X) | (~m_user_v_req(I0, c_u, X))) <=> ![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20679])).
% 88.09/88.29 tff(20681,axiom,(![I0: $i, X: $i] : (m_mutex_h_half_v_inp(I0, c_a, X) | (~m_user_v_req(I0, c_u, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_1')).
% 88.09/88.29 tff(20682,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20681, 20680])).
% 88.09/88.29 tff(20683,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20682, 20678])).
% 88.09/88.29 tff(20684,plain,(
% 88.09/88.29 ![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 88.09/88.29 inference(skolemize,[status(sab)],[20683])).
% 88.09/88.29 tff(20685,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20684, 20677])).
% 88.09/88.29 tff(20686,plain,
% 88.09/88.29 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20687,plain,
% 88.09/88.29 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2))),
% 88.09/88.29 inference(quant_inst,[status(thm)],[])).
% 88.09/88.29 tff(20688,plain,
% 88.09/88.29 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20687, 20686])).
% 88.09/88.29 tff(20689,plain,
% 88.09/88.29 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20688, 20685, 20675])).
% 88.09/88.29 tff(20690,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)), introduced(assumption)).
% 88.09/88.29 tff(20691,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)), introduced(assumption)).
% 88.09/88.29 tff(20692,assumption,(node12(c_e_h_3, c_a, s2, s3)), introduced(assumption)).
% 88.09/88.29 tff(20693,plain,
% 88.09/88.29 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) <=> ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20694,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20693])).
% 88.09/88.29 tff(20695,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20696,plain,
% 88.09/88.29 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) <=> ((~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))), (((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) | (~node12(I0, I1, X, Y))) <=> (((~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) | (~node12(I0, I1, X, Y))))), rewrite((((~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) | (~node12(I0, I1, X, Y))) <=> ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))), (((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) | (~node12(I0, I1, X, Y))) <=> ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20697,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) | (~node12(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20696])).
% 88.09/88.29 tff(20698,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) | (~node12(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_mutex_h_half_2')).
% 88.09/88.29 tff(20699,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20698, 20697])).
% 88.09/88.29 tff(20700,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20699, 20695])).
% 88.09/88.29 tff(20701,plain,(
% 88.09/88.29 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 88.09/88.29 inference(skolemize,[status(sab)],[20700])).
% 88.09/88.29 tff(20702,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20701, 20694])).
% 88.09/88.29 tff(20703,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20704,plain,
% 88.09/88.29 (((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) <=> (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20705,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3))))),
% 88.09/88.29 inference(monotonicity,[status(thm)],[20704])).
% 88.09/88.29 tff(20706,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 88.09/88.29 inference(transitivity,[status(thm)],[20705, 20703])).
% 88.09/88.29 tff(20707,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))),
% 88.09/88.29 inference(quant_inst,[status(thm)],[])).
% 88.09/88.29 tff(20708,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20707, 20706])).
% 88.09/88.29 tff(20709,plain,
% 88.09/88.29 ($false),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20708, 20702, 20690, 20692, 20691])).
% 88.09/88.29 tff(20710,plain,((~node12(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2))), inference(lemma,lemma(discharge,[]))).
% 88.09/88.29 tff(20711,plain,
% 88.09/88.29 (~node12(c_e_h_3, c_a, s2, s3)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20710, 20690, 20689])).
% 88.09/88.29 tff(20712,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20713,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3))),
% 88.09/88.29 inference(quant_inst,[status(thm)],[])).
% 88.09/88.29 tff(20714,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3)),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20713, 20712])).
% 88.09/88.29 tff(20715,plain,
% 88.09/88.29 (node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20714, 17707, 582])).
% 88.09/88.29 tff(20716,plain,
% 88.09/88.29 (node13(c_e_h_3, c_a, s2, s3)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20715, 20711])).
% 88.09/88.29 tff(20717,plain,
% 88.09/88.29 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X))) <=> (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X))))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20718,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20717])).
% 88.09/88.29 tff(20719,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20720,plain,
% 88.09/88.29 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) <=> (m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X)))), (((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))) <=> ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))))), rewrite(((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))) <=> (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))), (((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))) <=> (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20721,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20720])).
% 88.09/88.29 tff(20722,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_mutex_h_half_4')).
% 88.09/88.29 tff(20723,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20722, 20721])).
% 88.09/88.29 tff(20724,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20723, 20719])).
% 88.09/88.29 tff(20725,plain,(
% 88.09/88.29 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 88.09/88.29 inference(skolemize,[status(sab)],[20724])).
% 88.09/88.29 tff(20726,plain,
% 88.09/88.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20725, 20718])).
% 88.09/88.29 tff(20727,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3)))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20728,plain,
% 88.09/88.29 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~node13(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2))) <=> (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3)))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20729,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~node13(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3))))),
% 88.09/88.29 inference(monotonicity,[status(thm)],[20728])).
% 88.09/88.29 tff(20730,plain,
% 88.09/88.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~node13(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3)))),
% 88.09/88.29 inference(transitivity,[status(thm)],[20729, 20727])).
% 88.09/88.29 tff(20731,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~node13(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))),
% 88.09/88.29 inference(quant_inst,[status(thm)],[])).
% 88.09/88.29 tff(20732,plain,
% 88.09/88.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20731, 20730])).
% 88.09/88.29 tff(20733,plain,
% 88.09/88.29 ($false),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20732, 20726, 20690, 20560, 20716])).
% 88.09/88.29 tff(20734,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2))), inference(lemma,lemma(discharge,[]))).
% 88.09/88.29 tff(20735,plain,
% 88.09/88.29 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20734, 20559])).
% 88.09/88.29 tff(20736,plain,
% 88.09/88.29 (^[I0: $i, X: $i] : refl(((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)) <=> ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20737,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20736])).
% 88.09/88.29 tff(20738,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20739,plain,
% 88.09/88.29 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in1(I0, c_c, X) | (~m_mutex_h_half_v_out(I0, c_a, X))) <=> ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20740,plain,
% 88.09/88.29 (![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_c, X) | (~m_mutex_h_half_v_out(I0, c_a, X))) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20739])).
% 88.09/88.29 tff(20741,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_c, X) | (~m_mutex_h_half_v_out(I0, c_a, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_10')).
% 88.09/88.29 tff(20742,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20741, 20740])).
% 88.09/88.29 tff(20743,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20742, 20738])).
% 88.09/88.29 tff(20744,plain,(
% 88.09/88.29 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 88.09/88.29 inference(skolemize,[status(sab)],[20743])).
% 88.09/88.29 tff(20745,plain,
% 88.09/88.29 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20744, 20737])).
% 88.09/88.29 tff(20746,plain,
% 88.09/88.29 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20747,plain,
% 88.09/88.29 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))),
% 88.09/88.29 inference(quant_inst,[status(thm)],[])).
% 88.09/88.29 tff(20748,plain,
% 88.09/88.29 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20747, 20746])).
% 88.09/88.29 tff(20749,plain,
% 88.09/88.29 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20748, 20745, 20735])).
% 88.09/88.29 tff(20750,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s3)), introduced(assumption)).
% 88.09/88.29 tff(20751,assumption,(node21(c_e_h_3, c_c, s3, s4)), introduced(assumption)).
% 88.09/88.29 tff(20752,plain,
% 88.09/88.29 (^[I0: $i, X: $i, J0: $i] : refl(((~m_cell_v_left(I0, J0)) | node2(I0, J0, X)) <=> ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X)))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20753,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20752])).
% 88.09/88.29 tff(20754,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20755,axiom,(![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_14')).
% 88.09/88.29 tff(20756,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20755, 20754])).
% 88.09/88.29 tff(20757,plain,(
% 88.09/88.29 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 88.09/88.29 inference(skolemize,[status(sab)],[20756])).
% 88.09/88.29 tff(20758,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20757, 20753])).
% 88.09/88.29 tff(20759,plain,
% 88.09/88.29 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s3))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20760,plain,
% 88.09/88.29 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s3))),
% 88.09/88.29 inference(quant_inst,[status(thm)],[])).
% 88.09/88.29 tff(20761,plain,
% 88.09/88.29 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s3)),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20760, 20759])).
% 88.09/88.29 tff(20762,plain,
% 88.09/88.29 (node2(c_e_h_3, c_e_h_1, s3)),
% 88.09/88.29 inference(unit_resolution,[status(thm)],[20761, 3860, 20758])).
% 88.09/88.29 tff(20763,plain,
% 88.09/88.29 (^[I0: $i, X: $i, J0: $i] : refl(((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) <=> ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20764,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20763])).
% 88.09/88.29 tff(20765,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 88.09/88.29 inference(rewrite,[status(thm)],[])).
% 88.09/88.29 tff(20766,plain,
% 88.09/88.29 (^[I0: $i, X: $i, J0: $i] : trans(monotonicity(rewrite((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) <=> (m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))), (((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) | (~node2(I0, J0, X))) <=> ((m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) | (~node2(I0, J0, X))))), rewrite(((m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) | (~node2(I0, J0, X))) <=> ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))), (((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) | (~node2(I0, J0, X))) <=> ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))))),
% 88.09/88.29 inference(bind,[status(th)],[])).
% 88.09/88.29 tff(20767,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) | (~node2(I0, J0, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 88.09/88.29 inference(quant_intro,[status(thm)],[20766])).
% 88.09/88.29 tff(20768,axiom,(![I0: $i, X: $i, J0: $i] : ((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) | (~node2(I0, J0, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_12')).
% 88.09/88.29 tff(20769,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20768, 20767])).
% 88.09/88.29 tff(20770,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20769, 20765])).
% 88.09/88.29 tff(20771,plain,(
% 88.09/88.29 ![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 88.09/88.29 inference(skolemize,[status(sab)],[20770])).
% 88.09/88.29 tff(20772,plain,
% 88.09/88.29 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 88.09/88.29 inference(modus_ponens,[status(thm)],[20771, 20764])).
% 88.09/88.30 tff(20773,plain,
% 88.09/88.30 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s3)) | m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s3)) | m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3))),
% 88.09/88.30 inference(rewrite,[status(thm)],[])).
% 88.09/88.30 tff(20774,plain,
% 88.09/88.30 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s3)) | m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3))),
% 88.09/88.30 inference(quant_inst,[status(thm)],[])).
% 88.09/88.30 tff(20775,plain,
% 88.09/88.30 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s3)) | m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3)),
% 88.09/88.30 inference(modus_ponens,[status(thm)],[20774, 20773])).
% 88.09/88.30 tff(20776,plain,
% 88.09/88.30 (m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3)),
% 88.09/88.30 inference(unit_resolution,[status(thm)],[20775, 20772, 20762])).
% 88.09/88.30 tff(20777,plain,
% 88.09/88.30 (m_and_h_gate_v_in2(c_e_h_3, c_c, s3)),
% 88.09/88.30 inference(unit_resolution,[status(thm)],[20776, 6541])).
% 88.09/88.30 tff(20778,plain,
% 88.09/88.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) <=> ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)))),
% 88.09/88.30 inference(bind,[status(th)],[])).
% 88.09/88.30 tff(20779,plain,
% 88.09/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 88.09/88.30 inference(quant_intro,[status(thm)],[20778])).
% 88.09/88.30 tff(20780,plain,
% 88.09/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 88.09/88.30 inference(rewrite,[status(thm)],[])).
% 88.09/88.30 tff(20781,plain,
% 88.09/88.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(trans(monotonicity(rewrite((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) <=> ((~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))), (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) <=> (((~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) | (~m_and_h_gate_v_in2(I0, I1, X))))), rewrite((((~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) | (~m_and_h_gate_v_in2(I0, I1, X))) <=> ((~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))), (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) <=> ((~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)))), ((((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) | (~node21(I0, I1, X, Y))) <=> (((~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))))), rewrite((((~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))), ((((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) | (~node21(I0, I1, X, Y))) <=> ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20782,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20781])).
% 88.12/88.30 tff(20783,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) | (~node21(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_and_h_gate_4')).
% 88.12/88.30 tff(20784,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20783, 20782])).
% 88.12/88.30 tff(20785,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20784, 20780])).
% 88.12/88.30 tff(20786,plain,(
% 88.12/88.30 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(skolemize,[status(sab)],[20785])).
% 88.12/88.30 tff(20787,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20786, 20779])).
% 88.12/88.30 tff(20788,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4)))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20789,plain,
% 88.12/88.30 (((~node21(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4)))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20790,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4))))),
% 88.12/88.30 inference(monotonicity,[status(thm)],[20789])).
% 88.12/88.30 tff(20791,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4)))),
% 88.12/88.30 inference(transitivity,[status(thm)],[20790, 20788])).
% 88.12/88.30 tff(20792,plain,
% 88.12/88.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))),
% 88.12/88.30 inference(quant_inst,[status(thm)],[])).
% 88.12/88.30 tff(20793,plain,
% 88.12/88.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20792, 20791])).
% 88.12/88.30 tff(20794,plain,
% 88.12/88.30 ($false),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20793, 20787, 20777, 20500, 20751, 20750])).
% 88.12/88.30 tff(20795,plain,((~node21(c_e_h_3, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3))), inference(lemma,lemma(discharge,[]))).
% 88.12/88.30 tff(20796,plain,
% 88.12/88.30 (~node21(c_e_h_3, c_c, s3, s4)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20795, 20500, 20749])).
% 88.12/88.30 tff(20797,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20798,plain,
% 88.12/88.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4))),
% 88.12/88.30 inference(quant_inst,[status(thm)],[])).
% 88.12/88.30 tff(20799,plain,
% 88.12/88.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4)),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20798, 20797])).
% 88.12/88.30 tff(20800,plain,
% 88.12/88.30 (node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20799, 81, 679])).
% 88.12/88.30 tff(20801,plain,
% 88.12/88.30 ($false),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20800, 20796, 20520])).
% 88.12/88.30 tff(20802,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3))), inference(lemma,lemma(discharge,[]))).
% 88.12/88.30 tff(20803,plain,
% 88.12/88.30 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20802, 20498])).
% 88.12/88.30 tff(20804,plain,
% 88.12/88.30 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)) <=> ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20805,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20804])).
% 88.12/88.30 tff(20806,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20807,plain,
% 88.12/88.30 (^[I0: $i, X: $i] : rewrite((m_or_h_gate_v_in1(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_c, X))) <=> ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20808,plain,
% 88.12/88.30 (![I0: $i, X: $i] : (m_or_h_gate_v_in1(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_c, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20807])).
% 88.12/88.30 tff(20809,axiom,(![I0: $i, X: $i] : (m_or_h_gate_v_in1(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_c, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_27')).
% 88.12/88.30 tff(20810,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20809, 20808])).
% 88.12/88.30 tff(20811,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20810, 20806])).
% 88.12/88.30 tff(20812,plain,(
% 88.12/88.30 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 88.12/88.30 inference(skolemize,[status(sab)],[20811])).
% 88.12/88.30 tff(20813,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20812, 20805])).
% 88.12/88.30 tff(20814,plain,
% 88.12/88.30 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20815,plain,
% 88.12/88.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4))),
% 88.12/88.30 inference(quant_inst,[status(thm)],[])).
% 88.12/88.30 tff(20816,plain,
% 88.12/88.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20815, 20814])).
% 88.12/88.30 tff(20817,plain,
% 88.12/88.30 (m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20816, 20813, 20803])).
% 88.12/88.30 tff(20818,plain,
% 88.12/88.30 (^[I0: $i, X: $i, I1: $i] : refl(((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X))) <=> ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X))))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20819,plain,
% 88.12/88.30 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20818])).
% 88.12/88.30 tff(20820,plain,
% 88.12/88.30 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20821,axiom,(![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_or_h_gate_2')).
% 88.12/88.30 tff(20822,plain,
% 88.12/88.30 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20821, 20820])).
% 88.12/88.30 tff(20823,plain,(
% 88.12/88.30 ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 88.12/88.30 inference(skolemize,[status(sab)],[20822])).
% 88.12/88.30 tff(20824,plain,
% 88.12/88.30 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20823, 20819])).
% 88.12/88.30 tff(20825,plain,
% 88.12/88.30 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | (~node4(c_e_h_3, c_g, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | (~node4(c_e_h_3, c_g, s4)))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20826,plain,
% 88.12/88.30 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | (~node4(c_e_h_3, c_g, s4)))),
% 88.12/88.30 inference(quant_inst,[status(thm)],[])).
% 88.12/88.30 tff(20827,plain,
% 88.12/88.30 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | (~node4(c_e_h_3, c_g, s4))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20826, 20825])).
% 88.12/88.30 tff(20828,plain,
% 88.12/88.30 (~node4(c_e_h_3, c_g, s4)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20827, 20824, 20817])).
% 88.12/88.30 tff(20829,assumption,(~node4(c_e_h_3, c_g, s4)), introduced(assumption)).
% 88.12/88.30 tff(20830,assumption,(node5(c_e_h_3, c_g, s4, s5)), introduced(assumption)).
% 88.12/88.30 tff(20831,plain,
% 88.12/88.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)) <=> (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20832,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20831])).
% 88.12/88.30 tff(20833,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20834,plain,
% 88.12/88.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((m_or_h_gate_v_out(I0, I1, Y) | node4(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20835,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_or_h_gate_v_out(I0, I1, Y) | node4(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20834])).
% 88.12/88.30 tff(20836,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_or_h_gate_v_out(I0, I1, Y) | node4(I0, I1, X)) | (~node5(I0, I1, X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_or_h_gate_4')).
% 88.12/88.30 tff(20837,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20836, 20835])).
% 88.12/88.30 tff(20838,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20837, 20833])).
% 88.12/88.30 tff(20839,plain,(
% 88.12/88.30 ![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(skolemize,[status(sab)],[20838])).
% 88.12/88.30 tff(20840,plain,
% 88.12/88.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20839, 20832])).
% 88.12/88.30 tff(20841,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | ((~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | node4(c_e_h_3, c_g, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | node4(c_e_h_3, c_g, s4))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20842,plain,
% 88.12/88.30 ((node4(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)) <=> ((~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | node4(c_e_h_3, c_g, s4))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20843,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | ((~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | node4(c_e_h_3, c_g, s4)))),
% 88.12/88.30 inference(monotonicity,[status(thm)],[20842])).
% 88.12/88.30 tff(20844,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | node4(c_e_h_3, c_g, s4))),
% 88.12/88.30 inference(transitivity,[status(thm)],[20843, 20841])).
% 88.12/88.30 tff(20845,plain,
% 88.12/88.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))),
% 88.12/88.30 inference(quant_inst,[status(thm)],[])).
% 88.12/88.30 tff(20846,plain,
% 88.12/88.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | node4(c_e_h_3, c_g, s4)),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20845, 20844])).
% 88.12/88.30 tff(20847,plain,
% 88.12/88.30 ($false),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20846, 20840, 20830, 20317, 20829])).
% 88.12/88.30 tff(20848,plain,((~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | node4(c_e_h_3, c_g, s4)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.30 tff(20849,plain,
% 88.12/88.30 (~node5(c_e_h_3, c_g, s4, s5)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20848, 20317, 20828])).
% 88.12/88.30 tff(20850,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20851,plain,
% 88.12/88.30 ((node6(c_e_h_3, c_g, s4, s5) | node5(c_e_h_3, c_g, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20852,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s4, s5) | node5(c_e_h_3, c_g, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5)))),
% 88.12/88.30 inference(monotonicity,[status(thm)],[20851])).
% 88.12/88.30 tff(20853,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s4, s5) | node5(c_e_h_3, c_g, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5))),
% 88.12/88.30 inference(transitivity,[status(thm)],[20852, 20850])).
% 88.12/88.30 tff(20854,plain,
% 88.12/88.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s4, s5) | node5(c_e_h_3, c_g, s4, s5) | (~trans(s4, s5)))),
% 88.12/88.30 inference(quant_inst,[status(thm)],[])).
% 88.12/88.30 tff(20855,plain,
% 88.12/88.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5)),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20854, 20853])).
% 88.12/88.30 tff(20856,plain,
% 88.12/88.30 (node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20855, 881, 1432])).
% 88.12/88.30 tff(20857,plain,
% 88.12/88.30 ($false),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20856, 20849, 20337])).
% 88.12/88.30 tff(20858,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4))), inference(lemma,lemma(discharge,[]))).
% 88.12/88.30 tff(20859,plain,
% 88.12/88.30 (m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20858, 20315])).
% 88.12/88.30 tff(20860,plain,
% 88.12/88.30 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)) <=> ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20861,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20860])).
% 88.12/88.30 tff(20862,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20863,plain,
% 88.12/88.30 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in1(I0, c_k, X) | (~m_or_h_gate_v_out(I0, c_g, X))) <=> ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20864,plain,
% 88.12/88.30 (![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_k, X) | (~m_or_h_gate_v_out(I0, c_g, X))) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20863])).
% 88.12/88.30 tff(20865,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_k, X) | (~m_or_h_gate_v_out(I0, c_g, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_43')).
% 88.12/88.30 tff(20866,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20865, 20864])).
% 88.12/88.30 tff(20867,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20866, 20862])).
% 88.12/88.30 tff(20868,plain,(
% 88.12/88.30 ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 88.12/88.30 inference(skolemize,[status(sab)],[20867])).
% 88.12/88.30 tff(20869,plain,
% 88.12/88.30 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20868, 20861])).
% 88.12/88.30 tff(20870,plain,
% 88.12/88.30 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20871,plain,
% 88.12/88.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))),
% 88.12/88.30 inference(quant_inst,[status(thm)],[])).
% 88.12/88.30 tff(20872,plain,
% 88.12/88.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20871, 20870])).
% 88.12/88.30 tff(20873,plain,
% 88.12/88.30 (m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20872, 20869, 20859])).
% 88.12/88.30 tff(20874,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s5)), introduced(assumption)).
% 88.12/88.30 tff(20875,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s6)), introduced(assumption)).
% 88.12/88.30 tff(20876,assumption,(node21(c_e_h_3, c_k, s5, s6)), introduced(assumption)).
% 88.12/88.30 tff(20877,plain,
% 88.12/88.30 (^[I0: $i, X: $i] : refl((m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X)) <=> (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X)))),
% 88.12/88.30 inference(bind,[status(th)],[])).
% 88.12/88.30 tff(20878,plain,
% 88.12/88.30 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 88.12/88.30 inference(quant_intro,[status(thm)],[20877])).
% 88.12/88.30 tff(20879,plain,
% 88.12/88.30 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20880,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_45')).
% 88.12/88.30 tff(20881,plain,
% 88.12/88.30 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20880, 20879])).
% 88.12/88.30 tff(20882,plain,(
% 88.12/88.30 ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 88.12/88.30 inference(skolemize,[status(sab)],[20881])).
% 88.12/88.30 tff(20883,plain,
% 88.12/88.30 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20882, 20878])).
% 88.12/88.30 tff(20884,plain,
% 88.12/88.30 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 88.12/88.30 inference(rewrite,[status(thm)],[])).
% 88.12/88.30 tff(20885,plain,
% 88.12/88.30 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 88.12/88.30 inference(quant_inst,[status(thm)],[])).
% 88.12/88.30 tff(20886,plain,
% 88.12/88.30 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 88.12/88.30 inference(modus_ponens,[status(thm)],[20885, 20884])).
% 88.12/88.30 tff(20887,plain,
% 88.12/88.30 (m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20886, 20883])).
% 88.12/88.30 tff(20888,plain,
% 88.12/88.30 (m_and_h_gate_v_in2(c_e_h_3, c_k, s5)),
% 88.12/88.30 inference(unit_resolution,[status(thm)],[20887, 16250])).
% 88.12/88.30 tff(20889,plain,
% 88.12/88.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20890,plain,
% 88.12/88.31 (((~node21(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6)) <=> ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20891,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6))))),
% 88.12/88.31 inference(monotonicity,[status(thm)],[20890])).
% 88.12/88.31 tff(20892,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6)))),
% 88.12/88.31 inference(transitivity,[status(thm)],[20891, 20889])).
% 88.12/88.31 tff(20893,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20894,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20893, 20892])).
% 88.12/88.31 tff(20895,plain,
% 88.12/88.31 ($false),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20894, 20787, 20888, 20875, 20876, 20874])).
% 88.12/88.31 tff(20896,plain,((~node21(c_e_h_3, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 88.12/88.31 tff(20897,plain,
% 88.12/88.31 (~node21(c_e_h_3, c_k, s5, s6)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20896, 20875, 20874])).
% 88.12/88.31 tff(20898,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20899,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20900,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6)),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20899, 20898])).
% 88.12/88.31 tff(20901,plain,
% 88.12/88.31 (node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20900, 81, 1499])).
% 88.12/88.31 tff(20902,plain,
% 88.12/88.31 (node22(c_e_h_3, c_k, s5, s6)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20901, 20897])).
% 88.12/88.31 tff(20903,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20904,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20905,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20904, 20903])).
% 88.12/88.31 tff(20906,plain,
% 88.12/88.31 ($false),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20905, 20511, 20280, 20875, 20902])).
% 88.12/88.31 tff(20907,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 88.12/88.31 tff(20908,plain,
% 88.12/88.31 (m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20907, 20873, 20273])).
% 88.12/88.31 tff(20909,plain,
% 88.12/88.31 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)) <=> ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)))),
% 88.12/88.31 inference(bind,[status(th)],[])).
% 88.12/88.31 tff(20910,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 88.12/88.31 inference(quant_intro,[status(thm)],[20909])).
% 88.12/88.31 tff(20911,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20912,plain,
% 88.12/88.31 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in1(I0, c_l, X) | (~m_and_h_gate_v_out(I0, c_k, X))) <=> ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)))),
% 88.12/88.31 inference(bind,[status(th)],[])).
% 88.12/88.31 tff(20913,plain,
% 88.12/88.31 (![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_l, X) | (~m_and_h_gate_v_out(I0, c_k, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 88.12/88.31 inference(quant_intro,[status(thm)],[20912])).
% 88.12/88.31 tff(20914,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_l, X) | (~m_and_h_gate_v_out(I0, c_k, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_47')).
% 88.12/88.31 tff(20915,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20914, 20913])).
% 88.12/88.31 tff(20916,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20915, 20911])).
% 88.12/88.31 tff(20917,plain,(
% 88.12/88.31 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 88.12/88.31 inference(skolemize,[status(sab)],[20916])).
% 88.12/88.31 tff(20918,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20917, 20910])).
% 88.12/88.31 tff(20919,plain,
% 88.12/88.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20920,plain,
% 88.12/88.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20921,plain,
% 88.12/88.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20920, 20919])).
% 88.12/88.31 tff(20922,plain,
% 88.12/88.31 (m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20921, 20918, 20908])).
% 88.12/88.31 tff(20923,plain,
% 88.12/88.31 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s8))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20924,plain,
% 88.12/88.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s8))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20925,plain,
% 88.12/88.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s8)),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20924, 20923])).
% 88.12/88.31 tff(20926,plain,
% 88.12/88.31 (m_and_h_gate_v_in2(c_e_h_3, c_i, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20925, 1535, 20019])).
% 88.12/88.31 tff(20927,plain,
% 88.12/88.31 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X))) <=> ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X))))),
% 88.12/88.31 inference(bind,[status(th)],[])).
% 88.12/88.31 tff(20928,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 88.12/88.31 inference(quant_intro,[status(thm)],[20927])).
% 88.12/88.31 tff(20929,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20930,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_38')).
% 88.12/88.31 tff(20931,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20930, 20929])).
% 88.12/88.31 tff(20932,plain,(
% 88.12/88.31 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 88.12/88.31 inference(skolemize,[status(sab)],[20931])).
% 88.12/88.31 tff(20933,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20932, 20928])).
% 88.12/88.31 tff(20934,plain,
% 88.12/88.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20935,plain,
% 88.12/88.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20936,plain,
% 88.12/88.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20935, 20934])).
% 88.12/88.31 tff(20937,plain,
% 88.12/88.31 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20936, 20933, 20926])).
% 88.12/88.31 tff(20938,plain,
% 88.12/88.31 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20234, 20177, 20197])).
% 88.12/88.31 tff(20939,plain,
% 88.12/88.31 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20026, 23, 20938])).
% 88.12/88.31 tff(20940,plain,
% 88.12/88.31 (~node20(c_e_h_3, c_i, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20022, 37, 20939])).
% 88.12/88.31 tff(20941,plain,
% 88.12/88.31 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[18223, 23, 20177])).
% 88.12/88.31 tff(20942,plain,
% 88.12/88.31 (~node20(c_e_h_3, c_i, s7)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[18227, 37, 20941])).
% 88.12/88.31 tff(20943,plain,
% 88.12/88.31 (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[18252, 20942, 18239])).
% 88.12/88.31 tff(20944,plain,
% 88.12/88.31 (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20017, 20943, 20940])).
% 88.12/88.31 tff(20945,plain,
% 88.12/88.31 (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[19998, 20944])).
% 88.12/88.31 tff(20946,plain,
% 88.12/88.31 (m_c_h_element_v_out(c_e_h_3, c_e, s9)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[19989, 20945, 19243])).
% 88.12/88.31 tff(20947,plain,
% 88.12/88.31 (m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[19927, 20946, 19853])).
% 88.12/88.31 tff(20948,plain,
% 88.12/88.31 ($false),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[19850, 365, 20943, 20947])).
% 88.12/88.31 tff(20949,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s7) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.31 tff(20950,plain,
% 88.12/88.31 ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20949, 19846, 18220, 19768])).
% 88.12/88.31 tff(20951,plain,
% 88.12/88.31 (m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20950, 19243])).
% 88.12/88.31 tff(20952,plain,
% 88.12/88.31 (m_or_h_gate_v_out(c_e_h_3, c_j, s7)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20175, 309, 20951])).
% 88.12/88.31 tff(20953,assumption,(node6(c_e_h_3, c_j, s7, s8)), introduced(assumption)).
% 88.12/88.31 tff(20954,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s8)), introduced(assumption)).
% 88.12/88.31 tff(20955,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s7, s8)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20956,plain,
% 88.12/88.31 ((m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7))) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s7, s8)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20957,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s7, s8))))),
% 88.12/88.31 inference(monotonicity,[status(thm)],[20956])).
% 88.12/88.31 tff(20958,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s7, s8)))),
% 88.12/88.31 inference(transitivity,[status(thm)],[20957, 20955])).
% 88.12/88.31 tff(20959,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20960,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | (~node6(c_e_h_3, c_j, s7, s8))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20959, 20958])).
% 88.12/88.31 tff(20961,plain,
% 88.12/88.31 ($false),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20960, 20328, 20143, 20954, 20953])).
% 88.12/88.31 tff(20962,plain,((~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.31 tff(20963,plain,
% 88.12/88.31 (~node6(c_e_h_3, c_j, s7, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20962, 20952, 20937])).
% 88.12/88.31 tff(20964,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20965,plain,
% 88.12/88.31 ((node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8) | (~trans(s7, s8))) <=> ((~trans(s7, s8)) | node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20966,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8)))),
% 88.12/88.31 inference(monotonicity,[status(thm)],[20965])).
% 88.12/88.31 tff(20967,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8))),
% 88.12/88.31 inference(transitivity,[status(thm)],[20966, 20964])).
% 88.12/88.31 tff(20968,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8) | (~trans(s7, s8)))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20969,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8)),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20968, 20967])).
% 88.12/88.31 tff(20970,plain,
% 88.12/88.31 (node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20969, 881, 2152])).
% 88.12/88.31 tff(20971,plain,
% 88.12/88.31 (node5(c_e_h_3, c_j, s7, s8)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20970, 20963])).
% 88.12/88.31 tff(20972,assumption,(~node4(c_e_h_3, c_j, s7)), introduced(assumption)).
% 88.12/88.31 tff(20973,assumption,(node5(c_e_h_3, c_j, s7, s8)), introduced(assumption)).
% 88.12/88.31 tff(20974,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20975,plain,
% 88.12/88.31 ((node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20976,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8))))),
% 88.12/88.31 inference(monotonicity,[status(thm)],[20975])).
% 88.12/88.31 tff(20977,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)))),
% 88.12/88.31 inference(transitivity,[status(thm)],[20976, 20974])).
% 88.12/88.31 tff(20978,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20979,plain,
% 88.12/88.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20978, 20977])).
% 88.12/88.31 tff(20980,plain,
% 88.12/88.31 ($false),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20979, 20840, 20954, 20973, 20972])).
% 88.12/88.31 tff(20981,plain,((~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.31 tff(20982,plain,
% 88.12/88.31 (node4(c_e_h_3, c_j, s7)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20981, 20971, 20937])).
% 88.12/88.31 tff(20983,plain,
% 88.12/88.31 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | (~node4(c_e_h_3, c_j, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | (~node4(c_e_h_3, c_j, s7)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20984,plain,
% 88.12/88.31 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | (~node4(c_e_h_3, c_j, s7)))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20985,plain,
% 88.12/88.31 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | (~node4(c_e_h_3, c_j, s7))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20984, 20983])).
% 88.12/88.31 tff(20986,plain,
% 88.12/88.31 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20985, 20824, 20982])).
% 88.12/88.31 tff(20987,plain,
% 88.12/88.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20988,plain,
% 88.12/88.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(20989,plain,
% 88.12/88.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7)),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20988, 20987])).
% 88.12/88.31 tff(20990,plain,
% 88.12/88.31 (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[20989, 8451, 20986])).
% 88.12/88.31 tff(20991,assumption,(node21(c_e_h_3, c_l, s6, s7)), introduced(assumption)).
% 88.12/88.31 tff(20992,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s6)), introduced(assumption)).
% 88.12/88.31 tff(20993,plain,
% 88.12/88.31 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)) <=> ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)))),
% 88.12/88.31 inference(bind,[status(th)],[])).
% 88.12/88.31 tff(20994,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 88.12/88.31 inference(quant_intro,[status(thm)],[20993])).
% 88.12/88.31 tff(20995,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(20996,plain,
% 88.12/88.31 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in2(I0, c_l, X) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)))),
% 88.12/88.31 inference(bind,[status(th)],[])).
% 88.12/88.31 tff(20997,plain,
% 88.12/88.31 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_l, X) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 88.12/88.31 inference(quant_intro,[status(thm)],[20996])).
% 88.12/88.31 tff(20998,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_l, X) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_cell_49')).
% 88.12/88.31 tff(20999,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20998, 20997])).
% 88.12/88.31 tff(21000,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[20999, 20995])).
% 88.12/88.31 tff(21001,plain,(
% 88.12/88.31 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 88.12/88.31 inference(skolemize,[status(sab)],[21000])).
% 88.12/88.31 tff(21002,plain,
% 88.12/88.31 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[21001, 20994])).
% 88.12/88.31 tff(21003,plain,
% 88.12/88.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s6))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(21004,plain,
% 88.12/88.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s6))),
% 88.12/88.31 inference(quant_inst,[status(thm)],[])).
% 88.12/88.31 tff(21005,plain,
% 88.12/88.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s6)),
% 88.12/88.31 inference(modus_ponens,[status(thm)],[21004, 21003])).
% 88.12/88.31 tff(21006,plain,
% 88.12/88.31 (m_and_h_gate_v_in2(c_e_h_3, c_l, s6)),
% 88.12/88.31 inference(unit_resolution,[status(thm)],[21005, 21002, 11984])).
% 88.12/88.31 tff(21007,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s7)), introduced(assumption)).
% 88.12/88.31 tff(21008,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(21009,plain,
% 88.12/88.31 (((~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)))),
% 88.12/88.31 inference(rewrite,[status(thm)],[])).
% 88.12/88.31 tff(21010,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6))))),
% 88.12/88.31 inference(monotonicity,[status(thm)],[21009])).
% 88.12/88.31 tff(21011,plain,
% 88.12/88.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)))),
% 88.12/88.32 inference(transitivity,[status(thm)],[21010, 21008])).
% 88.12/88.32 tff(21012,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21013,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6))),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21012, 21011])).
% 88.12/88.32 tff(21014,plain,
% 88.12/88.32 ($false),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21013, 20787, 21007, 21006, 20992, 20991])).
% 88.12/88.32 tff(21015,plain,((~node21(c_e_h_3, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6))), inference(lemma,lemma(discharge,[]))).
% 88.12/88.32 tff(21016,plain,
% 88.12/88.32 (~node21(c_e_h_3, c_l, s6, s7)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21015, 20990, 20922])).
% 88.12/88.32 tff(21017,plain,
% 88.12/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21018,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21019,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21018, 21017])).
% 88.12/88.32 tff(21020,plain,
% 88.12/88.32 (node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21019, 81, 1552])).
% 88.12/88.32 tff(21021,plain,
% 88.12/88.32 (node22(c_e_h_3, c_l, s6, s7)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21020, 21016])).
% 88.12/88.32 tff(21022,plain,
% 88.12/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s6, s7)))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21023,plain,
% 88.12/88.32 ((m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6))) <=> (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s6, s7)))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21024,plain,
% 88.12/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s6, s7))))),
% 88.12/88.32 inference(monotonicity,[status(thm)],[21023])).
% 88.12/88.32 tff(21025,plain,
% 88.12/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s6, s7)))),
% 88.12/88.32 inference(transitivity,[status(thm)],[21024, 21022])).
% 88.12/88.32 tff(21026,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21027,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s6, s7))),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21026, 21025])).
% 88.12/88.32 tff(21028,plain,
% 88.12/88.32 ($false),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21027, 20511, 20990, 21021, 20245])).
% 88.12/88.32 tff(21029,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.32 tff(21030,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s10)), introduced(assumption)).
% 88.12/88.32 tff(21031,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s10)), introduced(assumption)).
% 88.12/88.32 tff(21032,plain,
% 88.12/88.32 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21033,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21034,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21033, 21032])).
% 88.12/88.32 tff(21035,plain,
% 88.12/88.32 ($false),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21034, 1884, 21031, 21030])).
% 88.12/88.32 tff(21036,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.32 tff(21037,plain,
% 88.12/88.32 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21036, 21029])).
% 88.12/88.32 tff(21038,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)), introduced(assumption)).
% 88.12/88.32 tff(21039,assumption,(node20(c_e_h_3, c_r, s10)), introduced(assumption)).
% 88.12/88.32 tff(21040,plain,
% 88.12/88.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21041,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21042,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21041, 21040])).
% 88.12/88.32 tff(21043,plain,
% 88.12/88.32 ($false),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21042, 37, 21039, 21038])).
% 88.12/88.32 tff(21044,plain,((~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.32 tff(21045,plain,
% 88.12/88.32 (~node20(c_e_h_3, c_r, s10)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21044, 21037])).
% 88.12/88.32 tff(21046,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s7)), introduced(assumption)).
% 88.12/88.32 tff(21047,plain,
% 88.12/88.32 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21048,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21049,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21048, 21047])).
% 88.12/88.32 tff(21050,plain,
% 88.12/88.32 ($false),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21049, 1884, 19774, 21046])).
% 88.12/88.32 tff(21051,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.32 tff(21052,plain,
% 88.12/88.32 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21051, 19767])).
% 88.12/88.32 tff(21053,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)), introduced(assumption)).
% 88.12/88.32 tff(21054,assumption,(node20(c_e_h_3, c_r, s7)), introduced(assumption)).
% 88.12/88.32 tff(21055,plain,
% 88.12/88.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21056,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21057,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21056, 21055])).
% 88.12/88.32 tff(21058,plain,
% 88.12/88.32 ($false),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21057, 37, 21054, 21053])).
% 88.12/88.32 tff(21059,plain,((~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 88.12/88.32 tff(21060,plain,
% 88.12/88.32 (~node20(c_e_h_3, c_r, s7)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21059, 21052])).
% 88.12/88.32 tff(21061,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s6)), introduced(assumption)).
% 88.12/88.32 tff(21062,plain,
% 88.12/88.32 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21063,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21064,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21063, 21062])).
% 88.12/88.32 tff(21065,plain,
% 88.12/88.32 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21064, 1884, 19427])).
% 88.12/88.32 tff(21066,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s4)), introduced(assumption)).
% 88.12/88.32 tff(21067,plain,
% 88.12/88.32 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21068,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21069,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21068, 21067])).
% 88.12/88.32 tff(21070,plain,
% 88.12/88.32 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21069, 1884, 19473])).
% 88.12/88.32 tff(21071,plain,
% 88.12/88.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21072,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21073,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21072, 21071])).
% 88.12/88.32 tff(21074,plain,
% 88.12/88.32 (~node20(c_e_h_3, c_r, s3)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21073, 37, 21070])).
% 88.12/88.32 tff(21075,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)), introduced(assumption)).
% 88.12/88.32 tff(21076,plain,
% 88.12/88.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21077,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21078,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21077, 21076])).
% 88.12/88.32 tff(21079,plain,
% 88.12/88.32 (~node20(c_e_h_3, c_r, s2)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21078, 37, 21075])).
% 88.12/88.32 tff(21080,plain,
% 88.12/88.32 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21081,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21082,plain,
% 88.12/88.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21081, 21080])).
% 88.12/88.32 tff(21083,plain,
% 88.12/88.32 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21082, 1884, 19371])).
% 88.12/88.32 tff(21084,plain,
% 88.12/88.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21085,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21086,plain,
% 88.12/88.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21085, 21084])).
% 88.12/88.32 tff(21087,plain,
% 88.12/88.32 (~node20(c_e_h_3, c_r, s1)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21086, 37, 21083])).
% 88.12/88.32 tff(21088,assumption,(~node20(c_e_h_3, c_r, s1)), introduced(assumption)).
% 88.12/88.32 tff(21089,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s2)), introduced(assumption)).
% 88.12/88.32 tff(21090,plain,
% 88.12/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21091,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21092,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2))),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21091, 21090])).
% 88.12/88.32 tff(21093,plain,
% 88.12/88.32 (node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2))),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21092, 51])).
% 88.12/88.32 tff(21094,plain,
% 88.12/88.32 (~node21(c_e_h_3, c_r, s1, s2)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21093, 21089, 21088])).
% 88.12/88.32 tff(21095,plain,
% 88.12/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2))),
% 88.12/88.32 inference(rewrite,[status(thm)],[])).
% 88.12/88.32 tff(21096,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2))),
% 88.12/88.32 inference(quant_inst,[status(thm)],[])).
% 88.12/88.32 tff(21097,plain,
% 88.12/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2)),
% 88.12/88.32 inference(modus_ponens,[status(thm)],[21096, 21095])).
% 88.12/88.32 tff(21098,plain,
% 88.12/88.32 (node22(c_e_h_3, c_r, s1, s2)),
% 88.12/88.32 inference(unit_resolution,[status(thm)],[21097, 81, 344, 21094])).
% 88.15/88.32 tff(21099,plain,
% 88.15/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 88.15/88.32 inference(rewrite,[status(thm)],[])).
% 88.15/88.32 tff(21100,plain,
% 88.15/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 88.15/88.32 inference(quant_inst,[status(thm)],[])).
% 88.15/88.32 tff(21101,plain,
% 88.15/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)),
% 88.15/88.32 inference(modus_ponens,[status(thm)],[21100, 21099])).
% 88.15/88.32 tff(21102,plain,
% 88.15/88.32 ($false),
% 88.15/88.32 inference(unit_resolution,[status(thm)],[21101, 107, 20616, 21089, 21098])).
% 88.15/88.32 tff(21103,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | node20(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.32 tff(21104,plain,
% 88.15/88.32 (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 88.15/88.32 inference(unit_resolution,[status(thm)],[21103, 21087])).
% 88.15/88.32 tff(21105,assumption,(~node20(c_e_h_3, c_r, s2)), introduced(assumption)).
% 88.15/88.32 tff(21106,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 88.15/88.32 tff(21107,plain,
% 88.15/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 88.15/88.32 inference(rewrite,[status(thm)],[])).
% 88.15/88.32 tff(21108,plain,
% 88.15/88.32 ((node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 88.15/88.32 inference(rewrite,[status(thm)],[])).
% 88.15/88.32 tff(21109,plain,
% 88.15/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3))))),
% 88.15/88.32 inference(monotonicity,[status(thm)],[21108])).
% 88.15/88.32 tff(21110,plain,
% 88.15/88.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 88.15/88.32 inference(transitivity,[status(thm)],[21109, 21107])).
% 88.15/88.32 tff(21111,plain,
% 88.15/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 88.15/88.32 inference(quant_inst,[status(thm)],[])).
% 88.15/88.32 tff(21112,plain,
% 88.15/88.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3))),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21111, 21110])).
% 88.15/88.33 tff(21113,plain,
% 88.15/88.33 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3))),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21112, 51])).
% 88.15/88.33 tff(21114,plain,
% 88.15/88.33 (~node21(c_e_h_3, c_r, s2, s3)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21113, 21106, 21105])).
% 88.15/88.33 tff(21115,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21116,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21117,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21116, 21115])).
% 88.15/88.33 tff(21118,plain,
% 88.15/88.33 (node22(c_e_h_3, c_r, s2, s3)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21117, 81, 582, 21114])).
% 88.15/88.33 tff(21119,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s2)), introduced(assumption)).
% 88.15/88.33 tff(21120,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21121,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21122,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21121, 21120])).
% 88.15/88.33 tff(21123,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21122, 107, 21119, 21106, 21118])).
% 88.15/88.33 tff(21124,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2) | node20(c_e_h_3, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21125,plain,
% 88.15/88.33 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21124, 21104])).
% 88.15/88.33 tff(21126,plain,
% 88.15/88.33 (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21125, 21079])).
% 88.15/88.33 tff(21127,assumption,(~node20(c_e_h_3, c_r, s3)), introduced(assumption)).
% 88.15/88.33 tff(21128,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21129,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21130,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4))),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21129, 21128])).
% 88.15/88.33 tff(21131,plain,
% 88.15/88.33 (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4))),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21130, 51])).
% 88.15/88.33 tff(21132,plain,
% 88.15/88.33 (~node21(c_e_h_3, c_r, s3, s4)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21131, 21066, 21127])).
% 88.15/88.33 tff(21133,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21134,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21135,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21134, 21133])).
% 88.15/88.33 tff(21136,plain,
% 88.15/88.33 (node22(c_e_h_3, c_r, s3, s4)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21135, 81, 679, 21132])).
% 88.15/88.33 tff(21137,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 88.15/88.33 tff(21138,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21139,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21140,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21139, 21138])).
% 88.15/88.33 tff(21141,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21140, 107, 21137, 21066, 21136])).
% 88.15/88.33 tff(21142,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3) | node20(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21143,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21142, 21126, 21074, 21066])).
% 88.15/88.33 tff(21144,plain,(m_and_h_gate_v_in1(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21145,plain,
% 88.15/88.33 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21144, 21065])).
% 88.15/88.33 tff(21146,plain,
% 88.15/88.33 (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21145, 19471])).
% 88.15/88.33 tff(21147,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s4)), introduced(assumption)).
% 88.15/88.33 tff(21148,plain,
% 88.15/88.33 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21149,plain,
% 88.15/88.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21150,plain,
% 88.15/88.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21149, 21148])).
% 88.15/88.33 tff(21151,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21150, 1884, 19543, 21147])).
% 88.15/88.33 tff(21152,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21153,plain,
% 88.15/88.33 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21152, 19534])).
% 88.15/88.33 tff(21154,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)), introduced(assumption)).
% 88.15/88.33 tff(21155,assumption,(node20(c_e_h_3, c_r, s4)), introduced(assumption)).
% 88.15/88.33 tff(21156,plain,
% 88.15/88.33 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21157,plain,
% 88.15/88.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21158,plain,
% 88.15/88.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21157, 21156])).
% 88.15/88.33 tff(21159,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21158, 37, 21155, 21154])).
% 88.15/88.33 tff(21160,plain,((~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21161,plain,
% 88.15/88.33 (~node20(c_e_h_3, c_r, s4)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21160, 21153])).
% 88.15/88.33 tff(21162,assumption,(~node20(c_e_h_3, c_r, s4)), introduced(assumption)).
% 88.15/88.33 tff(21163,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s5)), introduced(assumption)).
% 88.15/88.33 tff(21164,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5)))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21165,plain,
% 88.15/88.33 ((node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5)))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21166,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5))))),
% 88.15/88.33 inference(monotonicity,[status(thm)],[21165])).
% 88.15/88.33 tff(21167,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5)))),
% 88.15/88.33 inference(transitivity,[status(thm)],[21166, 21164])).
% 88.15/88.33 tff(21168,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5)))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21169,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5))),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21168, 21167])).
% 88.15/88.33 tff(21170,plain,
% 88.15/88.33 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5))),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21169, 51])).
% 88.15/88.33 tff(21171,plain,
% 88.15/88.33 (~node21(c_e_h_3, c_r, s4, s5)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21170, 21163, 21162])).
% 88.15/88.33 tff(21172,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21173,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21174,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21173, 21172])).
% 88.15/88.33 tff(21175,plain,
% 88.15/88.33 (node22(c_e_h_3, c_r, s4, s5)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21174, 81, 1432, 21171])).
% 88.15/88.33 tff(21176,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s4)), introduced(assumption)).
% 88.15/88.33 tff(21177,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21178,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21179,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21178, 21177])).
% 88.15/88.33 tff(21180,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21179, 107, 21176, 21163, 21175])).
% 88.15/88.33 tff(21181,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4) | node20(c_e_h_3, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21182,plain,
% 88.15/88.33 (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21181, 21161, 21146])).
% 88.15/88.33 tff(21183,assumption,(node22(c_e_h_3, c_r, s5, s6)), introduced(assumption)).
% 88.15/88.33 tff(21184,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s5)), introduced(assumption)).
% 88.15/88.33 tff(21185,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21186,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21187,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21186, 21185])).
% 88.15/88.33 tff(21188,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21187, 107, 21061, 21184, 21183])).
% 88.15/88.33 tff(21189,plain,((~node22(c_e_h_3, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21190,plain,
% 88.15/88.33 ((~node22(c_e_h_3, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21189, 21182])).
% 88.15/88.33 tff(21191,plain,
% 88.15/88.33 (~node22(c_e_h_3, c_r, s5, s6)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21190, 21061])).
% 88.15/88.33 tff(21192,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s5)), introduced(assumption)).
% 88.15/88.33 tff(21193,plain,
% 88.15/88.33 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21194,plain,
% 88.15/88.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21195,plain,
% 88.15/88.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21194, 21193])).
% 88.15/88.33 tff(21196,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21195, 1884, 19611, 21192])).
% 88.15/88.33 tff(21197,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21198,plain,
% 88.15/88.33 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21197, 19601])).
% 88.15/88.33 tff(21199,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)), introduced(assumption)).
% 88.15/88.33 tff(21200,assumption,(node20(c_e_h_3, c_r, s5)), introduced(assumption)).
% 88.15/88.33 tff(21201,plain,
% 88.15/88.33 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21202,plain,
% 88.15/88.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21203,plain,
% 88.15/88.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21202, 21201])).
% 88.15/88.33 tff(21204,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21203, 37, 21200, 21199])).
% 88.15/88.33 tff(21205,plain,((~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21206,plain,
% 88.15/88.33 (~node20(c_e_h_3, c_r, s5)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21205, 21198])).
% 88.15/88.33 tff(21207,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6)))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21208,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6)))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21209,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6))),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21208, 21207])).
% 88.15/88.33 tff(21210,plain,
% 88.15/88.33 (node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6))),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21209, 51])).
% 88.15/88.33 tff(21211,plain,
% 88.15/88.33 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6))),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21210, 21206])).
% 88.15/88.33 tff(21212,plain,
% 88.15/88.33 (~node21(c_e_h_3, c_r, s5, s6)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21211, 21061])).
% 88.15/88.33 tff(21213,assumption,(~node22(c_e_h_3, c_r, s5, s6)), introduced(assumption)).
% 88.15/88.33 tff(21214,assumption,(~node21(c_e_h_3, c_r, s5, s6)), introduced(assumption)).
% 88.15/88.33 tff(21215,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21216,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21217,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21216, 21215])).
% 88.15/88.33 tff(21218,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21217, 81, 1499, 21214, 21213])).
% 88.15/88.33 tff(21219,plain,(node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21220,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21219, 21212, 21191])).
% 88.15/88.33 tff(21221,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21222,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s6)), introduced(assumption)).
% 88.15/88.33 tff(21223,plain,
% 88.15/88.33 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21224,plain,
% 88.15/88.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21225,plain,
% 88.15/88.33 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21224, 21223])).
% 88.15/88.33 tff(21226,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21225, 1884, 19677, 21222])).
% 88.15/88.33 tff(21227,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21228,plain,
% 88.15/88.33 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21227, 19675])).
% 88.15/88.33 tff(21229,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)), introduced(assumption)).
% 88.15/88.33 tff(21230,assumption,(node20(c_e_h_3, c_r, s6)), introduced(assumption)).
% 88.15/88.33 tff(21231,plain,
% 88.15/88.33 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21232,plain,
% 88.15/88.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21233,plain,
% 88.15/88.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6)),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21232, 21231])).
% 88.15/88.33 tff(21234,plain,
% 88.15/88.33 ($false),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21233, 37, 21230, 21229])).
% 88.15/88.33 tff(21235,plain,((~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.33 tff(21236,plain,
% 88.15/88.33 (~node20(c_e_h_3, c_r, s6)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21235, 21228])).
% 88.15/88.33 tff(21237,assumption,(~node20(c_e_h_3, c_r, s6)), introduced(assumption)).
% 88.15/88.33 tff(21238,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s7)), introduced(assumption)).
% 88.15/88.33 tff(21239,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7)))),
% 88.15/88.33 inference(rewrite,[status(thm)],[])).
% 88.15/88.33 tff(21240,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7)))),
% 88.15/88.33 inference(quant_inst,[status(thm)],[])).
% 88.15/88.33 tff(21241,plain,
% 88.15/88.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7))),
% 88.15/88.33 inference(modus_ponens,[status(thm)],[21240, 21239])).
% 88.15/88.33 tff(21242,plain,
% 88.15/88.33 (node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7))),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21241, 51])).
% 88.15/88.33 tff(21243,plain,
% 88.15/88.33 (~node21(c_e_h_3, c_r, s6, s7)),
% 88.15/88.33 inference(unit_resolution,[status(thm)],[21242, 21238, 21237])).
% 88.15/88.33 tff(21244,plain,
% 88.15/88.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7))),
% 88.15/88.34 inference(rewrite,[status(thm)],[])).
% 88.15/88.34 tff(21245,plain,
% 88.15/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7))),
% 88.15/88.34 inference(quant_inst,[status(thm)],[])).
% 88.15/88.34 tff(21246,plain,
% 88.15/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7)),
% 88.15/88.34 inference(modus_ponens,[status(thm)],[21245, 21244])).
% 88.15/88.34 tff(21247,plain,
% 88.15/88.34 (node22(c_e_h_3, c_r, s6, s7)),
% 88.15/88.34 inference(unit_resolution,[status(thm)],[21246, 81, 1552, 21243])).
% 88.15/88.34 tff(21248,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s6)), introduced(assumption)).
% 88.15/88.34 tff(21249,plain,
% 88.15/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 88.15/88.34 inference(rewrite,[status(thm)],[])).
% 88.15/88.34 tff(21250,plain,
% 88.15/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 88.15/88.34 inference(quant_inst,[status(thm)],[])).
% 88.15/88.34 tff(21251,plain,
% 88.15/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 88.15/88.34 inference(modus_ponens,[status(thm)],[21250, 21249])).
% 88.15/88.34 tff(21252,plain,
% 88.15/88.34 ($false),
% 88.15/88.34 inference(unit_resolution,[status(thm)],[21251, 107, 21238, 21248, 21247])).
% 88.15/88.34 tff(21253,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6) | node20(c_e_h_3, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 88.15/88.34 tff(21254,plain,
% 88.15/88.34 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 88.15/88.34 inference(unit_resolution,[status(thm)],[21253, 21236])).
% 88.15/88.34 tff(21255,plain,
% 88.15/88.34 (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 88.15/88.34 inference(unit_resolution,[status(thm)],[21254, 21221])).
% 88.15/88.34 tff(21256,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s7)), introduced(assumption)).
% 88.15/88.34 tff(21257,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s8)), introduced(assumption)).
% 88.15/88.34 tff(21258,assumption,(node22(c_e_h_3, c_r, s7, s8)), introduced(assumption)).
% 88.15/88.34 tff(21259,plain,
% 88.15/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))),
% 88.15/88.34 inference(rewrite,[status(thm)],[])).
% 88.15/88.34 tff(21260,plain,
% 88.15/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))),
% 88.15/88.34 inference(quant_inst,[status(thm)],[])).
% 88.15/88.34 tff(21261,plain,
% 88.15/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21260, 21259])).
% 88.16/88.34 tff(21262,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21261, 107, 21257, 21256, 21258])).
% 88.16/88.34 tff(21263,plain,((~node22(c_e_h_3, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21264,plain,
% 88.16/88.34 (~node22(c_e_h_3, c_r, s7, s8)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21263, 21257, 21256])).
% 88.16/88.34 tff(21265,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21266,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21267,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21266, 21265])).
% 88.16/88.34 tff(21268,plain,
% 88.16/88.34 (node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21267, 81, 2152])).
% 88.16/88.34 tff(21269,plain,
% 88.16/88.34 (node21(c_e_h_3, c_r, s7, s8)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21268, 21264])).
% 88.16/88.34 tff(21270,assumption,(~node20(c_e_h_3, c_r, s7)), introduced(assumption)).
% 88.16/88.34 tff(21271,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node21(c_e_h_3, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node21(c_e_h_3, c_r, s7, s8)))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21272,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node21(c_e_h_3, c_r, s7, s8)))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21273,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node21(c_e_h_3, c_r, s7, s8))),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21272, 21271])).
% 88.16/88.34 tff(21274,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21273, 51, 21270, 21257, 21269])).
% 88.16/88.34 tff(21275,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21276,plain,
% 88.16/88.34 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21275, 21255])).
% 88.16/88.34 tff(21277,plain,
% 88.16/88.34 (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21276, 21060])).
% 88.16/88.34 tff(21278,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s8)), introduced(assumption)).
% 88.16/88.34 tff(21279,plain,
% 88.16/88.34 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21280,plain,
% 88.16/88.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21281,plain,
% 88.16/88.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21280, 21279])).
% 88.16/88.34 tff(21282,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21281, 1884, 19853, 21278])).
% 88.16/88.34 tff(21283,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21284,plain,
% 88.16/88.34 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21283, 19846])).
% 88.16/88.34 tff(21285,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)), introduced(assumption)).
% 88.16/88.34 tff(21286,assumption,(node20(c_e_h_3, c_r, s8)), introduced(assumption)).
% 88.16/88.34 tff(21287,plain,
% 88.16/88.34 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21288,plain,
% 88.16/88.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21289,plain,
% 88.16/88.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21288, 21287])).
% 88.16/88.34 tff(21290,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21289, 37, 21286, 21285])).
% 88.16/88.34 tff(21291,plain,((~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21292,plain,
% 88.16/88.34 (~node20(c_e_h_3, c_r, s8)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21291, 21284])).
% 88.16/88.34 tff(21293,assumption,(~node20(c_e_h_3, c_r, s8)), introduced(assumption)).
% 88.16/88.34 tff(21294,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s9)), introduced(assumption)).
% 88.16/88.34 tff(21295,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s8) | (~node21(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s8) | (~node21(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21296,plain,
% 88.16/88.34 ((node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9))) <=> (node20(c_e_h_3, c_r, s8) | (~node21(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21297,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s8) | (~node21(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9))))),
% 88.16/88.34 inference(monotonicity,[status(thm)],[21296])).
% 88.16/88.34 tff(21298,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s8) | (~node21(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)))),
% 88.16/88.34 inference(transitivity,[status(thm)],[21297, 21295])).
% 88.16/88.34 tff(21299,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9)))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21300,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s8) | (~node21(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21299, 21298])).
% 88.16/88.34 tff(21301,plain,
% 88.16/88.34 (node20(c_e_h_3, c_r, s8) | (~node21(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21300, 51])).
% 88.16/88.34 tff(21302,plain,
% 88.16/88.34 (~node21(c_e_h_3, c_r, s8, s9)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21301, 21294, 21293])).
% 88.16/88.34 tff(21303,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21304,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21305,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21304, 21303])).
% 88.16/88.34 tff(21306,plain,
% 88.16/88.34 (node22(c_e_h_3, c_r, s8, s9)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21305, 81, 2636, 21302])).
% 88.16/88.34 tff(21307,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s8)), introduced(assumption)).
% 88.16/88.34 tff(21308,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21309,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21310,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21309, 21308])).
% 88.16/88.34 tff(21311,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21310, 107, 21307, 21294, 21306])).
% 88.16/88.34 tff(21312,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8) | node20(c_e_h_3, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21313,plain,
% 88.16/88.34 (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21312, 21292, 21277])).
% 88.16/88.34 tff(21314,plain,
% 88.16/88.34 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21315,plain,
% 88.16/88.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21316,plain,
% 88.16/88.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s9)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21315, 21314])).
% 88.16/88.34 tff(21317,plain,
% 88.16/88.34 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21316, 1884, 19928])).
% 88.16/88.34 tff(21318,plain,
% 88.16/88.34 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s9))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21319,plain,
% 88.16/88.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s9))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21320,plain,
% 88.16/88.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s9)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21319, 21318])).
% 88.16/88.34 tff(21321,plain,
% 88.16/88.34 (~node20(c_e_h_3, c_r, s9)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21320, 37, 21317])).
% 88.16/88.34 tff(21322,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s9)), introduced(assumption)).
% 88.16/88.34 tff(21323,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s10)), introduced(assumption)).
% 88.16/88.34 tff(21324,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21325,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21326,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21325, 21324])).
% 88.16/88.34 tff(21327,plain,
% 88.16/88.34 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21326, 107])).
% 88.16/88.34 tff(21328,plain,
% 88.16/88.34 (~node22(c_e_h_3, c_r, s9, s10)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21327, 21323, 21322])).
% 88.16/88.34 tff(21329,assumption,(~node20(c_e_h_3, c_r, s9)), introduced(assumption)).
% 88.16/88.34 tff(21330,assumption,(node21(c_e_h_3, c_r, s9, s10)), introduced(assumption)).
% 88.16/88.34 tff(21331,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node21(c_e_h_3, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node21(c_e_h_3, c_r, s9, s10)))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21332,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node21(c_e_h_3, c_r, s9, s10)))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21333,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node21(c_e_h_3, c_r, s9, s10))),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21332, 21331])).
% 88.16/88.34 tff(21334,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21333, 51, 21329, 21323, 21330])).
% 88.16/88.34 tff(21335,plain,((~node21(c_e_h_3, c_r, s9, s10)) | node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21336,plain,
% 88.16/88.34 (~node21(c_e_h_3, c_r, s9, s10)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21335, 21323, 21329])).
% 88.16/88.34 tff(21337,assumption,(~node21(c_e_h_3, c_r, s9, s10)), introduced(assumption)).
% 88.16/88.34 tff(21338,assumption,(~node22(c_e_h_3, c_r, s9, s10)), introduced(assumption)).
% 88.16/88.34 tff(21339,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21340,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21341,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21340, 21339])).
% 88.16/88.34 tff(21342,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21341, 81, 3175, 21338, 21337])).
% 88.16/88.34 tff(21343,plain,(node22(c_e_h_3, c_r, s9, s10) | node21(c_e_h_3, c_r, s9, s10)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21344,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21343, 21336, 21328])).
% 88.16/88.34 tff(21345,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | node20(c_e_h_3, c_r, s9) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21346,plain,
% 88.16/88.34 (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21345, 21321, 21313])).
% 88.16/88.34 tff(21347,assumption,(~node20(c_e_h_3, c_r, s10)), introduced(assumption)).
% 88.16/88.34 tff(21348,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s11)), introduced(assumption)).
% 88.16/88.34 tff(21349,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11)))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21350,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11)))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21351,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11))),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21350, 21349])).
% 88.16/88.34 tff(21352,plain,
% 88.16/88.34 (node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11))),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21351, 51])).
% 88.16/88.34 tff(21353,plain,
% 88.16/88.34 (~node21(c_e_h_3, c_r, s10, s11)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21352, 21348, 21347])).
% 88.16/88.34 tff(21354,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21355,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21356,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21355, 21354])).
% 88.16/88.34 tff(21357,plain,
% 88.16/88.34 (node22(c_e_h_3, c_r, s10, s11)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21356, 81, 3778, 21353])).
% 88.16/88.34 tff(21358,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s10)), introduced(assumption)).
% 88.16/88.34 tff(21359,plain,
% 88.16/88.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node22(c_e_h_3, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node22(c_e_h_3, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21360,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node22(c_e_h_3, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21361,plain,
% 88.16/88.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node22(c_e_h_3, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)),
% 88.16/88.34 inference(modus_ponens,[status(thm)],[21360, 21359])).
% 88.16/88.34 tff(21362,plain,
% 88.16/88.34 ($false),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21361, 107, 21358, 21348, 21357])).
% 88.16/88.34 tff(21363,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10) | node20(c_e_h_3, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.34 tff(21364,plain,
% 88.16/88.34 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | node20(c_e_h_3, c_r, s10)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21363, 21346])).
% 88.16/88.34 tff(21365,plain,
% 88.16/88.34 (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)),
% 88.16/88.34 inference(unit_resolution,[status(thm)],[21364, 21045])).
% 88.16/88.34 tff(21366,plain,
% 88.16/88.34 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))),
% 88.16/88.34 inference(rewrite,[status(thm)],[])).
% 88.16/88.34 tff(21367,plain,
% 88.16/88.34 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))),
% 88.16/88.34 inference(quant_inst,[status(thm)],[])).
% 88.16/88.34 tff(21368,plain,
% 88.16/88.34 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21367, 21366])).
% 88.16/88.35 tff(21369,plain,
% 88.16/88.35 (~m_user_v_ack(c_e_h_3, c_u, s11)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21368, 4481, 21365])).
% 88.16/88.35 tff(21370,plain,
% 88.16/88.35 (^[X: $i] : refl((m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X))) <=> (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X))))),
% 88.16/88.35 inference(bind,[status(th)],[])).
% 88.16/88.35 tff(21371,plain,
% 88.16/88.35 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 88.16/88.35 inference(quant_intro,[status(thm)],[21370])).
% 88.16/88.35 tff(21372,plain,
% 88.16/88.35 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X))) <=> ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21373,axiom,(![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty6')).
% 88.16/88.35 tff(21374,plain,
% 88.16/88.35 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21373, 21372])).
% 88.16/88.35 tff(21375,plain,(
% 88.16/88.35 ![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 88.16/88.35 inference(skolemize,[status(sab)],[21374])).
% 88.16/88.35 tff(21376,plain,
% 88.16/88.35 (![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21375, 21371])).
% 88.16/88.35 tff(21377,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s11) | (~node25(s11)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s11) | (~node25(s11)))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21378,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s11) | (~node25(s11)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21379,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s11) | (~node25(s11))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21378, 21377])).
% 88.16/88.35 tff(21380,plain,
% 88.16/88.35 (~node25(s11)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21379, 21376, 21369])).
% 88.16/88.35 tff(21381,plain,
% 88.16/88.35 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21382,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21383,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21382, 21381])).
% 88.16/88.35 tff(21384,plain,
% 88.16/88.35 (~m_user_v_ack(c_e_h_1, c_u, s11)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21383, 4481, 7404])).
% 88.16/88.35 tff(21385,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s11)) | m_user_v_ack(c_e_h_1, c_u, s11))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s11)) | m_user_v_ack(c_e_h_1, c_u, s11))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21386,plain,
% 88.16/88.35 ((m_user_v_ack(c_e_h_1, c_u, s11) | (~node24(s11))) <=> ((~node24(s11)) | m_user_v_ack(c_e_h_1, c_u, s11))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21387,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s11) | (~node24(s11)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s11)) | m_user_v_ack(c_e_h_1, c_u, s11)))),
% 88.16/88.35 inference(monotonicity,[status(thm)],[21386])).
% 88.16/88.35 tff(21388,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s11) | (~node24(s11)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s11)) | m_user_v_ack(c_e_h_1, c_u, s11))),
% 88.16/88.35 inference(transitivity,[status(thm)],[21387, 21385])).
% 88.16/88.35 tff(21389,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s11) | (~node24(s11)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21390,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s11)) | m_user_v_ack(c_e_h_1, c_u, s11)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21389, 21388])).
% 88.16/88.35 tff(21391,plain,
% 88.16/88.35 (~node24(s11)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21390, 8407, 21384])).
% 88.16/88.35 tff(21392,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s11)) | m_user_v_ack(c_e_h_1, c_u, s11))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s11)) | m_user_v_ack(c_e_h_1, c_u, s11))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21393,plain,
% 88.16/88.35 ((m_user_v_ack(c_e_h_1, c_u, s11) | (~node23(s11))) <=> ((~node23(s11)) | m_user_v_ack(c_e_h_1, c_u, s11))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21394,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s11) | (~node23(s11)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s11)) | m_user_v_ack(c_e_h_1, c_u, s11)))),
% 88.16/88.35 inference(monotonicity,[status(thm)],[21393])).
% 88.16/88.35 tff(21395,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s11) | (~node23(s11)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s11)) | m_user_v_ack(c_e_h_1, c_u, s11))),
% 88.16/88.35 inference(transitivity,[status(thm)],[21394, 21392])).
% 88.16/88.35 tff(21396,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s11) | (~node23(s11)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21397,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s11)) | m_user_v_ack(c_e_h_1, c_u, s11)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21396, 21395])).
% 88.16/88.35 tff(21398,plain,
% 88.16/88.35 (~node23(s11)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21397, 8418, 21384])).
% 88.16/88.35 tff(21399,plain,
% 88.16/88.35 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s11) | node24(s11) | node25(s11) | (~node26(s11)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s11) | node24(s11) | node25(s11) | (~node26(s11)))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21400,plain,
% 88.16/88.35 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s11) | node24(s11) | node25(s11) | (~node26(s11)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21401,plain,
% 88.16/88.35 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s11) | node24(s11) | node25(s11) | (~node26(s11))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21400, 21399])).
% 88.16/88.35 tff(21402,plain,
% 88.16/88.35 (node25(s11) | (~node26(s11))),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21401, 8435, 21398, 21391])).
% 88.16/88.35 tff(21403,plain,
% 88.16/88.35 (~node26(s11)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21402, 21380])).
% 88.16/88.35 tff(21404,assumption,(~node26(s16)), introduced(assumption)).
% 88.16/88.35 tff(21405,assumption,(~node26(s12)), introduced(assumption)).
% 88.16/88.35 tff(21406,assumption,(~node26(s14)), introduced(assumption)).
% 88.16/88.35 tff(21407,assumption,(~node26(s11)), introduced(assumption)).
% 88.16/88.35 tff(21408,assumption,(~node26(s13)), introduced(assumption)).
% 88.16/88.35 tff(21409,assumption,(~node26(s15)), introduced(assumption)).
% 88.16/88.35 tff(21410,assumption,(~node26(s19)), introduced(assumption)).
% 88.16/88.35 tff(21411,plain,
% 88.16/88.35 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21412,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21413,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s17)) | m_and_h_gate_v_out(c_e_h_2, c_r, s17)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21412, 21411])).
% 88.16/88.35 tff(21414,plain,
% 88.16/88.35 (~m_user_v_ack(c_e_h_2, c_u, s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21413, 4481, 15667])).
% 88.16/88.35 tff(21415,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s17) | (~node25(s17)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s17) | (~node25(s17)))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21416,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s17) | (~node25(s17)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21417,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s17) | (~node25(s17))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21416, 21415])).
% 88.16/88.35 tff(21418,plain,
% 88.16/88.35 (~node25(s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21417, 4492, 21414])).
% 88.16/88.35 tff(21419,assumption,(m_user_v_ack(c_e_h_1, c_u, s17)), introduced(assumption)).
% 88.16/88.35 tff(21420,plain,
% 88.16/88.35 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21421,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21422,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21421, 21420])).
% 88.16/88.35 tff(21423,plain,
% 88.16/88.35 ($false),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21422, 4481, 21419, 18795])).
% 88.16/88.35 tff(21424,plain,((~m_user_v_ack(c_e_h_1, c_u, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.35 tff(21425,plain,
% 88.16/88.35 (~m_user_v_ack(c_e_h_1, c_u, s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21424, 18794])).
% 88.16/88.35 tff(21426,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s17)) | m_user_v_ack(c_e_h_1, c_u, s17))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s17)) | m_user_v_ack(c_e_h_1, c_u, s17))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21427,plain,
% 88.16/88.35 ((m_user_v_ack(c_e_h_1, c_u, s17) | (~node24(s17))) <=> ((~node24(s17)) | m_user_v_ack(c_e_h_1, c_u, s17))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21428,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s17) | (~node24(s17)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s17)) | m_user_v_ack(c_e_h_1, c_u, s17)))),
% 88.16/88.35 inference(monotonicity,[status(thm)],[21427])).
% 88.16/88.35 tff(21429,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s17) | (~node24(s17)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s17)) | m_user_v_ack(c_e_h_1, c_u, s17))),
% 88.16/88.35 inference(transitivity,[status(thm)],[21428, 21426])).
% 88.16/88.35 tff(21430,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s17) | (~node24(s17)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21431,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s17)) | m_user_v_ack(c_e_h_1, c_u, s17)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21430, 21429])).
% 88.16/88.35 tff(21432,plain,
% 88.16/88.35 (~node24(s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21431, 8407, 21425])).
% 88.16/88.35 tff(21433,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s17)) | m_user_v_ack(c_e_h_1, c_u, s17))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s17)) | m_user_v_ack(c_e_h_1, c_u, s17))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21434,plain,
% 88.16/88.35 ((m_user_v_ack(c_e_h_1, c_u, s17) | (~node23(s17))) <=> ((~node23(s17)) | m_user_v_ack(c_e_h_1, c_u, s17))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21435,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s17) | (~node23(s17)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s17)) | m_user_v_ack(c_e_h_1, c_u, s17)))),
% 88.16/88.35 inference(monotonicity,[status(thm)],[21434])).
% 88.16/88.35 tff(21436,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s17) | (~node23(s17)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s17)) | m_user_v_ack(c_e_h_1, c_u, s17))),
% 88.16/88.35 inference(transitivity,[status(thm)],[21435, 21433])).
% 88.16/88.35 tff(21437,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s17) | (~node23(s17)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21438,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s17)) | m_user_v_ack(c_e_h_1, c_u, s17)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21437, 21436])).
% 88.16/88.35 tff(21439,plain,
% 88.16/88.35 (~node23(s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21438, 8418, 21425])).
% 88.16/88.35 tff(21440,plain,
% 88.16/88.35 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s17) | node24(s17) | node25(s17) | (~node26(s17)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s17) | node24(s17) | node25(s17) | (~node26(s17)))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21441,plain,
% 88.16/88.35 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s17) | node24(s17) | node25(s17) | (~node26(s17)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21442,plain,
% 88.16/88.35 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s17) | node24(s17) | node25(s17) | (~node26(s17))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21441, 21440])).
% 88.16/88.35 tff(21443,plain,
% 88.16/88.35 (node25(s17) | (~node26(s17))),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21442, 8435, 21439, 21432])).
% 88.16/88.35 tff(21444,plain,
% 88.16/88.35 (~node26(s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21443, 21418])).
% 88.16/88.35 tff(21445,plain,
% 88.16/88.35 (~m_and_h_gate_v_out(c_e_h_2, c_r, s18)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[15711, 15667, 15684])).
% 88.16/88.35 tff(21446,plain,
% 88.16/88.35 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21447,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21448,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s18)) | m_and_h_gate_v_out(c_e_h_2, c_r, s18)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21447, 21446])).
% 88.16/88.35 tff(21449,plain,
% 88.16/88.35 (~m_user_v_ack(c_e_h_2, c_u, s18)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21448, 4481, 21445])).
% 88.16/88.35 tff(21450,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s18)) | m_user_v_ack(c_e_h_2, c_u, s18))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s18)) | m_user_v_ack(c_e_h_2, c_u, s18))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21451,plain,
% 88.16/88.35 ((m_user_v_ack(c_e_h_2, c_u, s18) | (~node25(s18))) <=> ((~node25(s18)) | m_user_v_ack(c_e_h_2, c_u, s18))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21452,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s18) | (~node25(s18)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s18)) | m_user_v_ack(c_e_h_2, c_u, s18)))),
% 88.16/88.35 inference(monotonicity,[status(thm)],[21451])).
% 88.16/88.35 tff(21453,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s18) | (~node25(s18)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s18)) | m_user_v_ack(c_e_h_2, c_u, s18))),
% 88.16/88.35 inference(transitivity,[status(thm)],[21452, 21450])).
% 88.16/88.35 tff(21454,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s18) | (~node25(s18)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21455,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s18)) | m_user_v_ack(c_e_h_2, c_u, s18)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21454, 21453])).
% 88.16/88.35 tff(21456,plain,
% 88.16/88.35 (~node25(s18)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21455, 4492, 21449])).
% 88.16/88.35 tff(21457,plain,
% 88.16/88.35 ($false),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[19029, 19022, 19024, 18930])).
% 88.16/88.35 tff(21458,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.35 tff(21459,plain,
% 88.16/88.35 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15))),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21458, 18690])).
% 88.16/88.35 tff(21460,plain,
% 88.16/88.35 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21459, 18683])).
% 88.16/88.35 tff(21461,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s17)), introduced(assumption)).
% 88.16/88.35 tff(21462,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)), introduced(assumption)).
% 88.16/88.35 tff(21463,plain,
% 88.16/88.35 ($false),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[19033, 1521, 21462, 21461])).
% 88.16/88.35 tff(21464,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s17))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.35 tff(21465,plain,
% 88.16/88.35 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21464, 21460])).
% 88.16/88.35 tff(21466,plain,
% 88.16/88.35 (~node20(c_e_h_1, c_r, s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[19019, 21465])).
% 88.16/88.35 tff(21467,plain,
% 88.16/88.35 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[19011, 18794])).
% 88.16/88.35 tff(21468,plain,
% 88.16/88.35 (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21467, 21466])).
% 88.16/88.35 tff(21469,assumption,(m_user_v_ack(c_e_h_1, c_u, s18)), introduced(assumption)).
% 88.16/88.35 tff(21470,plain,
% 88.16/88.35 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21471,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21472,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21471, 21470])).
% 88.16/88.35 tff(21473,plain,
% 88.16/88.35 ($false),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21472, 4481, 21469, 18968])).
% 88.16/88.35 tff(21474,plain,((~m_user_v_ack(c_e_h_1, c_u, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.35 tff(21475,plain,
% 88.16/88.35 (~m_user_v_ack(c_e_h_1, c_u, s18)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21474, 21468])).
% 88.16/88.35 tff(21476,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s18)) | m_user_v_ack(c_e_h_1, c_u, s18))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s18)) | m_user_v_ack(c_e_h_1, c_u, s18))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21477,plain,
% 88.16/88.35 ((m_user_v_ack(c_e_h_1, c_u, s18) | (~node24(s18))) <=> ((~node24(s18)) | m_user_v_ack(c_e_h_1, c_u, s18))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21478,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s18) | (~node24(s18)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s18)) | m_user_v_ack(c_e_h_1, c_u, s18)))),
% 88.16/88.35 inference(monotonicity,[status(thm)],[21477])).
% 88.16/88.35 tff(21479,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s18) | (~node24(s18)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s18)) | m_user_v_ack(c_e_h_1, c_u, s18))),
% 88.16/88.35 inference(transitivity,[status(thm)],[21478, 21476])).
% 88.16/88.35 tff(21480,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s18) | (~node24(s18)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21481,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s18)) | m_user_v_ack(c_e_h_1, c_u, s18)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21480, 21479])).
% 88.16/88.35 tff(21482,plain,
% 88.16/88.35 (~node24(s18)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21481, 8407, 21475])).
% 88.16/88.35 tff(21483,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s18) | (~node23(s18)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s18) | (~node23(s18)))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21484,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s18) | (~node23(s18)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21485,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s18) | (~node23(s18))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21484, 21483])).
% 88.16/88.35 tff(21486,plain,
% 88.16/88.35 (~node23(s18)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21485, 8418, 21475])).
% 88.16/88.35 tff(21487,plain,
% 88.16/88.35 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s18) | node24(s18) | node25(s18) | (~node26(s18)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s18) | node24(s18) | node25(s18) | (~node26(s18)))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21488,plain,
% 88.16/88.35 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s18) | node24(s18) | node25(s18) | (~node26(s18)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21489,plain,
% 88.16/88.35 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s18) | node24(s18) | node25(s18) | (~node26(s18))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21488, 21487])).
% 88.16/88.35 tff(21490,plain,
% 88.16/88.35 (node25(s18) | (~node26(s18))),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21489, 8435, 21486, 21482])).
% 88.16/88.35 tff(21491,plain,
% 88.16/88.35 (~node26(s18)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21490, 21456])).
% 88.16/88.35 tff(21492,plain,
% 88.16/88.35 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21493,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21494,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21493, 21492])).
% 88.16/88.35 tff(21495,plain,
% 88.16/88.35 (~m_user_v_ack(c_e_h_3, c_u, s8)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21494, 4481, 21277])).
% 88.16/88.35 tff(21496,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | ((~node25(s8)) | m_user_v_ack(c_e_h_3, c_u, s8))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s8)) | m_user_v_ack(c_e_h_3, c_u, s8))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21497,plain,
% 88.16/88.35 ((m_user_v_ack(c_e_h_3, c_u, s8) | (~node25(s8))) <=> ((~node25(s8)) | m_user_v_ack(c_e_h_3, c_u, s8))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21498,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s8) | (~node25(s8)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | ((~node25(s8)) | m_user_v_ack(c_e_h_3, c_u, s8)))),
% 88.16/88.35 inference(monotonicity,[status(thm)],[21497])).
% 88.16/88.35 tff(21499,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s8) | (~node25(s8)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s8)) | m_user_v_ack(c_e_h_3, c_u, s8))),
% 88.16/88.35 inference(transitivity,[status(thm)],[21498, 21496])).
% 88.16/88.35 tff(21500,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s8) | (~node25(s8)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21501,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s8)) | m_user_v_ack(c_e_h_3, c_u, s8)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21500, 21499])).
% 88.16/88.35 tff(21502,plain,
% 88.16/88.35 (~node25(s8)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21501, 21376, 21495])).
% 88.16/88.35 tff(21503,assumption,(m_user_v_ack(c_e_h_1, c_u, s8)), introduced(assumption)).
% 88.16/88.35 tff(21504,plain,
% 88.16/88.35 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21505,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21506,plain,
% 88.16/88.35 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21505, 21504])).
% 88.16/88.35 tff(21507,plain,
% 88.16/88.35 ($false),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21506, 4481, 21503, 6307])).
% 88.16/88.35 tff(21508,plain,((~m_user_v_ack(c_e_h_1, c_u, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.35 tff(21509,plain,
% 88.16/88.35 (~m_user_v_ack(c_e_h_1, c_u, s8)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21508, 5806])).
% 88.16/88.35 tff(21510,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s8) | (~node24(s8)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s8) | (~node24(s8)))),
% 88.16/88.35 inference(rewrite,[status(thm)],[])).
% 88.16/88.35 tff(21511,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s8) | (~node24(s8)))),
% 88.16/88.35 inference(quant_inst,[status(thm)],[])).
% 88.16/88.35 tff(21512,plain,
% 88.16/88.35 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s8) | (~node24(s8))),
% 88.16/88.35 inference(modus_ponens,[status(thm)],[21511, 21510])).
% 88.16/88.35 tff(21513,plain,
% 88.16/88.35 (~node24(s8)),
% 88.16/88.35 inference(unit_resolution,[status(thm)],[21512, 8407, 21509])).
% 88.16/88.35 tff(21514,plain,
% 88.16/88.35 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s8) | (~node23(s8)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s8) | (~node23(s8)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21515,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s8) | (~node23(s8)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21516,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s8) | (~node23(s8))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21515, 21514])).
% 88.16/88.36 tff(21517,plain,
% 88.16/88.36 (~node23(s8)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21516, 8418, 21509])).
% 88.16/88.36 tff(21518,plain,
% 88.16/88.36 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s8) | node24(s8) | node25(s8) | (~node26(s8)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s8) | node24(s8) | node25(s8) | (~node26(s8)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21519,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s8) | node24(s8) | node25(s8) | (~node26(s8)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21520,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s8) | node24(s8) | node25(s8) | (~node26(s8))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21519, 21518])).
% 88.16/88.36 tff(21521,plain,
% 88.16/88.36 (node25(s8) | (~node26(s8))),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21520, 8435, 21517, 21513])).
% 88.16/88.36 tff(21522,plain,
% 88.16/88.36 (~node26(s8)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21521, 21502])).
% 88.16/88.36 tff(21523,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21524,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21525,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21524, 21523])).
% 88.16/88.36 tff(21526,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_3, c_u, s10)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21525, 4481, 21346])).
% 88.16/88.36 tff(21527,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s10) | (~node25(s10)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s10) | (~node25(s10)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21528,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s10) | (~node25(s10)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21529,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s10) | (~node25(s10))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21528, 21527])).
% 88.16/88.36 tff(21530,plain,
% 88.16/88.36 (~node25(s10)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21529, 21376, 21526])).
% 88.16/88.36 tff(21531,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21532,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21533,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21532, 21531])).
% 88.16/88.36 tff(21534,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_1, c_u, s10)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21533, 4481, 6905])).
% 88.16/88.36 tff(21535,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s10) | (~node24(s10)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s10) | (~node24(s10)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21536,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s10) | (~node24(s10)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21537,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s10) | (~node24(s10))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21536, 21535])).
% 88.16/88.36 tff(21538,plain,
% 88.16/88.36 (~node24(s10)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21537, 8407, 21534])).
% 88.16/88.36 tff(21539,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s10) | (~node23(s10)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s10) | (~node23(s10)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21540,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s10) | (~node23(s10)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21541,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s10) | (~node23(s10))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21540, 21539])).
% 88.16/88.36 tff(21542,plain,
% 88.16/88.36 (~node23(s10)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21541, 8418, 21534])).
% 88.16/88.36 tff(21543,plain,
% 88.16/88.36 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s10) | node24(s10) | node25(s10) | (~node26(s10)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s10) | node24(s10) | node25(s10) | (~node26(s10)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21544,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s10) | node24(s10) | node25(s10) | (~node26(s10)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21545,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s10) | node24(s10) | node25(s10) | (~node26(s10))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21544, 21543])).
% 88.16/88.36 tff(21546,plain,
% 88.16/88.36 (node25(s10) | (~node26(s10))),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21545, 8435, 21542, 21538])).
% 88.16/88.36 tff(21547,plain,
% 88.16/88.36 (~node26(s10)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21546, 21530])).
% 88.16/88.36 tff(21548,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21549,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21550,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21549, 21548])).
% 88.16/88.36 tff(21551,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_3, c_u, s9)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21550, 4481, 21313])).
% 88.16/88.36 tff(21552,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s9) | (~node25(s9)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s9) | (~node25(s9)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21553,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s9) | (~node25(s9)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21554,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s9) | (~node25(s9))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21553, 21552])).
% 88.16/88.36 tff(21555,plain,
% 88.16/88.36 (~node25(s9)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21554, 21376, 21551])).
% 88.16/88.36 tff(21556,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21557,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21558,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21557, 21556])).
% 88.16/88.36 tff(21559,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_1, c_u, s9)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21558, 4481, 6318])).
% 88.16/88.36 tff(21560,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node24(s9)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s9) | (~node24(s9)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21561,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node24(s9)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21562,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s9) | (~node24(s9))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21561, 21560])).
% 88.16/88.36 tff(21563,plain,
% 88.16/88.36 (~node24(s9)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21562, 8407, 21559])).
% 88.16/88.36 tff(21564,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node23(s9)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s9) | (~node23(s9)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21565,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s9) | (~node23(s9)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21566,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s9) | (~node23(s9))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21565, 21564])).
% 88.16/88.36 tff(21567,plain,
% 88.16/88.36 (~node23(s9)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21566, 8418, 21559])).
% 88.16/88.36 tff(21568,plain,
% 88.16/88.36 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s9) | node24(s9) | node25(s9) | (~node26(s9)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s9) | node24(s9) | node25(s9) | (~node26(s9)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21569,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s9) | node24(s9) | node25(s9) | (~node26(s9)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21570,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s9) | node24(s9) | node25(s9) | (~node26(s9))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21569, 21568])).
% 88.16/88.36 tff(21571,plain,
% 88.16/88.36 (node25(s9) | (~node26(s9))),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21570, 8435, 21567, 21563])).
% 88.16/88.36 tff(21572,plain,
% 88.16/88.36 (~node26(s9)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21571, 21555])).
% 88.16/88.36 tff(21573,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21574,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21575,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21574, 21573])).
% 88.16/88.36 tff(21576,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_3, c_u, s7)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21575, 4481, 21255])).
% 88.16/88.36 tff(21577,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s7) | (~node25(s7)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s7) | (~node25(s7)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21578,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s7) | (~node25(s7)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21579,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_3, c_u, s7) | (~node25(s7))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21578, 21577])).
% 88.16/88.36 tff(21580,plain,
% 88.16/88.36 (~node25(s7)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21579, 21376, 21576])).
% 88.16/88.36 tff(21581,assumption,(m_user_v_ack(c_e_h_1, c_u, s7)), introduced(assumption)).
% 88.16/88.36 tff(21582,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21583,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21584,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21583, 21582])).
% 88.16/88.36 tff(21585,plain,
% 88.16/88.36 ($false),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21584, 4481, 21581, 5404])).
% 88.16/88.36 tff(21586,plain,(~m_user_v_ack(c_e_h_1, c_u, s7)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.36 tff(21587,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s7) | (~node24(s7)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s7) | (~node24(s7)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21588,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s7) | (~node24(s7)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21589,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s7) | (~node24(s7))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21588, 21587])).
% 88.16/88.36 tff(21590,plain,
% 88.16/88.36 (~node24(s7)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21589, 8407, 21586])).
% 88.16/88.36 tff(21591,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s7) | (~node23(s7)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s7) | (~node23(s7)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21592,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s7) | (~node23(s7)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21593,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s7) | (~node23(s7))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21592, 21591])).
% 88.16/88.36 tff(21594,plain,
% 88.16/88.36 (~node23(s7)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21593, 8418, 21586])).
% 88.16/88.36 tff(21595,plain,
% 88.16/88.36 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s7) | node24(s7) | node25(s7) | (~node26(s7)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s7) | node24(s7) | node25(s7) | (~node26(s7)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21596,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s7) | node24(s7) | node25(s7) | (~node26(s7)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21597,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s7) | node24(s7) | node25(s7) | (~node26(s7))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21596, 21595])).
% 88.16/88.36 tff(21598,plain,
% 88.16/88.36 (node25(s7) | (~node26(s7))),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21597, 8435, 21594, 21590])).
% 88.16/88.36 tff(21599,plain,
% 88.16/88.36 (~node26(s7)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21598, 21580])).
% 88.16/88.36 tff(21600,assumption,(m_user_v_ack(c_e_h_2, c_u, s5)), introduced(assumption)).
% 88.16/88.36 tff(21601,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_r, s5)), introduced(assumption)).
% 88.16/88.36 tff(21602,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21603,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21604,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21603, 21602])).
% 88.16/88.36 tff(21605,plain,
% 88.16/88.36 ($false),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21604, 4481, 21601, 21600])).
% 88.16/88.36 tff(21606,plain,((~m_user_v_ack(c_e_h_2, c_u, s5)) | m_and_h_gate_v_out(c_e_h_2, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.36 tff(21607,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_2, c_u, s5)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21606, 2036])).
% 88.16/88.36 tff(21608,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s5)) | m_user_v_ack(c_e_h_2, c_u, s5))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s5)) | m_user_v_ack(c_e_h_2, c_u, s5))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21609,plain,
% 88.16/88.36 ((m_user_v_ack(c_e_h_2, c_u, s5) | (~node25(s5))) <=> ((~node25(s5)) | m_user_v_ack(c_e_h_2, c_u, s5))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21610,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s5) | (~node25(s5)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s5)) | m_user_v_ack(c_e_h_2, c_u, s5)))),
% 88.16/88.36 inference(monotonicity,[status(thm)],[21609])).
% 88.16/88.36 tff(21611,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s5) | (~node25(s5)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s5)) | m_user_v_ack(c_e_h_2, c_u, s5))),
% 88.16/88.36 inference(transitivity,[status(thm)],[21610, 21608])).
% 88.16/88.36 tff(21612,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s5) | (~node25(s5)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21613,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s5)) | m_user_v_ack(c_e_h_2, c_u, s5)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21612, 21611])).
% 88.16/88.36 tff(21614,plain,
% 88.16/88.36 (~node25(s5)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21613, 4492, 21607])).
% 88.16/88.36 tff(21615,assumption,(m_user_v_ack(c_e_h_1, c_u, s5)), introduced(assumption)).
% 88.16/88.36 tff(21616,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21617,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21618,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21617, 21616])).
% 88.16/88.36 tff(21619,plain,
% 88.16/88.36 ($false),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21618, 4481, 21615, 5188])).
% 88.16/88.36 tff(21620,plain,((~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.36 tff(21621,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_1, c_u, s5)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21620, 5035])).
% 88.16/88.36 tff(21622,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s5) | (~node24(s5)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s5) | (~node24(s5)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21623,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s5) | (~node24(s5)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21624,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s5) | (~node24(s5))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21623, 21622])).
% 88.16/88.36 tff(21625,plain,
% 88.16/88.36 (~node24(s5)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21624, 8407, 21621])).
% 88.16/88.36 tff(21626,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s5) | (~node23(s5)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s5) | (~node23(s5)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21627,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s5) | (~node23(s5)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21628,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s5) | (~node23(s5))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21627, 21626])).
% 88.16/88.36 tff(21629,plain,
% 88.16/88.36 (~node23(s5)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21628, 8418, 21621])).
% 88.16/88.36 tff(21630,plain,
% 88.16/88.36 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s5) | node24(s5) | node25(s5) | (~node26(s5)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s5) | node24(s5) | node25(s5) | (~node26(s5)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21631,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s5) | node24(s5) | node25(s5) | (~node26(s5)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21632,plain,
% 88.16/88.36 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s5) | node24(s5) | node25(s5) | (~node26(s5))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21631, 21630])).
% 88.16/88.36 tff(21633,plain,
% 88.16/88.36 (node25(s5) | (~node26(s5))),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21632, 8435, 21629, 21625])).
% 88.16/88.36 tff(21634,plain,
% 88.16/88.36 (~node26(s5)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21633, 21614])).
% 88.16/88.36 tff(21635,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21636,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21637,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s6)) | m_and_h_gate_v_out(c_e_h_2, c_r, s6)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21636, 21635])).
% 88.16/88.36 tff(21638,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_2, c_u, s6)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21637, 4481, 2041])).
% 88.16/88.36 tff(21639,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s6) | (~node25(s6)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s6) | (~node25(s6)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21640,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s6) | (~node25(s6)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21641,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s6) | (~node25(s6))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21640, 21639])).
% 88.16/88.36 tff(21642,plain,
% 88.16/88.36 (~node25(s6)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21641, 4492, 21638])).
% 88.16/88.36 tff(21643,plain,
% 88.16/88.36 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21644,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21645,plain,
% 88.16/88.36 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21644, 21643])).
% 88.16/88.36 tff(21646,plain,
% 88.16/88.36 (~m_user_v_ack(c_e_h_1, c_u, s6)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21645, 4481, 5209])).
% 88.16/88.36 tff(21647,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s6) | (~node24(s6)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s6) | (~node24(s6)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21648,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s6) | (~node24(s6)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21649,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s6) | (~node24(s6))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21648, 21647])).
% 88.16/88.36 tff(21650,plain,
% 88.16/88.36 (~node24(s6)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21649, 8407, 21646])).
% 88.16/88.36 tff(21651,plain,
% 88.16/88.36 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6)))),
% 88.16/88.36 inference(rewrite,[status(thm)],[])).
% 88.16/88.36 tff(21652,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6)))),
% 88.16/88.36 inference(quant_inst,[status(thm)],[])).
% 88.16/88.36 tff(21653,plain,
% 88.16/88.36 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s6) | (~node23(s6))),
% 88.16/88.36 inference(modus_ponens,[status(thm)],[21652, 21651])).
% 88.16/88.36 tff(21654,plain,
% 88.16/88.36 (~node23(s6)),
% 88.16/88.36 inference(unit_resolution,[status(thm)],[21653, 8418, 21646])).
% 88.16/88.36 tff(21655,plain,
% 88.16/88.36 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s6) | node24(s6) | node25(s6) | (~node26(s6)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s6) | node24(s6) | node25(s6) | (~node26(s6)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21656,plain,
% 88.16/88.37 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s6) | node24(s6) | node25(s6) | (~node26(s6)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21657,plain,
% 88.16/88.37 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s6) | node24(s6) | node25(s6) | (~node26(s6))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21656, 21655])).
% 88.16/88.37 tff(21658,plain,
% 88.16/88.37 (node25(s6) | (~node26(s6))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21657, 8435, 21654, 21650])).
% 88.16/88.37 tff(21659,plain,
% 88.16/88.37 (~node26(s6)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21658, 21642])).
% 88.16/88.37 tff(21660,plain,
% 88.16/88.37 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21661,plain,
% 88.16/88.37 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21662,plain,
% 88.16/88.37 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s4)) | m_and_h_gate_v_out(c_e_h_2, c_r, s4)),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21661, 21660])).
% 88.16/88.37 tff(21663,plain,
% 88.16/88.37 (~m_user_v_ack(c_e_h_2, c_u, s4)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21662, 4481, 2031])).
% 88.16/88.37 tff(21664,plain,
% 88.16/88.37 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21665,plain,
% 88.16/88.37 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21666,plain,
% 88.16/88.37 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s4) | (~node25(s4))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21665, 21664])).
% 88.16/88.37 tff(21667,plain,
% 88.16/88.37 (~node25(s4)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21666, 4492, 21663])).
% 88.16/88.37 tff(21668,plain,
% 88.16/88.37 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21669,plain,
% 88.16/88.37 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21670,plain,
% 88.16/88.37 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21669, 21668])).
% 88.16/88.37 tff(21671,plain,
% 88.16/88.37 (~m_user_v_ack(c_e_h_1, c_u, s4)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21670, 4481, 4848])).
% 88.16/88.37 tff(21672,plain,
% 88.16/88.37 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21673,plain,
% 88.16/88.37 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21674,plain,
% 88.16/88.37 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s4) | (~node24(s4))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21673, 21672])).
% 88.16/88.37 tff(21675,plain,
% 88.16/88.37 (~node24(s4)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21674, 8407, 21671])).
% 88.16/88.37 tff(21676,plain,
% 88.16/88.37 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21677,plain,
% 88.16/88.37 ((m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4))) <=> ((~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21678,plain,
% 88.16/88.37 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4)))),
% 88.16/88.37 inference(monotonicity,[status(thm)],[21677])).
% 88.16/88.37 tff(21679,plain,
% 88.16/88.37 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4))),
% 88.16/88.37 inference(transitivity,[status(thm)],[21678, 21676])).
% 88.16/88.37 tff(21680,plain,
% 88.16/88.37 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s4) | (~node23(s4)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21681,plain,
% 88.16/88.37 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s4)) | m_user_v_ack(c_e_h_1, c_u, s4)),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21680, 21679])).
% 88.16/88.37 tff(21682,plain,
% 88.16/88.37 (~node23(s4)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21681, 8418, 21671])).
% 88.16/88.37 tff(21683,plain,
% 88.16/88.37 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21684,plain,
% 88.16/88.37 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s4) | node24(s4) | node25(s4) | (~node26(s4)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21685,plain,
% 88.16/88.37 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s4) | node24(s4) | node25(s4) | (~node26(s4))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21684, 21683])).
% 88.16/88.37 tff(21686,plain,
% 88.16/88.37 (node25(s4) | (~node26(s4))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21685, 8435, 21682, 21675])).
% 88.16/88.37 tff(21687,plain,
% 88.16/88.37 (~node26(s4)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21686, 21667])).
% 88.16/88.37 tff(21688,assumption,(~node26(s6)), introduced(assumption)).
% 88.16/88.37 tff(21689,assumption,(~node26(s18)), introduced(assumption)).
% 88.16/88.37 tff(21690,plain,
% 88.16/88.37 (^[X: $i] : refl(((~last(X)) | (~xuntil2p30(X))) <=> ((~last(X)) | (~xuntil2p30(X))))),
% 88.16/88.37 inference(bind,[status(th)],[])).
% 88.16/88.37 tff(21691,plain,
% 88.16/88.37 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(quant_intro,[status(thm)],[21690])).
% 88.16/88.37 tff(21692,plain,
% 88.16/88.37 (![X: $i] : ((~last(X)) | (~xuntil2p30(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21693,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p30(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty14')).
% 88.16/88.37 tff(21694,plain,
% 88.16/88.37 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21693, 21692])).
% 88.16/88.37 tff(21695,plain,(
% 88.16/88.37 ![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(skolemize,[status(sab)],[21694])).
% 88.16/88.37 tff(21696,plain,
% 88.16/88.37 (![X: $i] : ((~last(X)) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21695, 21691])).
% 88.16/88.37 tff(21697,plain,
% 88.16/88.37 (last(s19) <=> last(s19)),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21698,axiom,(last(s19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound20')).
% 88.16/88.37 tff(21699,plain,
% 88.16/88.37 (last(s19)),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21698, 21697])).
% 88.16/88.37 tff(21700,plain,
% 88.16/88.37 (((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s19)) | (~xuntil2p30(s19)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s19)) | (~xuntil2p30(s19)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21701,plain,
% 88.16/88.37 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | ((~last(s19)) | (~xuntil2p30(s19)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21702,plain,
% 88.16/88.37 ((~![X: $i] : ((~last(X)) | (~xuntil2p30(X)))) | (~last(s19)) | (~xuntil2p30(s19))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21701, 21700])).
% 88.16/88.37 tff(21703,plain,
% 88.16/88.37 (~xuntil2p30(s19)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21702, 21699, 21696])).
% 88.16/88.37 tff(21704,plain,
% 88.16/88.37 (^[X: $i] : refl((node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 88.16/88.37 inference(bind,[status(th)],[])).
% 88.16/88.37 tff(21705,plain,
% 88.16/88.37 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 88.16/88.37 inference(quant_intro,[status(thm)],[21704])).
% 88.16/88.37 tff(21706,plain,
% 88.16/88.37 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21707,plain,
% 88.16/88.37 (^[X: $i] : rewrite(((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> (node26(X) | xuntil2p30(X) | (~until2p29(X))))),
% 88.16/88.37 inference(bind,[status(th)],[])).
% 88.16/88.37 tff(21708,plain,
% 88.16/88.37 (![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X))) <=> ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 88.16/88.37 inference(quant_intro,[status(thm)],[21707])).
% 88.16/88.37 tff(21709,axiom,(![X: $i] : ((node26(X) | xuntil2p30(X)) | (~until2p29(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty12')).
% 88.16/88.37 tff(21710,plain,
% 88.16/88.37 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21709, 21708])).
% 88.16/88.37 tff(21711,plain,
% 88.16/88.37 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21710, 21706])).
% 88.16/88.37 tff(21712,plain,(
% 88.16/88.37 ![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 88.16/88.37 inference(skolemize,[status(sab)],[21711])).
% 88.16/88.37 tff(21713,plain,
% 88.16/88.37 (![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21712, 21705])).
% 88.16/88.37 tff(21714,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21715,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s19) | xuntil2p30(s19) | (~until2p29(s19)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21716,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s19) | xuntil2p30(s19) | (~until2p29(s19))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21715, 21714])).
% 88.16/88.37 tff(21717,plain,
% 88.16/88.37 (node26(s19) | (~until2p29(s19))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21716, 21713, 21703])).
% 88.16/88.37 tff(21718,plain,
% 88.16/88.37 (~until2p29(s19)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21717, 21410])).
% 88.16/88.37 tff(21719,plain,
% 88.16/88.37 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 88.16/88.37 inference(bind,[status(th)],[])).
% 88.16/88.37 tff(21720,plain,
% 88.16/88.37 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(quant_intro,[status(thm)],[21719])).
% 88.16/88.37 tff(21721,plain,
% 88.16/88.37 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21722,plain,
% 88.16/88.37 (^[Y: $i, X: $i] : rewrite(((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X))))),
% 88.16/88.37 inference(bind,[status(th)],[])).
% 88.16/88.37 tff(21723,plain,
% 88.16/88.37 (![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(quant_intro,[status(thm)],[21722])).
% 88.16/88.37 tff(21724,axiom,(![Y: $i, X: $i] : ((until2p29(Y) | (~succ(X, Y))) | (~xuntil2p30(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty13')).
% 88.16/88.37 tff(21725,plain,
% 88.16/88.37 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21724, 21723])).
% 88.16/88.37 tff(21726,plain,
% 88.16/88.37 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21725, 21721])).
% 88.16/88.37 tff(21727,plain,(
% 88.16/88.37 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(skolemize,[status(sab)],[21726])).
% 88.16/88.37 tff(21728,plain,
% 88.16/88.37 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21727, 21720])).
% 88.16/88.37 tff(21729,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21730,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21731,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s18, s19)) | until2p29(s19) | (~xuntil2p30(s18))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21730, 21729])).
% 88.16/88.37 tff(21732,plain,
% 88.16/88.37 (until2p29(s19) | (~xuntil2p30(s18))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21731, 15723, 21728])).
% 88.16/88.37 tff(21733,plain,
% 88.16/88.37 (~xuntil2p30(s18)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21732, 21718])).
% 88.16/88.37 tff(21734,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21735,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s18) | xuntil2p30(s18) | (~until2p29(s18)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21736,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s18) | xuntil2p30(s18) | (~until2p29(s18))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21735, 21734])).
% 88.16/88.37 tff(21737,plain,
% 88.16/88.37 (node26(s18) | (~until2p29(s18))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21736, 21713, 21733])).
% 88.16/88.37 tff(21738,plain,
% 88.16/88.37 (~until2p29(s18)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21737, 21689])).
% 88.16/88.37 tff(21739,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21740,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21741,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s17, s18)) | until2p29(s18) | (~xuntil2p30(s17))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21740, 21739])).
% 88.16/88.37 tff(21742,plain,
% 88.16/88.37 (until2p29(s18) | (~xuntil2p30(s17))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21741, 15697, 21728])).
% 88.16/88.37 tff(21743,plain,
% 88.16/88.37 (~xuntil2p30(s17)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21742, 21738])).
% 88.16/88.37 tff(21744,assumption,(~node26(s17)), introduced(assumption)).
% 88.16/88.37 tff(21745,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21746,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s17) | xuntil2p30(s17) | (~until2p29(s17)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21747,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s17) | xuntil2p30(s17) | (~until2p29(s17))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21746, 21745])).
% 88.16/88.37 tff(21748,plain,
% 88.16/88.37 (xuntil2p30(s17) | (~until2p29(s17))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21747, 21713, 21744])).
% 88.16/88.37 tff(21749,plain,
% 88.16/88.37 (~until2p29(s17)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21748, 21743])).
% 88.16/88.37 tff(21750,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21751,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21752,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s16, s17)) | until2p29(s17) | (~xuntil2p30(s16))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21751, 21750])).
% 88.16/88.37 tff(21753,plain,
% 88.16/88.37 (until2p29(s17) | (~xuntil2p30(s16))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21752, 14092, 21728])).
% 88.16/88.37 tff(21754,plain,
% 88.16/88.37 (~xuntil2p30(s16)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21753, 21749])).
% 88.16/88.37 tff(21755,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21756,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s16) | xuntil2p30(s16) | (~until2p29(s16)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21757,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s16) | xuntil2p30(s16) | (~until2p29(s16))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21756, 21755])).
% 88.16/88.37 tff(21758,plain,
% 88.16/88.37 (xuntil2p30(s16) | (~until2p29(s16))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21757, 21713, 21404])).
% 88.16/88.37 tff(21759,plain,
% 88.16/88.37 (~until2p29(s16)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21758, 21754])).
% 88.16/88.37 tff(21760,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21761,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21762,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s15, s16)) | until2p29(s16) | (~xuntil2p30(s15))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21761, 21760])).
% 88.16/88.37 tff(21763,plain,
% 88.16/88.37 (until2p29(s16) | (~xuntil2p30(s15))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21762, 12875, 21728])).
% 88.16/88.37 tff(21764,plain,
% 88.16/88.37 (~xuntil2p30(s15)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21763, 21759])).
% 88.16/88.37 tff(21765,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21766,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s15) | xuntil2p30(s15) | (~until2p29(s15)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21767,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s15) | xuntil2p30(s15) | (~until2p29(s15))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21766, 21765])).
% 88.16/88.37 tff(21768,plain,
% 88.16/88.37 (xuntil2p30(s15) | (~until2p29(s15))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21767, 21713, 21409])).
% 88.16/88.37 tff(21769,plain,
% 88.16/88.37 (~until2p29(s15)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21768, 21764])).
% 88.16/88.37 tff(21770,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21771,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21772,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s14, s15)) | until2p29(s15) | (~xuntil2p30(s14))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21771, 21770])).
% 88.16/88.37 tff(21773,plain,
% 88.16/88.37 (until2p29(s15) | (~xuntil2p30(s14))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21772, 10500, 21728])).
% 88.16/88.37 tff(21774,plain,
% 88.16/88.37 (~xuntil2p30(s14)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21773, 21769])).
% 88.16/88.37 tff(21775,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21776,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s14) | xuntil2p30(s14) | (~until2p29(s14)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21777,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s14) | xuntil2p30(s14) | (~until2p29(s14))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21776, 21775])).
% 88.16/88.37 tff(21778,plain,
% 88.16/88.37 (xuntil2p30(s14) | (~until2p29(s14))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21777, 21713, 21406])).
% 88.16/88.37 tff(21779,plain,
% 88.16/88.37 (~until2p29(s14)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21778, 21774])).
% 88.16/88.37 tff(21780,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21781,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21782,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s13, s14)) | until2p29(s14) | (~xuntil2p30(s13))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21781, 21780])).
% 88.16/88.37 tff(21783,plain,
% 88.16/88.37 (until2p29(s14) | (~xuntil2p30(s13))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21782, 10036, 21728])).
% 88.16/88.37 tff(21784,plain,
% 88.16/88.37 (~xuntil2p30(s13)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21783, 21779])).
% 88.16/88.37 tff(21785,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21786,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s13) | xuntil2p30(s13) | (~until2p29(s13)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21787,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s13) | xuntil2p30(s13) | (~until2p29(s13))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21786, 21785])).
% 88.16/88.37 tff(21788,plain,
% 88.16/88.37 (xuntil2p30(s13) | (~until2p29(s13))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21787, 21713, 21408])).
% 88.16/88.37 tff(21789,plain,
% 88.16/88.37 (~until2p29(s13)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21788, 21784])).
% 88.16/88.37 tff(21790,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21791,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21792,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s12, s13)) | until2p29(s13) | (~xuntil2p30(s12))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21791, 21790])).
% 88.16/88.37 tff(21793,plain,
% 88.16/88.37 (until2p29(s13) | (~xuntil2p30(s12))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21792, 9595, 21728])).
% 88.16/88.37 tff(21794,plain,
% 88.16/88.37 (~xuntil2p30(s12)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21793, 21789])).
% 88.16/88.37 tff(21795,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21796,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s12) | xuntil2p30(s12) | (~until2p29(s12)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21797,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s12) | xuntil2p30(s12) | (~until2p29(s12))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21796, 21795])).
% 88.16/88.37 tff(21798,plain,
% 88.16/88.37 (xuntil2p30(s12) | (~until2p29(s12))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21797, 21713, 21405])).
% 88.16/88.37 tff(21799,plain,
% 88.16/88.37 (~until2p29(s12)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21798, 21794])).
% 88.16/88.37 tff(21800,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21801,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21802,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s11, s12)) | until2p29(s12) | (~xuntil2p30(s11))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21801, 21800])).
% 88.16/88.37 tff(21803,plain,
% 88.16/88.37 (until2p29(s12) | (~xuntil2p30(s11))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21802, 4457, 21728])).
% 88.16/88.37 tff(21804,plain,
% 88.16/88.37 (~xuntil2p30(s11)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21803, 21799])).
% 88.16/88.37 tff(21805,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21806,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s11) | xuntil2p30(s11) | (~until2p29(s11)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21807,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s11) | xuntil2p30(s11) | (~until2p29(s11))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21806, 21805])).
% 88.16/88.37 tff(21808,plain,
% 88.16/88.37 (xuntil2p30(s11) | (~until2p29(s11))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21807, 21713, 21407])).
% 88.16/88.37 tff(21809,plain,
% 88.16/88.37 (~until2p29(s11)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21808, 21804])).
% 88.16/88.37 tff(21810,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21811,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21812,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s10, s11)) | until2p29(s11) | (~xuntil2p30(s10))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21811, 21810])).
% 88.16/88.37 tff(21813,plain,
% 88.16/88.37 (until2p29(s11) | (~xuntil2p30(s10))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21812, 3774, 21728])).
% 88.16/88.37 tff(21814,plain,
% 88.16/88.37 (~xuntil2p30(s10)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21813, 21809])).
% 88.16/88.37 tff(21815,assumption,(~node26(s10)), introduced(assumption)).
% 88.16/88.37 tff(21816,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21817,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s10) | xuntil2p30(s10) | (~until2p29(s10)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21818,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s10) | xuntil2p30(s10) | (~until2p29(s10))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21817, 21816])).
% 88.16/88.37 tff(21819,plain,
% 88.16/88.37 (xuntil2p30(s10) | (~until2p29(s10))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21818, 21713, 21815])).
% 88.16/88.37 tff(21820,plain,
% 88.16/88.37 (~until2p29(s10)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21819, 21814])).
% 88.16/88.37 tff(21821,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21822,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21823,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s9, s10)) | until2p29(s10) | (~xuntil2p30(s9))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21822, 21821])).
% 88.16/88.37 tff(21824,plain,
% 88.16/88.37 (until2p29(s10) | (~xuntil2p30(s9))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21823, 3171, 21728])).
% 88.16/88.37 tff(21825,plain,
% 88.16/88.37 (~xuntil2p30(s9)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21824, 21820])).
% 88.16/88.37 tff(21826,assumption,(~node26(s9)), introduced(assumption)).
% 88.16/88.37 tff(21827,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21828,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s9) | xuntil2p30(s9) | (~until2p29(s9)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21829,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s9) | xuntil2p30(s9) | (~until2p29(s9))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21828, 21827])).
% 88.16/88.37 tff(21830,plain,
% 88.16/88.37 (xuntil2p30(s9) | (~until2p29(s9))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21829, 21713, 21826])).
% 88.16/88.37 tff(21831,plain,
% 88.16/88.37 (~until2p29(s9)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21830, 21825])).
% 88.16/88.37 tff(21832,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21833,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21834,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s8, s9)) | until2p29(s9) | (~xuntil2p30(s8))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21833, 21832])).
% 88.16/88.37 tff(21835,plain,
% 88.16/88.37 (until2p29(s9) | (~xuntil2p30(s8))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21834, 2632, 21728])).
% 88.16/88.37 tff(21836,plain,
% 88.16/88.37 (~xuntil2p30(s8)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21835, 21831])).
% 88.16/88.37 tff(21837,assumption,(~node26(s8)), introduced(assumption)).
% 88.16/88.37 tff(21838,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21839,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s8) | xuntil2p30(s8) | (~until2p29(s8)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21840,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s8) | xuntil2p30(s8) | (~until2p29(s8))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21839, 21838])).
% 88.16/88.37 tff(21841,plain,
% 88.16/88.37 (xuntil2p30(s8) | (~until2p29(s8))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21840, 21713, 21837])).
% 88.16/88.37 tff(21842,plain,
% 88.16/88.37 (~until2p29(s8)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21841, 21836])).
% 88.16/88.37 tff(21843,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21844,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21845,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s7, s8)) | until2p29(s8) | (~xuntil2p30(s7))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21844, 21843])).
% 88.16/88.37 tff(21846,plain,
% 88.16/88.37 (until2p29(s8) | (~xuntil2p30(s7))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21845, 2148, 21728])).
% 88.16/88.37 tff(21847,plain,
% 88.16/88.37 (~xuntil2p30(s7)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21846, 21842])).
% 88.16/88.37 tff(21848,assumption,(~node26(s7)), introduced(assumption)).
% 88.16/88.37 tff(21849,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21850,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s7) | xuntil2p30(s7) | (~until2p29(s7)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21851,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s7) | xuntil2p30(s7) | (~until2p29(s7))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21850, 21849])).
% 88.16/88.37 tff(21852,plain,
% 88.16/88.37 (xuntil2p30(s7) | (~until2p29(s7))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21851, 21713, 21848])).
% 88.16/88.37 tff(21853,plain,
% 88.16/88.37 (~until2p29(s7)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21852, 21847])).
% 88.16/88.37 tff(21854,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21855,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21856,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s6, s7)) | until2p29(s7) | (~xuntil2p30(s6))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21855, 21854])).
% 88.16/88.37 tff(21857,plain,
% 88.16/88.37 (until2p29(s7) | (~xuntil2p30(s6))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21856, 1548, 21728])).
% 88.16/88.37 tff(21858,plain,
% 88.16/88.37 (~xuntil2p30(s6)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21857, 21853])).
% 88.16/88.37 tff(21859,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21860,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s6) | xuntil2p30(s6) | (~until2p29(s6)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21861,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s6) | xuntil2p30(s6) | (~until2p29(s6))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21860, 21859])).
% 88.16/88.37 tff(21862,plain,
% 88.16/88.37 (node26(s6) | (~until2p29(s6))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21861, 21713, 21858])).
% 88.16/88.37 tff(21863,plain,
% 88.16/88.37 (~until2p29(s6)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21862, 21688])).
% 88.16/88.37 tff(21864,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21865,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21866,plain,
% 88.16/88.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s5, s6)) | until2p29(s6) | (~xuntil2p30(s5))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21865, 21864])).
% 88.16/88.37 tff(21867,plain,
% 88.16/88.37 (until2p29(s6) | (~xuntil2p30(s5))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21866, 1495, 21728])).
% 88.16/88.37 tff(21868,plain,
% 88.16/88.37 (~xuntil2p30(s5)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21867, 21863])).
% 88.16/88.37 tff(21869,assumption,(~node26(s5)), introduced(assumption)).
% 88.16/88.37 tff(21870,plain,
% 88.16/88.37 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 88.16/88.37 inference(rewrite,[status(thm)],[])).
% 88.16/88.37 tff(21871,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s5) | xuntil2p30(s5) | (~until2p29(s5)))),
% 88.16/88.37 inference(quant_inst,[status(thm)],[])).
% 88.16/88.37 tff(21872,plain,
% 88.16/88.37 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s5) | xuntil2p30(s5) | (~until2p29(s5))),
% 88.16/88.37 inference(modus_ponens,[status(thm)],[21871, 21870])).
% 88.16/88.37 tff(21873,plain,
% 88.16/88.37 (xuntil2p30(s5) | (~until2p29(s5))),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21872, 21713, 21869])).
% 88.16/88.37 tff(21874,plain,
% 88.16/88.37 (~until2p29(s5)),
% 88.16/88.37 inference(unit_resolution,[status(thm)],[21873, 21868])).
% 88.16/88.37 tff(21875,plain,
% 88.16/88.37 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21876,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21877,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s4, s5)) | until2p29(s5) | (~xuntil2p30(s4))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21876, 21875])).
% 88.16/88.38 tff(21878,plain,
% 88.16/88.38 (until2p29(s5) | (~xuntil2p30(s4))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21877, 1428, 21728])).
% 88.16/88.38 tff(21879,plain,
% 88.16/88.38 (~xuntil2p30(s4)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21878, 21874])).
% 88.16/88.38 tff(21880,assumption,(~node26(s4)), introduced(assumption)).
% 88.16/88.38 tff(21881,plain,
% 88.16/88.38 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21882,plain,
% 88.16/88.38 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s4) | xuntil2p30(s4) | (~until2p29(s4)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21883,plain,
% 88.16/88.38 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s4) | xuntil2p30(s4) | (~until2p29(s4))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21882, 21881])).
% 88.16/88.38 tff(21884,plain,
% 88.16/88.38 (xuntil2p30(s4) | (~until2p29(s4))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21883, 21713, 21880])).
% 88.16/88.38 tff(21885,plain,
% 88.16/88.38 (~until2p29(s4)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21884, 21879])).
% 88.16/88.38 tff(21886,plain,
% 88.16/88.38 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21887,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21888,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s3, s4)) | until2p29(s4) | (~xuntil2p30(s3))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21887, 21886])).
% 88.16/88.38 tff(21889,plain,
% 88.16/88.38 (until2p29(s4) | (~xuntil2p30(s3))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21888, 675, 21728])).
% 88.16/88.38 tff(21890,plain,
% 88.16/88.38 (~xuntil2p30(s3)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21889, 21885])).
% 88.16/88.38 tff(21891,plain,
% 88.16/88.38 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21892,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21893,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s3)) | m_and_h_gate_v_out(c_e_h_2, c_r, s3)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21892, 21891])).
% 88.16/88.38 tff(21894,plain,
% 88.16/88.38 (~m_user_v_ack(c_e_h_2, c_u, s3)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21893, 4481, 2026])).
% 88.16/88.38 tff(21895,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s3) | (~node25(s3)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s3) | (~node25(s3)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21896,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s3) | (~node25(s3)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21897,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s3) | (~node25(s3))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21896, 21895])).
% 88.16/88.38 tff(21898,plain,
% 88.16/88.38 (~node25(s3)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21897, 4492, 21894])).
% 88.16/88.38 tff(21899,plain,
% 88.16/88.38 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21900,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21901,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21900, 21899])).
% 88.16/88.38 tff(21902,plain,
% 88.16/88.38 (~m_user_v_ack(c_e_h_1, c_u, s3)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21901, 4481, 4698])).
% 88.16/88.38 tff(21903,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s3) | (~node24(s3)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s3) | (~node24(s3)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21904,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s3) | (~node24(s3)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21905,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s3) | (~node24(s3))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21904, 21903])).
% 88.16/88.38 tff(21906,plain,
% 88.16/88.38 (~node24(s3)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21905, 8407, 21902])).
% 88.16/88.38 tff(21907,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s3)) | m_user_v_ack(c_e_h_1, c_u, s3))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s3)) | m_user_v_ack(c_e_h_1, c_u, s3))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21908,plain,
% 88.16/88.38 ((m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3))) <=> ((~node23(s3)) | m_user_v_ack(c_e_h_1, c_u, s3))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21909,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s3)) | m_user_v_ack(c_e_h_1, c_u, s3)))),
% 88.16/88.38 inference(monotonicity,[status(thm)],[21908])).
% 88.16/88.38 tff(21910,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s3)) | m_user_v_ack(c_e_h_1, c_u, s3))),
% 88.16/88.38 inference(transitivity,[status(thm)],[21909, 21907])).
% 88.16/88.38 tff(21911,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s3) | (~node23(s3)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21912,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s3)) | m_user_v_ack(c_e_h_1, c_u, s3)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21911, 21910])).
% 88.16/88.38 tff(21913,plain,
% 88.16/88.38 (~node23(s3)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21912, 8418, 21902])).
% 88.16/88.38 tff(21914,plain,
% 88.16/88.38 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21915,plain,
% 88.16/88.38 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s3) | node24(s3) | node25(s3) | (~node26(s3)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21916,plain,
% 88.16/88.38 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s3) | node24(s3) | node25(s3) | (~node26(s3))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21915, 21914])).
% 88.16/88.38 tff(21917,plain,
% 88.16/88.38 (node25(s3) | (~node26(s3))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21916, 8435, 21913, 21906])).
% 88.16/88.38 tff(21918,plain,
% 88.16/88.38 (~node26(s3)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21917, 21898])).
% 88.16/88.38 tff(21919,plain,
% 88.16/88.38 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21920,plain,
% 88.16/88.38 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s3) | xuntil2p30(s3) | (~until2p29(s3)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21921,plain,
% 88.16/88.38 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s3) | xuntil2p30(s3) | (~until2p29(s3))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21920, 21919])).
% 88.16/88.38 tff(21922,plain,
% 88.16/88.38 (xuntil2p30(s3) | (~until2p29(s3))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21921, 21713, 21918])).
% 88.16/88.38 tff(21923,plain,
% 88.16/88.38 (~until2p29(s3)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21922, 21890])).
% 88.16/88.38 tff(21924,plain,
% 88.16/88.38 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21925,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21926,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s2, s3)) | until2p29(s3) | (~xuntil2p30(s2))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21925, 21924])).
% 88.16/88.38 tff(21927,plain,
% 88.16/88.38 (until2p29(s3) | (~xuntil2p30(s2))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21926, 578, 21728])).
% 88.16/88.38 tff(21928,plain,
% 88.16/88.38 (~xuntil2p30(s2)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21927, 21923])).
% 88.16/88.38 tff(21929,plain,
% 88.16/88.38 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21930,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21931,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s2)) | m_and_h_gate_v_out(c_e_h_2, c_r, s2)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21930, 21929])).
% 88.16/88.38 tff(21932,plain,
% 88.16/88.38 (~m_user_v_ack(c_e_h_2, c_u, s2)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21931, 4481, 2021])).
% 88.16/88.38 tff(21933,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s2) | (~node25(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s2) | (~node25(s2)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21934,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s2) | (~node25(s2)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21935,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | m_user_v_ack(c_e_h_2, c_u, s2) | (~node25(s2))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21934, 21933])).
% 88.16/88.38 tff(21936,plain,
% 88.16/88.38 (~node25(s2)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21935, 4492, 21932])).
% 88.16/88.38 tff(21937,plain,
% 88.16/88.38 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21938,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21939,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21938, 21937])).
% 88.16/88.38 tff(21940,plain,
% 88.16/88.38 (~m_user_v_ack(c_e_h_1, c_u, s2)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21939, 4481, 4611])).
% 88.16/88.38 tff(21941,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21942,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21943,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node24(s2))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21942, 21941])).
% 88.16/88.38 tff(21944,plain,
% 88.16/88.38 (~node24(s2)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21943, 8407, 21940])).
% 88.16/88.38 tff(21945,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node23(s2)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node23(s2)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21946,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s2) | (~node23(s2)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21947,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | m_user_v_ack(c_e_h_1, c_u, s2) | (~node23(s2))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21946, 21945])).
% 88.16/88.38 tff(21948,plain,
% 88.16/88.38 (~node23(s2)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21947, 8418, 21940])).
% 88.16/88.38 tff(21949,plain,
% 88.16/88.38 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21950,plain,
% 88.16/88.38 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s2) | node24(s2) | node25(s2) | (~node26(s2)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21951,plain,
% 88.16/88.38 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s2) | node24(s2) | node25(s2) | (~node26(s2))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21950, 21949])).
% 88.16/88.38 tff(21952,plain,
% 88.16/88.38 (node25(s2) | (~node26(s2))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21951, 8435, 21948, 21944])).
% 88.16/88.38 tff(21953,plain,
% 88.16/88.38 (~node26(s2)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21952, 21936])).
% 88.16/88.38 tff(21954,plain,
% 88.16/88.38 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21955,plain,
% 88.16/88.38 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s2) | xuntil2p30(s2) | (~until2p29(s2)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21956,plain,
% 88.16/88.38 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s2) | xuntil2p30(s2) | (~until2p29(s2))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21955, 21954])).
% 88.16/88.38 tff(21957,plain,
% 88.16/88.38 (xuntil2p30(s2) | (~until2p29(s2))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21956, 21713, 21953])).
% 88.16/88.38 tff(21958,plain,
% 88.16/88.38 (~until2p29(s2)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21957, 21928])).
% 88.16/88.38 tff(21959,plain,
% 88.16/88.38 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21960,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21961,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s1, s2)) | until2p29(s2) | (~xuntil2p30(s1))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21960, 21959])).
% 88.16/88.38 tff(21962,plain,
% 88.16/88.38 (until2p29(s2) | (~xuntil2p30(s1))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21961, 340, 21728])).
% 88.16/88.38 tff(21963,plain,
% 88.16/88.38 (~xuntil2p30(s1)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21962, 21958])).
% 88.16/88.38 tff(21964,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | ((~node25(s1)) | m_user_v_ack(c_e_h_3, c_u, s1))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s1)) | m_user_v_ack(c_e_h_3, c_u, s1))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21965,plain,
% 88.16/88.38 ((m_user_v_ack(c_e_h_3, c_u, s1) | (~node25(s1))) <=> ((~node25(s1)) | m_user_v_ack(c_e_h_3, c_u, s1))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21966,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s1) | (~node25(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | ((~node25(s1)) | m_user_v_ack(c_e_h_3, c_u, s1)))),
% 88.16/88.38 inference(monotonicity,[status(thm)],[21965])).
% 88.16/88.38 tff(21967,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s1) | (~node25(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s1)) | m_user_v_ack(c_e_h_3, c_u, s1))),
% 88.16/88.38 inference(transitivity,[status(thm)],[21966, 21964])).
% 88.16/88.38 tff(21968,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_3, c_u, s1) | (~node25(s1)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21969,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_3, c_u, X) | (~node25(X)))) | (~node25(s1)) | m_user_v_ack(c_e_h_3, c_u, s1)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21968, 21967])).
% 88.16/88.38 tff(21970,plain,
% 88.16/88.38 (~node25(s1)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21969, 21376, 20620])).
% 88.16/88.38 tff(21971,plain,
% 88.16/88.38 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21972,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21973,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21972, 21971])).
% 88.16/88.38 tff(21974,plain,
% 88.16/88.38 (~m_user_v_ack(c_e_h_1, c_u, s1)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21973, 4481, 4551])).
% 88.16/88.38 tff(21975,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s1)) | m_user_v_ack(c_e_h_1, c_u, s1))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s1)) | m_user_v_ack(c_e_h_1, c_u, s1))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21976,plain,
% 88.16/88.38 ((m_user_v_ack(c_e_h_1, c_u, s1) | (~node24(s1))) <=> ((~node24(s1)) | m_user_v_ack(c_e_h_1, c_u, s1))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21977,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node24(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | ((~node24(s1)) | m_user_v_ack(c_e_h_1, c_u, s1)))),
% 88.16/88.38 inference(monotonicity,[status(thm)],[21976])).
% 88.16/88.38 tff(21978,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node24(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s1)) | m_user_v_ack(c_e_h_1, c_u, s1))),
% 88.16/88.38 inference(transitivity,[status(thm)],[21977, 21975])).
% 88.16/88.38 tff(21979,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node24(s1)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21980,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (~node24(s1)) | m_user_v_ack(c_e_h_1, c_u, s1)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21979, 21978])).
% 88.16/88.38 tff(21981,plain,
% 88.16/88.38 (~node24(s1)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21980, 8407, 21974])).
% 88.16/88.38 tff(21982,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s1)) | m_user_v_ack(c_e_h_1, c_u, s1))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s1)) | m_user_v_ack(c_e_h_1, c_u, s1))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21983,plain,
% 88.16/88.38 ((m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1))) <=> ((~node23(s1)) | m_user_v_ack(c_e_h_1, c_u, s1))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21984,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s1)) | m_user_v_ack(c_e_h_1, c_u, s1)))),
% 88.16/88.38 inference(monotonicity,[status(thm)],[21983])).
% 88.16/88.38 tff(21985,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s1)) | m_user_v_ack(c_e_h_1, c_u, s1))),
% 88.16/88.38 inference(transitivity,[status(thm)],[21984, 21982])).
% 88.16/88.38 tff(21986,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s1) | (~node23(s1)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21987,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s1)) | m_user_v_ack(c_e_h_1, c_u, s1)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21986, 21985])).
% 88.16/88.38 tff(21988,plain,
% 88.16/88.38 (~node23(s1)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21987, 8418, 21974])).
% 88.16/88.38 tff(21989,plain,
% 88.16/88.38 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21990,plain,
% 88.16/88.38 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s1) | node24(s1) | node25(s1) | (~node26(s1)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21991,plain,
% 88.16/88.38 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s1) | node24(s1) | node25(s1) | (~node26(s1))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21990, 21989])).
% 88.16/88.38 tff(21992,plain,
% 88.16/88.38 (node25(s1) | (~node26(s1))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21991, 8435, 21988, 21981])).
% 88.16/88.38 tff(21993,plain,
% 88.16/88.38 (~node26(s1)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21992, 21970])).
% 88.16/88.38 tff(21994,plain,
% 88.16/88.38 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(21995,plain,
% 88.16/88.38 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s1) | xuntil2p30(s1) | (~until2p29(s1)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(21996,plain,
% 88.16/88.38 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s1) | xuntil2p30(s1) | (~until2p29(s1))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[21995, 21994])).
% 88.16/88.38 tff(21997,plain,
% 88.16/88.38 (xuntil2p30(s1) | (~until2p29(s1))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21996, 21713, 21993])).
% 88.16/88.38 tff(21998,plain,
% 88.16/88.38 (~until2p29(s1)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[21997, 21963])).
% 88.16/88.38 tff(21999,plain,
% 88.16/88.38 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(22000,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | ((~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(22001,plain,
% 88.16/88.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p29(Y) | (~xuntil2p30(X)))) | (~succ(s0, s1)) | until2p29(s1) | (~xuntil2p30(s0))),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[22000, 21999])).
% 88.16/88.38 tff(22002,plain,
% 88.16/88.38 (until2p29(s1) | (~xuntil2p30(s0))),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[22001, 67, 21728])).
% 88.16/88.38 tff(22003,plain,
% 88.16/88.38 (~xuntil2p30(s0)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[22002, 21998])).
% 88.16/88.38 tff(22004,plain,
% 88.16/88.38 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(22005,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(22006,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_2, c_u, s0)) | m_and_h_gate_v_out(c_e_h_2, c_r, s0)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[22005, 22004])).
% 88.16/88.38 tff(22007,plain,
% 88.16/88.38 (~m_user_v_ack(c_e_h_2, c_u, s0)),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[22006, 4481, 2011])).
% 88.16/88.38 tff(22008,assumption,(node25(s0)), introduced(assumption)).
% 88.16/88.38 tff(22009,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(22010,plain,
% 88.16/88.38 ((m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0))) <=> ((~node25(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(22011,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | ((~node25(s0)) | m_user_v_ack(c_e_h_2, c_u, s0)))),
% 88.16/88.38 inference(monotonicity,[status(thm)],[22010])).
% 88.16/88.38 tff(22012,plain,
% 88.16/88.38 (((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s0)) | m_user_v_ack(c_e_h_2, c_u, s0))),
% 88.16/88.38 inference(transitivity,[status(thm)],[22011, 22009])).
% 88.16/88.38 tff(22013,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (m_user_v_ack(c_e_h_2, c_u, s0) | (~node25(s0)))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(22014,plain,
% 88.16/88.38 ((~![X: $i] : (m_user_v_ack(c_e_h_2, c_u, X) | (~node25(X)))) | (~node25(s0)) | m_user_v_ack(c_e_h_2, c_u, s0)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[22013, 22012])).
% 88.16/88.38 tff(22015,plain,
% 88.16/88.38 ($false),
% 88.16/88.38 inference(unit_resolution,[status(thm)],[22014, 4492, 22008, 22007])).
% 88.16/88.38 tff(22016,plain,(~node25(s0)), inference(lemma,lemma(discharge,[]))).
% 88.16/88.38 tff(22017,plain,
% 88.16/88.38 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 88.16/88.38 inference(rewrite,[status(thm)],[])).
% 88.16/88.38 tff(22018,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 88.16/88.38 inference(quant_inst,[status(thm)],[])).
% 88.16/88.38 tff(22019,plain,
% 88.16/88.38 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s0)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 88.16/88.38 inference(modus_ponens,[status(thm)],[22018, 22017])).
% 88.16/88.38 tff(22020,plain,
% 88.16/88.38 (~m_user_v_ack(c_e_h_1, c_u, s0)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22019, 4481, 4508])).
% 88.16/88.39 tff(22021,plain,
% 88.16/88.39 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22022,plain,
% 88.16/88.39 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0)))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22023,plain,
% 88.16/88.39 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node24(X)))) | m_user_v_ack(c_e_h_1, c_u, s0) | (~node24(s0))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22022, 22021])).
% 88.16/88.39 tff(22024,plain,
% 88.16/88.39 (~node24(s0)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22023, 8407, 22020])).
% 88.16/88.39 tff(22025,plain,
% 88.16/88.39 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22026,plain,
% 88.16/88.39 ((m_user_v_ack(c_e_h_1, c_u, s0) | (~node23(s0))) <=> ((~node23(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22027,plain,
% 88.16/88.39 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node23(s0)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | ((~node23(s0)) | m_user_v_ack(c_e_h_1, c_u, s0)))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22026])).
% 88.16/88.39 tff(22028,plain,
% 88.16/88.39 (((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node23(s0)))) <=> ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s0)) | m_user_v_ack(c_e_h_1, c_u, s0))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22027, 22025])).
% 88.16/88.39 tff(22029,plain,
% 88.16/88.39 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (m_user_v_ack(c_e_h_1, c_u, s0) | (~node23(s0)))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22030,plain,
% 88.16/88.39 ((~![X: $i] : (m_user_v_ack(c_e_h_1, c_u, X) | (~node23(X)))) | (~node23(s0)) | m_user_v_ack(c_e_h_1, c_u, s0)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22029, 22028])).
% 88.16/88.39 tff(22031,plain,
% 88.16/88.39 (~node23(s0)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22030, 8418, 22020])).
% 88.16/88.39 tff(22032,plain,
% 88.16/88.39 (((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))) <=> ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22033,plain,
% 88.16/88.39 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | (node23(s0) | node24(s0) | node25(s0) | (~node26(s0)))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22034,plain,
% 88.16/88.39 ((~![X: $i] : (node23(X) | node24(X) | node25(X) | (~node26(X)))) | node23(s0) | node24(s0) | node25(s0) | (~node26(s0))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22033, 22032])).
% 88.16/88.39 tff(22035,plain,
% 88.16/88.39 (node25(s0) | (~node26(s0))),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22034, 8435, 22031, 22024])).
% 88.16/88.39 tff(22036,plain,
% 88.16/88.39 (~node26(s0)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22035, 22016])).
% 88.16/88.39 tff(22037,plain,
% 88.16/88.39 (((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))) <=> ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22038,plain,
% 88.16/88.39 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | (node26(s0) | xuntil2p30(s0) | (~until2p29(s0)))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22039,plain,
% 88.16/88.39 ((~![X: $i] : (node26(X) | xuntil2p30(X) | (~until2p29(X)))) | node26(s0) | xuntil2p30(s0) | (~until2p29(s0))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22038, 22037])).
% 88.16/88.39 tff(22040,plain,
% 88.16/88.39 (xuntil2p30(s0) | (~until2p29(s0))),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22039, 21713, 22036])).
% 88.16/88.39 tff(22041,plain,
% 88.16/88.39 (~until2p29(s0)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22040, 22003])).
% 88.16/88.39 tff(22042,plain,
% 88.16/88.39 (until27(s0) <=> until27(s0)),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22043,axiom,(until27(s0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty15')).
% 88.16/88.39 tff(22044,plain,
% 88.16/88.39 (until27(s0)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22043, 22042])).
% 88.16/88.39 tff(22045,plain,
% 88.16/88.39 (^[X: $i] : refl(((~until27(X)) | node26(X) | xuntil28(X)) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 88.16/88.39 inference(bind,[status(th)],[])).
% 88.16/88.39 tff(22046,plain,
% 88.16/88.39 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 88.16/88.39 inference(quant_intro,[status(thm)],[22045])).
% 88.16/88.39 tff(22047,plain,
% 88.16/88.39 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X)) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22048,plain,
% 88.16/88.39 (^[X: $i] : rewrite(((node26(X) | xuntil28(X)) | (~until27(X))) <=> ((~until27(X)) | node26(X) | xuntil28(X)))),
% 88.16/88.39 inference(bind,[status(th)],[])).
% 88.16/88.39 tff(22049,plain,
% 88.16/88.39 (![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X))) <=> ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 88.16/88.39 inference(quant_intro,[status(thm)],[22048])).
% 88.16/88.39 tff(22050,axiom,(![X: $i] : ((node26(X) | xuntil28(X)) | (~until27(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty8')).
% 88.16/88.39 tff(22051,plain,
% 88.16/88.39 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22050, 22049])).
% 88.16/88.39 tff(22052,plain,
% 88.16/88.39 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22051, 22047])).
% 88.16/88.39 tff(22053,plain,(
% 88.16/88.39 ![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 88.16/88.39 inference(skolemize,[status(sab)],[22052])).
% 88.16/88.39 tff(22054,plain,
% 88.16/88.39 (![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22053, 22046])).
% 88.16/88.39 tff(22055,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s0) | (~until27(s0)) | node26(s0))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22056,plain,
% 88.16/88.39 (((~until27(s0)) | node26(s0) | xuntil28(s0)) <=> (xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22057,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s0) | (~until27(s0)) | node26(s0)))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22056])).
% 88.16/88.39 tff(22058,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22057, 22055])).
% 88.16/88.39 tff(22059,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s0)) | node26(s0) | xuntil28(s0))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22060,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s0) | (~until27(s0)) | node26(s0)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22059, 22058])).
% 88.16/88.39 tff(22061,plain,
% 88.16/88.39 (xuntil28(s0) | node26(s0)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22060, 22054, 22044])).
% 88.16/88.39 tff(22062,plain,
% 88.16/88.39 (xuntil28(s0)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22061, 22036])).
% 88.16/88.39 tff(22063,plain,
% 88.16/88.39 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 88.16/88.39 inference(bind,[status(th)],[])).
% 88.16/88.39 tff(22064,plain,
% 88.16/88.39 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 88.16/88.39 inference(quant_intro,[status(thm)],[22063])).
% 88.16/88.39 tff(22065,plain,
% 88.16/88.39 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22066,plain,
% 88.16/88.39 (^[Y: $i, X: $i] : rewrite(((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y)))),
% 88.16/88.39 inference(bind,[status(th)],[])).
% 88.16/88.39 tff(22067,plain,
% 88.16/88.39 (![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 88.16/88.39 inference(quant_intro,[status(thm)],[22066])).
% 88.16/88.39 tff(22068,axiom,(![Y: $i, X: $i] : ((until27(Y) | (~succ(X, Y))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty9')).
% 88.16/88.39 tff(22069,plain,
% 88.16/88.39 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22068, 22067])).
% 88.16/88.39 tff(22070,plain,
% 88.16/88.39 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22069, 22065])).
% 88.16/88.39 tff(22071,plain,(
% 88.16/88.39 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 88.16/88.39 inference(skolemize,[status(sab)],[22070])).
% 88.16/88.39 tff(22072,plain,
% 88.16/88.39 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22071, 22064])).
% 88.16/88.39 tff(22073,plain,
% 88.16/88.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22074,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22075,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s0, s1)) | (~xuntil28(s0)) | until27(s1)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22074, 22073])).
% 88.16/88.39 tff(22076,plain,
% 88.16/88.39 ((~xuntil28(s0)) | until27(s1)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22075, 67, 22072])).
% 88.16/88.39 tff(22077,plain,
% 88.16/88.39 (until27(s1)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22076, 22062])).
% 88.16/88.39 tff(22078,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s1) | node26(s1) | (~until27(s1)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22079,plain,
% 88.16/88.39 (((~until27(s1)) | node26(s1) | xuntil28(s1)) <=> (xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22080,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s1) | node26(s1) | (~until27(s1))))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22079])).
% 88.16/88.39 tff(22081,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1)))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22080, 22078])).
% 88.16/88.39 tff(22082,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s1)) | node26(s1) | xuntil28(s1))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22083,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s1) | node26(s1) | (~until27(s1))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22082, 22081])).
% 88.16/88.39 tff(22084,plain,
% 88.16/88.39 (xuntil28(s1) | node26(s1)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22083, 22054, 22077])).
% 88.16/88.39 tff(22085,plain,
% 88.16/88.39 (xuntil28(s1)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22084, 21993])).
% 88.16/88.39 tff(22086,plain,
% 88.16/88.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22087,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22088,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s1, s2)) | (~xuntil28(s1)) | until27(s2)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22087, 22086])).
% 88.16/88.39 tff(22089,plain,
% 88.16/88.39 ((~xuntil28(s1)) | until27(s2)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22088, 340, 22072])).
% 88.16/88.39 tff(22090,plain,
% 88.16/88.39 (until27(s2)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22089, 22085])).
% 88.16/88.39 tff(22091,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s2) | node26(s2) | (~until27(s2)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22092,plain,
% 88.16/88.39 (((~until27(s2)) | node26(s2) | xuntil28(s2)) <=> (xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22093,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s2) | node26(s2) | (~until27(s2))))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22092])).
% 88.16/88.39 tff(22094,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2)))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22093, 22091])).
% 88.16/88.39 tff(22095,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s2)) | node26(s2) | xuntil28(s2))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22096,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s2) | node26(s2) | (~until27(s2))),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22095, 22094])).
% 88.16/88.39 tff(22097,plain,
% 88.16/88.39 (xuntil28(s2) | node26(s2)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22096, 22054, 22090])).
% 88.16/88.39 tff(22098,plain,
% 88.16/88.39 (xuntil28(s2)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22097, 21953])).
% 88.16/88.39 tff(22099,plain,
% 88.16/88.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22100,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22101,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s2, s3)) | (~xuntil28(s2)) | until27(s3)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22100, 22099])).
% 88.16/88.39 tff(22102,plain,
% 88.16/88.39 ((~xuntil28(s2)) | until27(s3)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22101, 578, 22072])).
% 88.16/88.39 tff(22103,plain,
% 88.16/88.39 (until27(s3)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22102, 22098])).
% 88.16/88.39 tff(22104,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s3) | (~until27(s3)) | node26(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | (~until27(s3)) | node26(s3))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22105,plain,
% 88.16/88.39 (((~until27(s3)) | node26(s3) | xuntil28(s3)) <=> (xuntil28(s3) | (~until27(s3)) | node26(s3))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22106,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s3) | (~until27(s3)) | node26(s3)))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22105])).
% 88.16/88.39 tff(22107,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | (~until27(s3)) | node26(s3))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22106, 22104])).
% 88.16/88.39 tff(22108,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s3)) | node26(s3) | xuntil28(s3))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22109,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s3) | (~until27(s3)) | node26(s3)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22108, 22107])).
% 88.16/88.39 tff(22110,plain,
% 88.16/88.39 (xuntil28(s3) | node26(s3)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22109, 22054, 22103])).
% 88.16/88.39 tff(22111,plain,
% 88.16/88.39 (xuntil28(s3)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22110, 21918])).
% 88.16/88.39 tff(22112,plain,
% 88.16/88.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22113,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22114,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s3, s4)) | (~xuntil28(s3)) | until27(s4)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22113, 22112])).
% 88.16/88.39 tff(22115,plain,
% 88.16/88.39 ((~xuntil28(s3)) | until27(s4)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22114, 675, 22072])).
% 88.16/88.39 tff(22116,plain,
% 88.16/88.39 (until27(s4)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22115, 22111])).
% 88.16/88.39 tff(22117,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s4) | (~until27(s4)) | node26(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | (~until27(s4)) | node26(s4))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22118,plain,
% 88.16/88.39 (((~until27(s4)) | node26(s4) | xuntil28(s4)) <=> (xuntil28(s4) | (~until27(s4)) | node26(s4))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22119,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s4) | (~until27(s4)) | node26(s4)))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22118])).
% 88.16/88.39 tff(22120,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | (~until27(s4)) | node26(s4))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22119, 22117])).
% 88.16/88.39 tff(22121,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s4)) | node26(s4) | xuntil28(s4))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22122,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s4) | (~until27(s4)) | node26(s4)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22121, 22120])).
% 88.16/88.39 tff(22123,plain,
% 88.16/88.39 (xuntil28(s4) | node26(s4)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22122, 22054, 22116])).
% 88.16/88.39 tff(22124,plain,
% 88.16/88.39 (xuntil28(s4)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22123, 21880])).
% 88.16/88.39 tff(22125,plain,
% 88.16/88.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22126,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22127,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s4, s5)) | (~xuntil28(s4)) | until27(s5)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22126, 22125])).
% 88.16/88.39 tff(22128,plain,
% 88.16/88.39 ((~xuntil28(s4)) | until27(s5)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22127, 1428, 22072])).
% 88.16/88.39 tff(22129,plain,
% 88.16/88.39 (until27(s5)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22128, 22124])).
% 88.16/88.39 tff(22130,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s5) | (~until27(s5)) | node26(s5))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s5) | (~until27(s5)) | node26(s5))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22131,plain,
% 88.16/88.39 (((~until27(s5)) | node26(s5) | xuntil28(s5)) <=> (xuntil28(s5) | (~until27(s5)) | node26(s5))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22132,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s5)) | node26(s5) | xuntil28(s5))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s5) | (~until27(s5)) | node26(s5)))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22131])).
% 88.16/88.39 tff(22133,plain,
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% 88.16/88.39 inference(transitivity,[status(thm)],[22132, 22130])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22135,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s5) | (~until27(s5)) | node26(s5)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22134, 22133])).
% 88.16/88.39 tff(22136,plain,
% 88.16/88.39 (xuntil28(s5) | (~until27(s5))),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22135, 22054, 21869])).
% 88.16/88.39 tff(22137,plain,
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22136, 22129])).
% 88.16/88.39 tff(22138,plain,
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22140,plain,
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% 88.16/88.39 inference(modus_ponens,[status(thm)],[22139, 22138])).
% 88.16/88.39 tff(22141,plain,
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22140, 1495, 22072])).
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22141, 22137])).
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22145,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s6)) | node26(s6) | xuntil28(s6))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s6) | node26(s6) | (~until27(s6))))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22144])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s6)) | node26(s6) | xuntil28(s6))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s6) | node26(s6) | (~until27(s6)))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22145, 22143])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
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% 88.16/88.39 inference(modus_ponens,[status(thm)],[22147, 22146])).
% 88.16/88.39 tff(22149,plain,
% 88.16/88.39 (xuntil28(s6) | node26(s6)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22148, 22054, 22142])).
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22149, 21688])).
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22153,plain,
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% 88.16/88.39 inference(modus_ponens,[status(thm)],[22152, 22151])).
% 88.16/88.39 tff(22154,plain,
% 88.16/88.39 ((~xuntil28(s6)) | until27(s7)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22153, 1548, 22072])).
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22154, 22150])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s7) | node26(s7) | (~until27(s7)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s7)) | node26(s7) | xuntil28(s7))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s7) | node26(s7) | (~until27(s7))))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22157])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s7)) | node26(s7) | xuntil28(s7))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s7) | node26(s7) | (~until27(s7)))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22158, 22156])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22161,plain,
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% 88.16/88.39 inference(modus_ponens,[status(thm)],[22160, 22159])).
% 88.16/88.39 tff(22162,plain,
% 88.16/88.39 (xuntil28(s7) | (~until27(s7))),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22161, 22054, 21848])).
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22162, 22155])).
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
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% 88.16/88.39 inference(modus_ponens,[status(thm)],[22165, 22164])).
% 88.16/88.39 tff(22167,plain,
% 88.16/88.39 ((~xuntil28(s7)) | until27(s8)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22166, 2148, 22072])).
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22167, 22163])).
% 88.16/88.39 tff(22169,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s8) | node26(s8) | (~until27(s8)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s8)) | node26(s8) | xuntil28(s8))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s8) | node26(s8) | (~until27(s8))))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22170])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s8)) | node26(s8) | xuntil28(s8))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s8) | node26(s8) | (~until27(s8)))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22171, 22169])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
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% 88.16/88.39 inference(modus_ponens,[status(thm)],[22173, 22172])).
% 88.16/88.39 tff(22175,plain,
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22174, 22054, 21837])).
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
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% 88.16/88.39 inference(modus_ponens,[status(thm)],[22178, 22177])).
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22179, 2632, 22072])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s9) | (~until27(s9)) | node26(s9))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s9) | (~until27(s9)) | node26(s9))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s9)) | node26(s9) | xuntil28(s9))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s9) | (~until27(s9)) | node26(s9)))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22183])).
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22187, 22054, 21826])).
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% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
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% 88.16/88.39 inference(rewrite,[status(thm)],[])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s10)) | node26(s10) | xuntil28(s10))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s10) | (~until27(s10)) | node26(s10)))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22196])).
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% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s10)) | node26(s10) | xuntil28(s10))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s10) | (~until27(s10)) | node26(s10))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22197, 22195])).
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% 88.16/88.39 inference(unit_resolution,[status(thm)],[22201, 22194])).
% 88.16/88.39 tff(22203,plain,
% 88.16/88.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22204,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22205,plain,
% 88.16/88.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s10, s11)) | (~xuntil28(s10)) | until27(s11)),
% 88.16/88.39 inference(modus_ponens,[status(thm)],[22204, 22203])).
% 88.16/88.39 tff(22206,plain,
% 88.16/88.39 ((~xuntil28(s10)) | until27(s11)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22205, 3774, 22072])).
% 88.16/88.39 tff(22207,plain,
% 88.16/88.39 (until27(s11)),
% 88.16/88.39 inference(unit_resolution,[status(thm)],[22206, 22202])).
% 88.16/88.39 tff(22208,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s11) | (~until27(s11)) | node26(s11))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s11) | (~until27(s11)) | node26(s11))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22209,plain,
% 88.16/88.39 (((~until27(s11)) | node26(s11) | xuntil28(s11)) <=> (xuntil28(s11) | (~until27(s11)) | node26(s11))),
% 88.16/88.39 inference(rewrite,[status(thm)],[])).
% 88.16/88.39 tff(22210,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s11)) | node26(s11) | xuntil28(s11))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s11) | (~until27(s11)) | node26(s11)))),
% 88.16/88.39 inference(monotonicity,[status(thm)],[22209])).
% 88.16/88.39 tff(22211,plain,
% 88.16/88.39 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s11)) | node26(s11) | xuntil28(s11))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s11) | (~until27(s11)) | node26(s11))),
% 88.16/88.39 inference(transitivity,[status(thm)],[22210, 22208])).
% 88.16/88.39 tff(22212,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s11)) | node26(s11) | xuntil28(s11))),
% 88.16/88.39 inference(quant_inst,[status(thm)],[])).
% 88.16/88.39 tff(22213,plain,
% 88.16/88.39 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s11) | (~until27(s11)) | node26(s11)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22212, 22211])).
% 88.16/88.40 tff(22214,plain,
% 88.16/88.40 (xuntil28(s11) | (~until27(s11))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22213, 22054, 21407])).
% 88.16/88.40 tff(22215,plain,
% 88.16/88.40 (xuntil28(s11)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22214, 22207])).
% 88.16/88.40 tff(22216,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22217,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22218,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s11, s12)) | (~xuntil28(s11)) | until27(s12)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22217, 22216])).
% 88.16/88.40 tff(22219,plain,
% 88.16/88.40 ((~xuntil28(s11)) | until27(s12)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22218, 4457, 22072])).
% 88.16/88.40 tff(22220,plain,
% 88.16/88.40 (until27(s12)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22219, 22215])).
% 88.16/88.40 tff(22221,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s12) | (~until27(s12)) | node26(s12))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s12) | (~until27(s12)) | node26(s12))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22222,plain,
% 88.16/88.40 (((~until27(s12)) | node26(s12) | xuntil28(s12)) <=> (xuntil28(s12) | (~until27(s12)) | node26(s12))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22223,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s12)) | node26(s12) | xuntil28(s12))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s12) | (~until27(s12)) | node26(s12)))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22222])).
% 88.16/88.40 tff(22224,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s12)) | node26(s12) | xuntil28(s12))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s12) | (~until27(s12)) | node26(s12))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22223, 22221])).
% 88.16/88.40 tff(22225,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s12)) | node26(s12) | xuntil28(s12))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22226,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s12) | (~until27(s12)) | node26(s12)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22225, 22224])).
% 88.16/88.40 tff(22227,plain,
% 88.16/88.40 (xuntil28(s12) | (~until27(s12))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22226, 22054, 21405])).
% 88.16/88.40 tff(22228,plain,
% 88.16/88.40 (xuntil28(s12)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22227, 22220])).
% 88.16/88.40 tff(22229,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22230,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22231,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s12, s13)) | (~xuntil28(s12)) | until27(s13)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22230, 22229])).
% 88.16/88.40 tff(22232,plain,
% 88.16/88.40 ((~xuntil28(s12)) | until27(s13)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22231, 9595, 22072])).
% 88.16/88.40 tff(22233,plain,
% 88.16/88.40 (until27(s13)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22232, 22228])).
% 88.16/88.40 tff(22234,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s13) | node26(s13) | (~until27(s13)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22235,plain,
% 88.16/88.40 (((~until27(s13)) | node26(s13) | xuntil28(s13)) <=> (xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22236,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s13)) | node26(s13) | xuntil28(s13))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s13) | node26(s13) | (~until27(s13))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22235])).
% 88.16/88.40 tff(22237,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s13)) | node26(s13) | xuntil28(s13))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22236, 22234])).
% 88.16/88.40 tff(22238,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s13)) | node26(s13) | xuntil28(s13))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22239,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s13) | node26(s13) | (~until27(s13))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22238, 22237])).
% 88.16/88.40 tff(22240,plain,
% 88.16/88.40 (xuntil28(s13) | (~until27(s13))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22239, 22054, 21408])).
% 88.16/88.40 tff(22241,plain,
% 88.16/88.40 (xuntil28(s13)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22240, 22233])).
% 88.16/88.40 tff(22242,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22243,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22244,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s13, s14)) | (~xuntil28(s13)) | until27(s14)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22243, 22242])).
% 88.16/88.40 tff(22245,plain,
% 88.16/88.40 ((~xuntil28(s13)) | until27(s14)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22244, 10036, 22072])).
% 88.16/88.40 tff(22246,plain,
% 88.16/88.40 (until27(s14)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22245, 22241])).
% 88.16/88.40 tff(22247,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s14) | node26(s14) | (~until27(s14)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22248,plain,
% 88.16/88.40 (((~until27(s14)) | node26(s14) | xuntil28(s14)) <=> (xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22249,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s14)) | node26(s14) | xuntil28(s14))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s14) | node26(s14) | (~until27(s14))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22248])).
% 88.16/88.40 tff(22250,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s14)) | node26(s14) | xuntil28(s14))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22249, 22247])).
% 88.16/88.40 tff(22251,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s14)) | node26(s14) | xuntil28(s14))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22252,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s14) | node26(s14) | (~until27(s14))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22251, 22250])).
% 88.16/88.40 tff(22253,plain,
% 88.16/88.40 (xuntil28(s14) | (~until27(s14))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22252, 22054, 21406])).
% 88.16/88.40 tff(22254,plain,
% 88.16/88.40 (xuntil28(s14)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22253, 22246])).
% 88.16/88.40 tff(22255,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22256,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22257,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s14, s15)) | (~xuntil28(s14)) | until27(s15)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22256, 22255])).
% 88.16/88.40 tff(22258,plain,
% 88.16/88.40 ((~xuntil28(s14)) | until27(s15)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22257, 10500, 22072])).
% 88.16/88.40 tff(22259,plain,
% 88.16/88.40 (until27(s15)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22258, 22254])).
% 88.16/88.40 tff(22260,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s15) | (~until27(s15)) | node26(s15))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s15) | (~until27(s15)) | node26(s15))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22261,plain,
% 88.16/88.40 (((~until27(s15)) | node26(s15) | xuntil28(s15)) <=> (xuntil28(s15) | (~until27(s15)) | node26(s15))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22262,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s15)) | node26(s15) | xuntil28(s15))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s15) | (~until27(s15)) | node26(s15)))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22261])).
% 88.16/88.40 tff(22263,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s15)) | node26(s15) | xuntil28(s15))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s15) | (~until27(s15)) | node26(s15))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22262, 22260])).
% 88.16/88.40 tff(22264,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s15)) | node26(s15) | xuntil28(s15))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22265,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s15) | (~until27(s15)) | node26(s15)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22264, 22263])).
% 88.16/88.40 tff(22266,plain,
% 88.16/88.40 (xuntil28(s15) | (~until27(s15))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22265, 22054, 21409])).
% 88.16/88.40 tff(22267,plain,
% 88.16/88.40 (xuntil28(s15)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22266, 22259])).
% 88.16/88.40 tff(22268,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22269,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22270,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s15, s16)) | (~xuntil28(s15)) | until27(s16)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22269, 22268])).
% 88.16/88.40 tff(22271,plain,
% 88.16/88.40 ((~xuntil28(s15)) | until27(s16)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22270, 12875, 22072])).
% 88.16/88.40 tff(22272,plain,
% 88.16/88.40 (until27(s16)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22271, 22267])).
% 88.16/88.40 tff(22273,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s16) | node26(s16) | (~until27(s16)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22274,plain,
% 88.16/88.40 (((~until27(s16)) | node26(s16) | xuntil28(s16)) <=> (xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22275,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s16)) | node26(s16) | xuntil28(s16))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s16) | node26(s16) | (~until27(s16))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22274])).
% 88.16/88.40 tff(22276,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s16)) | node26(s16) | xuntil28(s16))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22275, 22273])).
% 88.16/88.40 tff(22277,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s16)) | node26(s16) | xuntil28(s16))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22278,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s16) | node26(s16) | (~until27(s16))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22277, 22276])).
% 88.16/88.40 tff(22279,plain,
% 88.16/88.40 (xuntil28(s16) | (~until27(s16))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22278, 22054, 21404])).
% 88.16/88.40 tff(22280,plain,
% 88.16/88.40 (xuntil28(s16)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22279, 22272])).
% 88.16/88.40 tff(22281,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22282,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22283,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s16, s17)) | (~xuntil28(s16)) | until27(s17)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22282, 22281])).
% 88.16/88.40 tff(22284,plain,
% 88.16/88.40 ((~xuntil28(s16)) | until27(s17)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22283, 14092, 22072])).
% 88.16/88.40 tff(22285,plain,
% 88.16/88.40 (until27(s17)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22284, 22280])).
% 88.16/88.40 tff(22286,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s17) | (~until27(s17)) | node26(s17))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s17) | (~until27(s17)) | node26(s17))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22287,plain,
% 88.16/88.40 (((~until27(s17)) | node26(s17) | xuntil28(s17)) <=> (xuntil28(s17) | (~until27(s17)) | node26(s17))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22288,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s17)) | node26(s17) | xuntil28(s17))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s17) | (~until27(s17)) | node26(s17)))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22287])).
% 88.16/88.40 tff(22289,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s17)) | node26(s17) | xuntil28(s17))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s17) | (~until27(s17)) | node26(s17))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22288, 22286])).
% 88.16/88.40 tff(22290,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s17)) | node26(s17) | xuntil28(s17))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22291,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s17) | (~until27(s17)) | node26(s17)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22290, 22289])).
% 88.16/88.40 tff(22292,plain,
% 88.16/88.40 (xuntil28(s17) | (~until27(s17))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22291, 22054, 21744])).
% 88.16/88.40 tff(22293,plain,
% 88.16/88.40 (xuntil28(s17)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22292, 22285])).
% 88.16/88.40 tff(22294,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22295,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22296,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s17, s18)) | (~xuntil28(s17)) | until27(s18)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22295, 22294])).
% 88.16/88.40 tff(22297,plain,
% 88.16/88.40 ((~xuntil28(s17)) | until27(s18)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22296, 15697, 22072])).
% 88.16/88.40 tff(22298,plain,
% 88.16/88.40 (until27(s18)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22297, 22293])).
% 88.16/88.40 tff(22299,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s18) | node26(s18) | (~until27(s18)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22300,plain,
% 88.16/88.40 (((~until27(s18)) | node26(s18) | xuntil28(s18)) <=> (xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22301,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s18)) | node26(s18) | xuntil28(s18))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s18) | node26(s18) | (~until27(s18))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22300])).
% 88.16/88.40 tff(22302,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s18)) | node26(s18) | xuntil28(s18))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22301, 22299])).
% 88.16/88.40 tff(22303,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s18)) | node26(s18) | xuntil28(s18))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22304,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s18) | node26(s18) | (~until27(s18))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22303, 22302])).
% 88.16/88.40 tff(22305,plain,
% 88.16/88.40 (xuntil28(s18) | (~until27(s18))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22304, 22054, 21689])).
% 88.16/88.40 tff(22306,plain,
% 88.16/88.40 (xuntil28(s18)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22305, 22298])).
% 88.16/88.40 tff(22307,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22308,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | ((~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22309,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil28(X)) | until27(Y))) | (~succ(s18, s19)) | (~xuntil28(s18)) | until27(s19)),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22308, 22307])).
% 88.16/88.40 tff(22310,plain,
% 88.16/88.40 ((~xuntil28(s18)) | until27(s19)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22309, 15723, 22072])).
% 88.16/88.40 tff(22311,plain,
% 88.16/88.40 (until27(s19)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22310, 22306])).
% 88.16/88.40 tff(22312,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s19) | node26(s19) | (~until27(s19)))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22313,plain,
% 88.16/88.40 (((~until27(s19)) | node26(s19) | xuntil28(s19)) <=> (xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22314,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s19)) | node26(s19) | xuntil28(s19))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | (xuntil28(s19) | node26(s19) | (~until27(s19))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22313])).
% 88.16/88.40 tff(22315,plain,
% 88.16/88.40 (((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s19)) | node26(s19) | xuntil28(s19))) <=> ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22314, 22312])).
% 88.16/88.40 tff(22316,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | ((~until27(s19)) | node26(s19) | xuntil28(s19))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22317,plain,
% 88.16/88.40 ((~![X: $i] : ((~until27(X)) | node26(X) | xuntil28(X))) | xuntil28(s19) | node26(s19) | (~until27(s19))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22316, 22315])).
% 88.16/88.40 tff(22318,plain,
% 88.16/88.40 (xuntil28(s19) | (~until27(s19))),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22317, 22054, 21410])).
% 88.16/88.40 tff(22319,plain,
% 88.16/88.40 (xuntil28(s19)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22318, 22311])).
% 88.16/88.40 tff(22320,plain,
% 88.16/88.40 (^[Y: $i, X: $i] : refl(((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)))),
% 88.16/88.40 inference(bind,[status(th)],[])).
% 88.16/88.40 tff(22321,plain,
% 88.16/88.40 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 88.16/88.40 inference(quant_intro,[status(thm)],[22320])).
% 88.16/88.40 tff(22322,plain,
% 88.16/88.40 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y)) <=> ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22323,plain,
% 88.16/88.40 (^[Y: $i, X: $i] : trans(monotonicity(rewrite(((until2p29(Y) | (~trans(X, Y))) | (~last(X))) <=> ((~last(X)) | (~trans(X, Y)) | until2p29(Y))), ((((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> (((~last(X)) | (~trans(X, Y)) | until2p29(Y)) | (~xuntil28(X))))), rewrite((((~last(X)) | (~trans(X, Y)) | until2p29(Y)) | (~xuntil28(X))) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))), ((((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))))),
% 88.16/88.40 inference(bind,[status(th)],[])).
% 88.16/88.40 tff(22324,plain,
% 88.16/88.40 (![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X))) <=> ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 88.16/88.40 inference(quant_intro,[status(thm)],[22323])).
% 88.16/88.40 tff(22325,axiom,(![Y: $i, X: $i] : (((until2p29(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty11')).
% 88.16/88.40 tff(22326,plain,
% 88.16/88.40 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22325, 22324])).
% 88.16/88.40 tff(22327,plain,
% 88.16/88.40 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22326, 22322])).
% 88.16/88.40 tff(22328,plain,(
% 88.16/88.40 ![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 88.16/88.40 inference(skolemize,[status(sab)],[22327])).
% 88.16/88.40 tff(22329,plain,
% 88.16/88.40 (![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22328, 22321])).
% 88.16/88.40 tff(22330,assumption,(xuntil28(s19)), introduced(assumption)).
% 88.16/88.40 tff(22331,assumption,(~until2p29(s11)), introduced(assumption)).
% 88.16/88.40 tff(22332,assumption,(trans(s19, s11)), introduced(assumption)).
% 88.16/88.40 tff(22333,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s11) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s11) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22334,plain,
% 88.16/88.40 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11)) | until2p29(s11)) <=> (until2p29(s11) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22335,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11)) | until2p29(s11))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s11) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22334])).
% 88.16/88.40 tff(22336,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11)) | until2p29(s11))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s11) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22335, 22333])).
% 88.16/88.40 tff(22337,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11)) | until2p29(s11))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22338,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s11) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s11))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22337, 22336])).
% 88.16/88.40 tff(22339,plain,
% 88.16/88.40 ($false),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22338, 21699, 22332, 22329, 22331, 22330])).
% 88.16/88.40 tff(22340,plain,((~trans(s19, s11)) | until2p29(s11) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.40 tff(22341,plain,
% 88.16/88.40 (~trans(s19, s11)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22340, 22319, 21809])).
% 88.16/88.40 tff(22342,assumption,(~until2p29(s17)), introduced(assumption)).
% 88.16/88.40 tff(22343,assumption,(trans(s19, s17)), introduced(assumption)).
% 88.16/88.40 tff(22344,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s17) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s17) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22345,plain,
% 88.16/88.40 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17)) | until2p29(s17)) <=> (until2p29(s17) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22346,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17)) | until2p29(s17))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s17) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22345])).
% 88.16/88.40 tff(22347,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17)) | until2p29(s17))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s17) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22346, 22344])).
% 88.16/88.40 tff(22348,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17)) | until2p29(s17))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22349,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s17) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s17))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22348, 22347])).
% 88.16/88.40 tff(22350,plain,
% 88.16/88.40 ($false),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22349, 21699, 22343, 22329, 22342, 22330])).
% 88.16/88.40 tff(22351,plain,((~trans(s19, s17)) | until2p29(s17) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.40 tff(22352,plain,
% 88.16/88.40 (~trans(s19, s17)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22351, 22319, 21749])).
% 88.16/88.40 tff(22353,assumption,(~until2p29(s13)), introduced(assumption)).
% 88.16/88.40 tff(22354,assumption,(trans(s19, s13)), introduced(assumption)).
% 88.16/88.40 tff(22355,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s13) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s13) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22356,plain,
% 88.16/88.40 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13)) | until2p29(s13)) <=> (until2p29(s13) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22357,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13)) | until2p29(s13))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s13) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22356])).
% 88.16/88.40 tff(22358,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13)) | until2p29(s13))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s13) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22357, 22355])).
% 88.16/88.40 tff(22359,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13)) | until2p29(s13))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22360,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s13) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s13))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22359, 22358])).
% 88.16/88.40 tff(22361,plain,
% 88.16/88.40 ($false),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22360, 21699, 22354, 22329, 22353, 22330])).
% 88.16/88.40 tff(22362,plain,((~trans(s19, s13)) | until2p29(s13) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.40 tff(22363,plain,
% 88.16/88.40 (~trans(s19, s13)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22362, 22319, 21789])).
% 88.16/88.40 tff(22364,assumption,(~until2p29(s3)), introduced(assumption)).
% 88.16/88.40 tff(22365,assumption,(trans(s19, s3)), introduced(assumption)).
% 88.16/88.40 tff(22366,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22367,plain,
% 88.16/88.40 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3)) | until2p29(s3)) <=> (until2p29(s3) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22368,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s3) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22367])).
% 88.16/88.40 tff(22369,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3)) | until2p29(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22368, 22366])).
% 88.16/88.40 tff(22370,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3)) | until2p29(s3))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22371,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s3) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s3))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22370, 22369])).
% 88.16/88.40 tff(22372,plain,
% 88.16/88.40 ($false),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22371, 21699, 22365, 22329, 22364, 22330])).
% 88.16/88.40 tff(22373,plain,((~trans(s19, s3)) | until2p29(s3) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.40 tff(22374,plain,
% 88.16/88.40 (~trans(s19, s3)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22373, 21923, 22319])).
% 88.16/88.40 tff(22375,assumption,(~until2p29(s8)), introduced(assumption)).
% 88.16/88.40 tff(22376,assumption,(trans(s19, s8)), introduced(assumption)).
% 88.16/88.40 tff(22377,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s8) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22378,plain,
% 88.16/88.40 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8)) | until2p29(s8)) <=> (until2p29(s8) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22379,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s8) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22378])).
% 88.16/88.40 tff(22380,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8)) | until2p29(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22379, 22377])).
% 88.16/88.40 tff(22381,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8)) | until2p29(s8))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22382,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s8) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s8))),
% 88.16/88.40 inference(modus_ponens,[status(thm)],[22381, 22380])).
% 88.16/88.40 tff(22383,plain,
% 88.16/88.40 ($false),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22382, 21699, 22376, 22329, 22375, 22330])).
% 88.16/88.40 tff(22384,plain,((~trans(s19, s8)) | until2p29(s8) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.40 tff(22385,plain,
% 88.16/88.40 (~trans(s19, s8)),
% 88.16/88.40 inference(unit_resolution,[status(thm)],[22384, 22319, 21842])).
% 88.16/88.40 tff(22386,assumption,(~until2p29(s9)), introduced(assumption)).
% 88.16/88.40 tff(22387,assumption,(trans(s19, s9)), introduced(assumption)).
% 88.16/88.40 tff(22388,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s9) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22389,plain,
% 88.16/88.40 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9)) | until2p29(s9)) <=> (until2p29(s9) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9)))),
% 88.16/88.40 inference(rewrite,[status(thm)],[])).
% 88.16/88.40 tff(22390,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s9) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9))))),
% 88.16/88.40 inference(monotonicity,[status(thm)],[22389])).
% 88.16/88.40 tff(22391,plain,
% 88.16/88.40 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9)) | until2p29(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9)))),
% 88.16/88.40 inference(transitivity,[status(thm)],[22390, 22388])).
% 88.16/88.40 tff(22392,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9)) | until2p29(s9))),
% 88.16/88.40 inference(quant_inst,[status(thm)],[])).
% 88.16/88.40 tff(22393,plain,
% 88.16/88.40 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s9) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s9))),
% 88.16/88.41 inference(modus_ponens,[status(thm)],[22392, 22391])).
% 88.16/88.41 tff(22394,plain,
% 88.16/88.41 ($false),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22393, 21699, 22387, 22329, 22386, 22330])).
% 88.16/88.41 tff(22395,plain,((~trans(s19, s9)) | until2p29(s9) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.41 tff(22396,plain,
% 88.16/88.41 (~trans(s19, s9)),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22395, 22319, 21831])).
% 88.16/88.41 tff(22397,assumption,(~until2p29(s6)), introduced(assumption)).
% 88.16/88.41 tff(22398,assumption,(trans(s19, s6)), introduced(assumption)).
% 88.16/88.41 tff(22399,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s6) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22400,plain,
% 88.16/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6)) | until2p29(s6)) <=> (until2p29(s6) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22401,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s6) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6))))),
% 88.16/88.41 inference(monotonicity,[status(thm)],[22400])).
% 88.16/88.41 tff(22402,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6)) | until2p29(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6)))),
% 88.16/88.41 inference(transitivity,[status(thm)],[22401, 22399])).
% 88.16/88.41 tff(22403,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6)) | until2p29(s6))),
% 88.16/88.41 inference(quant_inst,[status(thm)],[])).
% 88.16/88.41 tff(22404,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s6) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s6))),
% 88.16/88.41 inference(modus_ponens,[status(thm)],[22403, 22402])).
% 88.16/88.41 tff(22405,plain,
% 88.16/88.41 ($false),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22404, 21699, 22398, 22329, 22397, 22330])).
% 88.16/88.41 tff(22406,plain,((~trans(s19, s6)) | until2p29(s6) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.41 tff(22407,plain,
% 88.16/88.41 (~trans(s19, s6)),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22406, 21863, 22319])).
% 88.16/88.41 tff(22408,assumption,(~until2p29(s12)), introduced(assumption)).
% 88.16/88.41 tff(22409,assumption,(trans(s19, s12)), introduced(assumption)).
% 88.16/88.41 tff(22410,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s12) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s12) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22411,plain,
% 88.16/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12)) | until2p29(s12)) <=> (until2p29(s12) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22412,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12)) | until2p29(s12))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s12) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12))))),
% 88.16/88.41 inference(monotonicity,[status(thm)],[22411])).
% 88.16/88.41 tff(22413,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12)) | until2p29(s12))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s12) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12)))),
% 88.16/88.41 inference(transitivity,[status(thm)],[22412, 22410])).
% 88.16/88.41 tff(22414,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12)) | until2p29(s12))),
% 88.16/88.41 inference(quant_inst,[status(thm)],[])).
% 88.16/88.41 tff(22415,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s12) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s12))),
% 88.16/88.41 inference(modus_ponens,[status(thm)],[22414, 22413])).
% 88.16/88.41 tff(22416,plain,
% 88.16/88.41 ($false),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22415, 21699, 22409, 22329, 22408, 22330])).
% 88.16/88.41 tff(22417,plain,((~trans(s19, s12)) | until2p29(s12) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.41 tff(22418,plain,
% 88.16/88.41 (~trans(s19, s12)),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22417, 22319, 21799])).
% 88.16/88.41 tff(22419,assumption,(~until2p29(s15)), introduced(assumption)).
% 88.16/88.41 tff(22420,assumption,(trans(s19, s15)), introduced(assumption)).
% 88.16/88.41 tff(22421,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s15) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s15) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22422,plain,
% 88.16/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15)) | until2p29(s15)) <=> (until2p29(s15) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22423,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15)) | until2p29(s15))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s15) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15))))),
% 88.16/88.41 inference(monotonicity,[status(thm)],[22422])).
% 88.16/88.41 tff(22424,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15)) | until2p29(s15))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s15) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15)))),
% 88.16/88.41 inference(transitivity,[status(thm)],[22423, 22421])).
% 88.16/88.41 tff(22425,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15)) | until2p29(s15))),
% 88.16/88.41 inference(quant_inst,[status(thm)],[])).
% 88.16/88.41 tff(22426,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s15) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s15))),
% 88.16/88.41 inference(modus_ponens,[status(thm)],[22425, 22424])).
% 88.16/88.41 tff(22427,plain,
% 88.16/88.41 ($false),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22426, 21699, 22420, 22329, 22419, 22330])).
% 88.16/88.41 tff(22428,plain,((~trans(s19, s15)) | until2p29(s15) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.41 tff(22429,plain,
% 88.16/88.41 (~trans(s19, s15)),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22428, 22319, 21769])).
% 88.16/88.41 tff(22430,assumption,(~until2p29(s2)), introduced(assumption)).
% 88.16/88.41 tff(22431,assumption,(trans(s19, s2)), introduced(assumption)).
% 88.16/88.41 tff(22432,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22433,plain,
% 88.16/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2)) | until2p29(s2)) <=> (until2p29(s2) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22434,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s2) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2))))),
% 88.16/88.41 inference(monotonicity,[status(thm)],[22433])).
% 88.16/88.41 tff(22435,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2)) | until2p29(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2)))),
% 88.16/88.41 inference(transitivity,[status(thm)],[22434, 22432])).
% 88.16/88.41 tff(22436,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2)) | until2p29(s2))),
% 88.16/88.41 inference(quant_inst,[status(thm)],[])).
% 88.16/88.41 tff(22437,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s2) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s2))),
% 88.16/88.41 inference(modus_ponens,[status(thm)],[22436, 22435])).
% 88.16/88.41 tff(22438,plain,
% 88.16/88.41 ($false),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22437, 21699, 22431, 22329, 22430, 22330])).
% 88.16/88.41 tff(22439,plain,((~trans(s19, s2)) | until2p29(s2) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.41 tff(22440,plain,
% 88.16/88.41 (~trans(s19, s2)),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22439, 21958, 22319])).
% 88.16/88.41 tff(22441,assumption,(~until2p29(s7)), introduced(assumption)).
% 88.16/88.41 tff(22442,assumption,(trans(s19, s7)), introduced(assumption)).
% 88.16/88.41 tff(22443,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s7) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22444,plain,
% 88.16/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7)) | until2p29(s7)) <=> (until2p29(s7) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7)))),
% 88.16/88.41 inference(rewrite,[status(thm)],[])).
% 88.16/88.41 tff(22445,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s7) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7))))),
% 88.16/88.41 inference(monotonicity,[status(thm)],[22444])).
% 88.16/88.41 tff(22446,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7)) | until2p29(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7)))),
% 88.16/88.41 inference(transitivity,[status(thm)],[22445, 22443])).
% 88.16/88.41 tff(22447,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7)) | until2p29(s7))),
% 88.16/88.41 inference(quant_inst,[status(thm)],[])).
% 88.16/88.41 tff(22448,plain,
% 88.16/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s7) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s7))),
% 88.16/88.41 inference(modus_ponens,[status(thm)],[22447, 22446])).
% 88.16/88.41 tff(22449,plain,
% 88.16/88.41 ($false),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22448, 21699, 22442, 22329, 22441, 22330])).
% 88.16/88.41 tff(22450,plain,((~trans(s19, s7)) | until2p29(s7) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.16/88.41 tff(22451,plain,
% 88.16/88.41 (~trans(s19, s7)),
% 88.16/88.41 inference(unit_resolution,[status(thm)],[22450, 22319, 21853])).
% 88.16/88.41 tff(22452,assumption,(~until2p29(s4)), introduced(assumption)).
% 88.16/88.41 tff(22453,assumption,(trans(s19, s4)), introduced(assumption)).
% 88.16/88.41 tff(22454,plain,
% 88.16/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22455,plain,
% 88.23/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4)) | until2p29(s4)) <=> (until2p29(s4) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22456,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s4) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4))))),
% 88.23/88.41 inference(monotonicity,[status(thm)],[22455])).
% 88.23/88.41 tff(22457,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4)) | until2p29(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4)))),
% 88.23/88.41 inference(transitivity,[status(thm)],[22456, 22454])).
% 88.23/88.41 tff(22458,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4)) | until2p29(s4))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22459,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s4) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s4))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22458, 22457])).
% 88.23/88.41 tff(22460,plain,
% 88.23/88.41 ($false),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22459, 21699, 22453, 22329, 22452, 22330])).
% 88.23/88.41 tff(22461,plain,((~trans(s19, s4)) | until2p29(s4) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.23/88.41 tff(22462,plain,
% 88.23/88.41 (~trans(s19, s4)),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22461, 21885, 22319])).
% 88.23/88.41 tff(22463,assumption,(~until2p29(s1)), introduced(assumption)).
% 88.23/88.41 tff(22464,assumption,(trans(s19, s1)), introduced(assumption)).
% 88.23/88.41 tff(22465,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22466,plain,
% 88.23/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1)) | until2p29(s1)) <=> (until2p29(s1) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22467,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s1) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1))))),
% 88.23/88.41 inference(monotonicity,[status(thm)],[22466])).
% 88.23/88.41 tff(22468,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1)) | until2p29(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1)))),
% 88.23/88.41 inference(transitivity,[status(thm)],[22467, 22465])).
% 88.23/88.41 tff(22469,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1)) | until2p29(s1))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22470,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s1) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s1))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22469, 22468])).
% 88.23/88.41 tff(22471,plain,
% 88.23/88.41 ($false),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22470, 21699, 22464, 22329, 22463, 22330])).
% 88.23/88.41 tff(22472,plain,((~trans(s19, s1)) | until2p29(s1) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.23/88.41 tff(22473,plain,
% 88.23/88.41 (~trans(s19, s1)),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22472, 21998, 22319])).
% 88.23/88.41 tff(22474,assumption,(~until2p29(s19)), introduced(assumption)).
% 88.23/88.41 tff(22475,assumption,(trans(s19, s19)), introduced(assumption)).
% 88.23/88.41 tff(22476,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s19) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s19) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22477,plain,
% 88.23/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19)) | until2p29(s19)) <=> (until2p29(s19) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22478,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19)) | until2p29(s19))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s19) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19))))),
% 88.23/88.41 inference(monotonicity,[status(thm)],[22477])).
% 88.23/88.41 tff(22479,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19)) | until2p29(s19))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s19) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19)))),
% 88.23/88.41 inference(transitivity,[status(thm)],[22478, 22476])).
% 88.23/88.41 tff(22480,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19)) | until2p29(s19))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22481,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s19) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s19))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22480, 22479])).
% 88.23/88.41 tff(22482,plain,
% 88.23/88.41 ($false),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22481, 21699, 22475, 22329, 22474, 22330])).
% 88.23/88.41 tff(22483,plain,((~trans(s19, s19)) | until2p29(s19) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.23/88.41 tff(22484,plain,
% 88.23/88.41 (~trans(s19, s19)),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22483, 22319, 21718])).
% 88.23/88.41 tff(22485,assumption,(~until2p29(s10)), introduced(assumption)).
% 88.23/88.41 tff(22486,assumption,(trans(s19, s10)), introduced(assumption)).
% 88.23/88.41 tff(22487,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s10) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s10) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22488,plain,
% 88.23/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10)) | until2p29(s10)) <=> (until2p29(s10) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22489,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10)) | until2p29(s10))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s10) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10))))),
% 88.23/88.41 inference(monotonicity,[status(thm)],[22488])).
% 88.23/88.41 tff(22490,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10)) | until2p29(s10))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s10) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10)))),
% 88.23/88.41 inference(transitivity,[status(thm)],[22489, 22487])).
% 88.23/88.41 tff(22491,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10)) | until2p29(s10))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22492,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s10) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s10))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22491, 22490])).
% 88.23/88.41 tff(22493,plain,
% 88.23/88.41 ($false),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22492, 21699, 22486, 22329, 22485, 22330])).
% 88.23/88.41 tff(22494,plain,((~trans(s19, s10)) | until2p29(s10) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.23/88.41 tff(22495,plain,
% 88.23/88.41 (~trans(s19, s10)),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22494, 22319, 21820])).
% 88.23/88.41 tff(22496,assumption,(~until2p29(s5)), introduced(assumption)).
% 88.23/88.41 tff(22497,assumption,(trans(s19, s5)), introduced(assumption)).
% 88.23/88.41 tff(22498,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s5) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22499,plain,
% 88.23/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5)) | until2p29(s5)) <=> (until2p29(s5) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22500,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s5) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5))))),
% 88.23/88.41 inference(monotonicity,[status(thm)],[22499])).
% 88.23/88.41 tff(22501,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5)) | until2p29(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5)))),
% 88.23/88.41 inference(transitivity,[status(thm)],[22500, 22498])).
% 88.23/88.41 tff(22502,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5)) | until2p29(s5))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22503,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s5) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s5))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22502, 22501])).
% 88.23/88.41 tff(22504,plain,
% 88.23/88.41 ($false),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22503, 21699, 22497, 22329, 22496, 22330])).
% 88.23/88.41 tff(22505,plain,((~trans(s19, s5)) | until2p29(s5) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.23/88.41 tff(22506,plain,
% 88.23/88.41 (~trans(s19, s5)),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22505, 21874, 22319])).
% 88.23/88.41 tff(22507,assumption,(~until2p29(s16)), introduced(assumption)).
% 88.23/88.41 tff(22508,assumption,(trans(s19, s16)), introduced(assumption)).
% 88.23/88.41 tff(22509,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s16) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s16) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22510,plain,
% 88.23/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16)) | until2p29(s16)) <=> (until2p29(s16) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22511,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16)) | until2p29(s16))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s16) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16))))),
% 88.23/88.41 inference(monotonicity,[status(thm)],[22510])).
% 88.23/88.41 tff(22512,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16)) | until2p29(s16))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s16) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16)))),
% 88.23/88.41 inference(transitivity,[status(thm)],[22511, 22509])).
% 88.23/88.41 tff(22513,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16)) | until2p29(s16))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22514,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s16) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s16))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22513, 22512])).
% 88.23/88.41 tff(22515,plain,
% 88.23/88.41 ($false),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22514, 21699, 22508, 22329, 22507, 22330])).
% 88.23/88.41 tff(22516,plain,((~trans(s19, s16)) | until2p29(s16) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.23/88.41 tff(22517,plain,
% 88.23/88.41 (~trans(s19, s16)),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22516, 22319, 21759])).
% 88.23/88.41 tff(22518,assumption,(~until2p29(s14)), introduced(assumption)).
% 88.23/88.41 tff(22519,assumption,(trans(s19, s14)), introduced(assumption)).
% 88.23/88.41 tff(22520,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s14) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s14) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22521,plain,
% 88.23/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14)) | until2p29(s14)) <=> (until2p29(s14) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22522,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14)) | until2p29(s14))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s14) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14))))),
% 88.23/88.41 inference(monotonicity,[status(thm)],[22521])).
% 88.23/88.41 tff(22523,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14)) | until2p29(s14))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s14) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14)))),
% 88.23/88.41 inference(transitivity,[status(thm)],[22522, 22520])).
% 88.23/88.41 tff(22524,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14)) | until2p29(s14))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22525,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s14) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s14))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22524, 22523])).
% 88.23/88.41 tff(22526,plain,
% 88.23/88.41 ($false),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22525, 21699, 22519, 22329, 22518, 22330])).
% 88.23/88.41 tff(22527,plain,((~trans(s19, s14)) | until2p29(s14) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.23/88.41 tff(22528,plain,
% 88.23/88.41 (~trans(s19, s14)),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22527, 22319, 21779])).
% 88.23/88.41 tff(22529,plain,
% 88.23/88.41 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 88.23/88.41 inference(bind,[status(th)],[])).
% 88.23/88.41 tff(22530,plain,
% 88.23/88.41 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 88.23/88.41 inference(quant_intro,[status(thm)],[22529])).
% 88.23/88.41 tff(22531,plain,
% 88.23/88.41 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22532,plain,
% 88.23/88.41 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil28(X))) <=> (loop | (~last(X)) | (~xuntil28(X))))),
% 88.23/88.41 inference(bind,[status(th)],[])).
% 88.23/88.41 tff(22533,plain,
% 88.23/88.41 (![X: $i] : ((loop | (~last(X))) | (~xuntil28(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 88.23/88.41 inference(quant_intro,[status(thm)],[22532])).
% 88.23/88.41 tff(22534,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil28(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prpty10')).
% 88.23/88.41 tff(22535,plain,
% 88.23/88.41 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22534, 22533])).
% 88.23/88.41 tff(22536,plain,
% 88.23/88.41 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22535, 22531])).
% 88.23/88.41 tff(22537,plain,(
% 88.23/88.41 ![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 88.23/88.41 inference(skolemize,[status(sab)],[22536])).
% 88.23/88.41 tff(22538,plain,
% 88.23/88.41 (![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22537, 22530])).
% 88.23/88.41 tff(22539,plain,
% 88.23/88.41 (((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s19)) | (~xuntil28(s19)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s19)) | (~xuntil28(s19)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22540,plain,
% 88.23/88.41 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | (loop | (~last(s19)) | (~xuntil28(s19)))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22541,plain,
% 88.23/88.41 ((~![X: $i] : (loop | (~last(X)) | (~xuntil28(X)))) | loop | (~last(s19)) | (~xuntil28(s19))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22540, 22539])).
% 88.23/88.41 tff(22542,plain,
% 88.23/88.41 (loop | (~xuntil28(s19))),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22541, 21699, 22538])).
% 88.23/88.41 tff(22543,plain,
% 88.23/88.41 (loop),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22542, 22319])).
% 88.23/88.41 tff(22544,assumption,(~until2p29(s18)), introduced(assumption)).
% 88.23/88.41 tff(22545,assumption,(trans(s19, s18)), introduced(assumption)).
% 88.23/88.41 tff(22546,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s18) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s18) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22547,plain,
% 88.23/88.41 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18)) | until2p29(s18)) <=> (until2p29(s18) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18)))),
% 88.23/88.41 inference(rewrite,[status(thm)],[])).
% 88.23/88.41 tff(22548,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18)) | until2p29(s18))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (until2p29(s18) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18))))),
% 88.23/88.41 inference(monotonicity,[status(thm)],[22547])).
% 88.23/88.41 tff(22549,plain,
% 88.23/88.41 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18)) | until2p29(s18))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s18) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18)))),
% 88.23/88.41 inference(transitivity,[status(thm)],[22548, 22546])).
% 88.23/88.41 tff(22550,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18)) | until2p29(s18))),
% 88.23/88.41 inference(quant_inst,[status(thm)],[])).
% 88.23/88.41 tff(22551,plain,
% 88.23/88.41 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | until2p29(s18) | (~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s18))),
% 88.23/88.41 inference(modus_ponens,[status(thm)],[22550, 22549])).
% 88.23/88.41 tff(22552,plain,
% 88.23/88.41 ($false),
% 88.23/88.41 inference(unit_resolution,[status(thm)],[22551, 21699, 22545, 22329, 22544, 22330])).
% 88.23/88.41 tff(22553,plain,((~trans(s19, s18)) | until2p29(s18) | (~xuntil28(s19))), inference(lemma,lemma(discharge,[]))).
% 88.23/88.42 tff(22554,plain,
% 88.23/88.42 (~trans(s19, s18)),
% 88.23/88.42 inference(unit_resolution,[status(thm)],[22553, 22319, 21738])).
% 88.23/88.42 tff(22555,plain,
% 88.23/88.42 (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22556,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18)) | trans(s19, s19)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22557,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17)) | trans(s19, s18)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22558,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16)) | trans(s19, s17)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22559,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15)) | trans(s19, s16)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22560,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14)) | trans(s19, s15)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22561,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13)) | trans(s19, s14)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22562,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12)) | trans(s19, s13)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22563,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11)) | trans(s19, s12)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22564,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10)) | trans(s19, s11)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22565,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9)) | trans(s19, s10)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22566,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8)) | trans(s19, s9)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22567,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7)) | trans(s19, s8)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22568,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6)) | trans(s19, s7)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22569,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5)) | trans(s19, s6)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22570,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4)) | trans(s19, s5)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22571,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3)) | trans(s19, s4)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22572,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2)) | trans(s19, s3)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22573,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0) | trans(s19, s1)) | trans(s19, s2)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22574,plain,
% 88.23/88.42 ((((~loop) | trans(s19, s0)) | trans(s19, s1)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1))),
% 88.23/88.42 inference(rewrite,[status(thm)],[])).
% 88.23/88.42 tff(22575,plain,
% 88.23/88.42 (((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1)) | trans(s19, s2))),
% 88.23/88.42 inference(monotonicity,[status(thm)],[22574])).
% 88.23/88.42 tff(22576,plain,
% 88.23/88.42 (((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2))),
% 88.23/88.42 inference(transitivity,[status(thm)],[22575, 22573])).
% 88.23/88.42 tff(22577,plain,
% 88.23/88.42 ((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2)) | trans(s19, s3))),
% 88.23/88.42 inference(monotonicity,[status(thm)],[22576])).
% 88.23/88.42 tff(22578,plain,
% 88.23/88.42 ((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3))),
% 88.23/88.42 inference(transitivity,[status(thm)],[22577, 22572])).
% 88.23/88.42 tff(22579,plain,
% 88.23/88.42 (((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3)) | trans(s19, s4))),
% 88.23/88.42 inference(monotonicity,[status(thm)],[22578])).
% 88.23/88.42 tff(22580,plain,
% 88.23/88.42 (((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4))),
% 88.23/88.42 inference(transitivity,[status(thm)],[22579, 22571])).
% 88.23/88.42 tff(22581,plain,
% 88.23/88.42 ((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4)) | trans(s19, s5))),
% 88.23/88.42 inference(monotonicity,[status(thm)],[22580])).
% 88.23/88.42 tff(22582,plain,
% 88.23/88.42 ((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5))),
% 88.23/88.42 inference(transitivity,[status(thm)],[22581, 22570])).
% 88.23/88.42 tff(22583,plain,
% 88.23/88.42 (((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5)) | trans(s19, s6))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22582])).
% 88.23/88.43 tff(22584,plain,
% 88.23/88.43 (((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22583, 22569])).
% 88.23/88.43 tff(22585,plain,
% 88.23/88.43 ((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6)) | trans(s19, s7))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22584])).
% 88.23/88.43 tff(22586,plain,
% 88.23/88.43 ((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22585, 22568])).
% 88.23/88.43 tff(22587,plain,
% 88.23/88.43 (((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7)) | trans(s19, s8))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22586])).
% 88.23/88.43 tff(22588,plain,
% 88.23/88.43 (((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22587, 22567])).
% 88.23/88.43 tff(22589,plain,
% 88.23/88.43 ((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8)) | trans(s19, s9))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22588])).
% 88.23/88.43 tff(22590,plain,
% 88.23/88.43 ((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22589, 22566])).
% 88.23/88.43 tff(22591,plain,
% 88.23/88.43 (((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9)) | trans(s19, s10))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22590])).
% 88.23/88.43 tff(22592,plain,
% 88.23/88.43 (((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22591, 22565])).
% 88.23/88.43 tff(22593,plain,
% 88.23/88.43 ((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10)) | trans(s19, s11))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22592])).
% 88.23/88.43 tff(22594,plain,
% 88.23/88.43 ((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22593, 22564])).
% 88.23/88.43 tff(22595,plain,
% 88.23/88.43 (((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11)) | trans(s19, s12))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22594])).
% 88.23/88.43 tff(22596,plain,
% 88.23/88.43 (((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22595, 22563])).
% 88.23/88.43 tff(22597,plain,
% 88.23/88.43 ((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12)) | trans(s19, s13))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22596])).
% 88.23/88.43 tff(22598,plain,
% 88.23/88.43 ((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22597, 22562])).
% 88.23/88.43 tff(22599,plain,
% 88.23/88.43 (((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13)) | trans(s19, s14))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22598])).
% 88.23/88.43 tff(22600,plain,
% 88.23/88.43 (((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22599, 22561])).
% 88.23/88.43 tff(22601,plain,
% 88.23/88.43 ((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14)) | trans(s19, s15))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22600])).
% 88.23/88.43 tff(22602,plain,
% 88.23/88.43 ((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22601, 22560])).
% 88.23/88.43 tff(22603,plain,
% 88.23/88.43 (((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15)) | trans(s19, s16))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22602])).
% 88.23/88.43 tff(22604,plain,
% 88.23/88.43 (((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22603, 22559])).
% 88.23/88.43 tff(22605,plain,
% 88.23/88.43 ((((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) | trans(s19, s17)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16)) | trans(s19, s17))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22604])).
% 88.23/88.43 tff(22606,plain,
% 88.23/88.43 ((((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) | trans(s19, s17)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22605, 22558])).
% 88.23/88.43 tff(22607,plain,
% 88.23/88.43 (((((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) | trans(s19, s17)) | trans(s19, s18)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17)) | trans(s19, s18))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22606])).
% 88.23/88.43 tff(22608,plain,
% 88.23/88.43 (((((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) | trans(s19, s17)) | trans(s19, s18)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18))),
% 88.23/88.43 inference(transitivity,[status(thm)],[22607, 22557])).
% 88.23/88.43 tff(22609,plain,
% 88.23/88.43 ((((((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) | trans(s19, s17)) | trans(s19, s18)) | trans(s19, s19)) <=> (((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18)) | trans(s19, s19))),
% 88.23/88.43 inference(monotonicity,[status(thm)],[22608])).
% 88.23/88.43 tff(22610,plain,
% 88.23/88.43 ((((((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) | trans(s19, s17)) | trans(s19, s18)) | trans(s19, s19)) <=> ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19))),
% 88.23/88.44 inference(transitivity,[status(thm)],[22609, 22556])).
% 88.23/88.44 tff(22611,axiom,(((((((((((((((((((((~loop) | trans(s19, s0)) | trans(s19, s1)) | trans(s19, s2)) | trans(s19, s3)) | trans(s19, s4)) | trans(s19, s5)) | trans(s19, s6)) | trans(s19, s7)) | trans(s19, s8)) | trans(s19, s9)) | trans(s19, s10)) | trans(s19, s11)) | trans(s19, s12)) | trans(s19, s13)) | trans(s19, s14)) | trans(s19, s15)) | trans(s19, s16)) | trans(s19, s17)) | trans(s19, s18)) | trans(s19, s19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bound22')).
% 88.23/88.44 tff(22612,plain,
% 88.23/88.44 ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19)),
% 88.23/88.44 inference(modus_ponens,[status(thm)],[22611, 22610])).
% 88.23/88.44 tff(22613,plain,
% 88.23/88.44 ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19)),
% 88.23/88.44 inference(modus_ponens,[status(thm)],[22612, 22555])).
% 88.23/88.44 tff(22614,plain,
% 88.23/88.44 ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19)),
% 88.23/88.44 inference(modus_ponens,[status(thm)],[22613, 22555])).
% 88.23/88.44 tff(22615,plain,
% 88.23/88.44 ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19)),
% 88.23/88.44 inference(modus_ponens,[status(thm)],[22614, 22555])).
% 88.23/88.44 tff(22616,plain,
% 88.23/88.44 ((~loop) | trans(s19, s0) | trans(s19, s1) | trans(s19, s2) | trans(s19, s3) | trans(s19, s4) | trans(s19, s5) | trans(s19, s6) | trans(s19, s7) | trans(s19, s8) | trans(s19, s9) | trans(s19, s10) | trans(s19, s11) | trans(s19, s12) | trans(s19, s13) | trans(s19, s14) | trans(s19, s15) | trans(s19, s16) | trans(s19, s17) | trans(s19, s18) | trans(s19, s19)),
% 88.23/88.44 inference(modus_ponens,[status(thm)],[22615, 22555])).
% 88.23/88.44 tff(22617,plain,
% 88.23/88.44 (trans(s19, s0)),
% 88.23/88.44 inference(unit_resolution,[status(thm)],[22616, 22554, 22543, 22528, 22517, 22506, 22495, 22484, 22473, 22462, 22451, 22440, 22429, 22418, 22407, 22396, 22385, 22374, 22363, 22352, 22341])).
% 88.23/88.44 tff(22618,plain,
% 88.23/88.44 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | until2p29(s0) | (~trans(s19, s0)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s19)) | (~xuntil28(s19)) | until2p29(s0) | (~trans(s19, s0)))),
% 88.23/88.44 inference(rewrite,[status(thm)],[])).
% 88.23/88.44 tff(22619,plain,
% 88.23/88.44 (((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s0)) | until2p29(s0)) <=> ((~last(s19)) | (~xuntil28(s19)) | until2p29(s0) | (~trans(s19, s0)))),
% 88.23/88.44 inference(rewrite,[status(thm)],[])).
% 88.23/88.44 tff(22620,plain,
% 88.23/88.44 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | until2p29(s0) | (~trans(s19, s0))))),
% 88.23/88.44 inference(monotonicity,[status(thm)],[22619])).
% 88.23/88.44 tff(22621,plain,
% 88.23/88.44 (((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s0)) | until2p29(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s19)) | (~xuntil28(s19)) | until2p29(s0) | (~trans(s19, s0)))),
% 88.23/88.46 inference(transitivity,[status(thm)],[22620, 22618])).
% 88.23/88.46 tff(22622,plain,
% 88.23/88.46 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | ((~last(s19)) | (~xuntil28(s19)) | (~trans(s19, s0)) | until2p29(s0))),
% 88.23/88.46 inference(quant_inst,[status(thm)],[])).
% 88.23/88.46 tff(22623,plain,
% 88.23/88.46 ((~![Y: $i, X: $i] : ((~last(X)) | (~xuntil28(X)) | (~trans(X, Y)) | until2p29(Y))) | (~last(s19)) | (~xuntil28(s19)) | until2p29(s0) | (~trans(s19, s0))),
% 88.23/88.46 inference(modus_ponens,[status(thm)],[22622, 22621])).
% 88.23/88.46 tff(22624,plain,
% 88.23/88.46 ($false),
% 88.23/88.46 inference(unit_resolution,[status(thm)],[22623, 21699, 22617, 22329, 22319, 22041])).
% 88.23/88.46 tff(22625,plain,(node26(s6) | node26(s19) | node26(s18) | node26(s17) | node26(s16) | node26(s15) | node26(s14) | node26(s13) | node26(s12) | node26(s11) | node26(s10) | node26(s9) | node26(s4) | node26(s8) | node26(s5) | node26(s7)), inference(lemma,lemma(discharge,[]))).
% 88.23/88.46 tff(22626,plain,
% 88.23/88.46 (node26(s19) | node26(s18) | node26(s17) | node26(s16) | node26(s15) | node26(s14) | node26(s13) | node26(s12) | node26(s11) | node26(s10) | node26(s9) | node26(s8) | node26(s7)),
% 88.23/88.46 inference(unit_resolution,[status(thm)],[22625, 21687, 21659, 21634])).
% 88.23/88.46 tff(22627,plain,
% 88.23/88.46 (node26(s19) | node26(s18) | node26(s17) | node26(s16) | node26(s15) | node26(s14) | node26(s13) | node26(s12) | node26(s11) | node26(s10) | node26(s9) | node26(s8)),
% 88.23/88.46 inference(unit_resolution,[status(thm)],[22626, 21599])).
% 88.23/88.46 tff(22628,plain,
% 88.23/88.46 (node26(s19) | node26(s18) | node26(s17) | node26(s16) | node26(s15) | node26(s14) | node26(s13) | node26(s12) | node26(s11)),
% 88.23/88.46 inference(unit_resolution,[status(thm)],[22627, 21572, 21547, 21522])).
% 88.23/88.46 tff(22629,plain,
% 88.23/88.46 ($false),
% 88.23/88.46 inference(unit_resolution,[status(thm)],[22628, 21491, 21444, 21410, 21409, 21408, 21407, 21406, 21405, 21404])).
% 88.23/88.46 tff(22630,plain,(m_and_h_gate_v_out(c_e_h_2, c_r, s17) | node26(s19) | node26(s15) | node26(s13) | node26(s11) | node26(s14) | node26(s12) | node26(s16) | node20(c_e_h_2, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 88.23/88.46 tff(22631,plain,
% 88.23/88.46 (m_and_h_gate_v_out(c_e_h_2, c_r, s17) | node26(s19) | node26(s15) | node26(s13) | node26(s14) | node26(s12) | node26(s16) | node20(c_e_h_2, c_r, s17)),
% 88.23/88.46 inference(unit_resolution,[status(thm)],[22630, 21403])).
% 88.23/88.46 tff(22632,plain,
% 88.23/88.46 (m_and_h_gate_v_out(c_e_h_2, c_r, s17) | node26(s19) | node26(s15) | node26(s13) | node26(s14) | node26(s12) | node26(s16)),
% 88.23/88.46 inference(unit_resolution,[status(thm)],[22631, 19242])).
% 88.23/88.46 tff(22633,plain,
% 88.23/88.46 ($false),
% 88.23/88.46 inference(unit_resolution,[status(thm)],[22632, 19065, 14136, 14108, 13965, 13937, 12454, 8440])).
% 88.23/88.46 % SZS output end Proof
% 88.23/88.46 % E exiting
%------------------------------------------------------------------------------